diff options
Diffstat (limited to 'crypto/ec')
| -rw-r--r-- | crypto/ec/Makefile | 80 | ||||
| -rw-r--r-- | crypto/ec/ec.h | 875 | ||||
| -rw-r--r-- | crypto/ec/ec2_mult.c | 37 | ||||
| -rw-r--r-- | crypto/ec/ec2_oct.c | 407 | ||||
| -rw-r--r-- | crypto/ec/ec2_smpl.c | 297 | ||||
| -rw-r--r-- | crypto/ec/ec2_smpt.c | 141 | ||||
| -rw-r--r-- | crypto/ec/ec_ameth.c | 660 | ||||
| -rw-r--r-- | crypto/ec/ec_asn1.c | 24 | ||||
| -rw-r--r-- | crypto/ec/ec_curve.c | 2650 | ||||
| -rw-r--r-- | crypto/ec/ec_cvt.c | 28 | ||||
| -rw-r--r-- | crypto/ec/ec_err.c | 41 | ||||
| -rw-r--r-- | crypto/ec/ec_key.c | 102 | ||||
| -rw-r--r-- | crypto/ec/ec_lcl.h | 68 | ||||
| -rw-r--r-- | crypto/ec/ec_lib.c | 84 | ||||
| -rw-r--r-- | crypto/ec/ec_mult.c | 22 | ||||
| -rw-r--r-- | crypto/ec/ec_oct.c | 199 | ||||
| -rw-r--r-- | crypto/ec/ec_pmeth.c | 341 | ||||
| -rw-r--r-- | crypto/ec/eck_prn.c | 392 | ||||
| -rw-r--r-- | crypto/ec/ecp_mont.c | 14 | ||||
| -rw-r--r-- | crypto/ec/ecp_nist.c | 39 | ||||
| -rw-r--r-- | crypto/ec/ecp_nistp224.c | 1658 | ||||
| -rw-r--r-- | crypto/ec/ecp_nistp256.c | 2171 | ||||
| -rw-r--r-- | crypto/ec/ecp_nistp521.c | 2025 | ||||
| -rw-r--r-- | crypto/ec/ecp_nistputil.c | 197 | ||||
| -rw-r--r-- | crypto/ec/ecp_oct.c | 433 | ||||
| -rw-r--r-- | crypto/ec/ecp_smpl.c | 379 | ||||
| -rw-r--r-- | crypto/ec/ectest.c | 353 |
27 files changed, 11640 insertions, 2077 deletions
diff --git a/crypto/ec/Makefile b/crypto/ec/Makefile index b5bbc9faa1a21..f85fc845ca2b3 100644 --- a/crypto/ec/Makefile +++ b/crypto/ec/Makefile @@ -19,11 +19,15 @@ APPS= LIB=$(TOP)/libcrypto.a LIBSRC= ec_lib.c ecp_smpl.c ecp_mont.c ecp_nist.c ec_cvt.c ec_mult.c\ ec_err.c ec_curve.c ec_check.c ec_print.c ec_asn1.c ec_key.c\ - ec2_smpl.c ec2_smpt.c ec2_mult.c + ec2_smpl.c ec2_mult.c ec_ameth.c ec_pmeth.c eck_prn.c \ + ecp_nistp224.c ecp_nistp256.c ecp_nistp521.c ecp_nistputil.c \ + ecp_oct.c ec2_oct.c ec_oct.c LIBOBJ= ec_lib.o ecp_smpl.o ecp_mont.o ecp_nist.o ec_cvt.o ec_mult.o\ ec_err.o ec_curve.o ec_check.o ec_print.o ec_asn1.o ec_key.o\ - ec2_smpl.o ec2_mult.o + ec2_smpl.o ec2_mult.o ec_ameth.o ec_pmeth.o eck_prn.o \ + ecp_nistp224.o ecp_nistp256.o ecp_nistp521.o ecp_nistputil.o \ + ecp_oct.o ec2_oct.o ec_oct.o SRC= $(LIBSRC) @@ -38,7 +42,7 @@ top: all: lib lib: $(LIBOBJ) - $(ARX) $(LIB) $(LIBOBJ) + $(AR) $(LIB) $(LIBOBJ) $(RANLIB) $(LIB) || echo Never mind. @touch lib @@ -87,6 +91,14 @@ ec2_mult.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ec2_mult.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ec2_mult.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ec2_mult.o: ../../include/openssl/symhacks.h ec2_mult.c ec_lcl.h +ec2_oct.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h +ec2_oct.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h +ec2_oct.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h +ec2_oct.o: ../../include/openssl/err.h ../../include/openssl/lhash.h +ec2_oct.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h +ec2_oct.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +ec2_oct.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h +ec2_oct.o: ../../include/openssl/symhacks.h ec2_oct.c ec_lcl.h ec2_smpl.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h ec2_smpl.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h ec2_smpl.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h @@ -94,8 +106,22 @@ ec2_smpl.o: ../../include/openssl/err.h ../../include/openssl/lhash.h ec2_smpl.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ec2_smpl.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ec2_smpl.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h -ec2_smpl.o: ../../include/openssl/symhacks.h ec2_smpl.c ec2_smpt.c ec_lcl.h -ec2_smpt.o: ec2_smpt.c +ec2_smpl.o: ../../include/openssl/symhacks.h ec2_smpl.c ec_lcl.h +ec_ameth.o: ../../e_os.h ../../include/openssl/asn1.h +ec_ameth.o: ../../include/openssl/bio.h ../../include/openssl/bn.h +ec_ameth.o: ../../include/openssl/buffer.h ../../include/openssl/cms.h +ec_ameth.o: ../../include/openssl/crypto.h ../../include/openssl/e_os2.h +ec_ameth.o: ../../include/openssl/ec.h ../../include/openssl/ecdh.h +ec_ameth.o: ../../include/openssl/ecdsa.h ../../include/openssl/err.h +ec_ameth.o: ../../include/openssl/evp.h ../../include/openssl/lhash.h +ec_ameth.o: ../../include/openssl/obj_mac.h ../../include/openssl/objects.h +ec_ameth.o: ../../include/openssl/opensslconf.h +ec_ameth.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +ec_ameth.o: ../../include/openssl/pkcs7.h ../../include/openssl/safestack.h +ec_ameth.o: ../../include/openssl/sha.h ../../include/openssl/stack.h +ec_ameth.o: ../../include/openssl/symhacks.h ../../include/openssl/x509.h +ec_ameth.o: ../../include/openssl/x509_vfy.h ../asn1/asn1_locl.h ../cryptlib.h +ec_ameth.o: ec_ameth.c ec_asn1.o: ../../include/openssl/asn1.h ../../include/openssl/asn1t.h ec_asn1.o: ../../include/openssl/bio.h ../../include/openssl/bn.h ec_asn1.o: ../../include/openssl/crypto.h ../../include/openssl/e_os2.h @@ -160,6 +186,28 @@ ec_mult.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ec_mult.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ec_mult.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ec_mult.o: ../../include/openssl/symhacks.h ec_lcl.h ec_mult.c +ec_oct.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h +ec_oct.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h +ec_oct.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h +ec_oct.o: ../../include/openssl/err.h ../../include/openssl/lhash.h +ec_oct.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h +ec_oct.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +ec_oct.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h +ec_oct.o: ../../include/openssl/symhacks.h ec_lcl.h ec_oct.c +ec_pmeth.o: ../../e_os.h ../../include/openssl/asn1.h +ec_pmeth.o: ../../include/openssl/asn1t.h ../../include/openssl/bio.h +ec_pmeth.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h +ec_pmeth.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h +ec_pmeth.o: ../../include/openssl/ecdh.h ../../include/openssl/ecdsa.h +ec_pmeth.o: ../../include/openssl/err.h ../../include/openssl/evp.h +ec_pmeth.o: ../../include/openssl/lhash.h ../../include/openssl/obj_mac.h +ec_pmeth.o: ../../include/openssl/objects.h ../../include/openssl/opensslconf.h +ec_pmeth.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +ec_pmeth.o: ../../include/openssl/pkcs7.h ../../include/openssl/safestack.h +ec_pmeth.o: ../../include/openssl/sha.h ../../include/openssl/stack.h +ec_pmeth.o: ../../include/openssl/symhacks.h ../../include/openssl/x509.h +ec_pmeth.o: ../../include/openssl/x509_vfy.h ../cryptlib.h ../evp/evp_locl.h +ec_pmeth.o: ec_pmeth.c ec_print.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h ec_print.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h ec_print.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h @@ -167,6 +215,16 @@ ec_print.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ec_print.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ec_print.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ec_print.o: ../../include/openssl/symhacks.h ec_lcl.h ec_print.c +eck_prn.o: ../../e_os.h ../../include/openssl/asn1.h +eck_prn.o: ../../include/openssl/bio.h ../../include/openssl/bn.h +eck_prn.o: ../../include/openssl/buffer.h ../../include/openssl/crypto.h +eck_prn.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h +eck_prn.o: ../../include/openssl/err.h ../../include/openssl/evp.h +eck_prn.o: ../../include/openssl/lhash.h ../../include/openssl/obj_mac.h +eck_prn.o: ../../include/openssl/objects.h ../../include/openssl/opensslconf.h +eck_prn.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +eck_prn.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h +eck_prn.o: ../../include/openssl/symhacks.h ../cryptlib.h eck_prn.c ecp_mont.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h ecp_mont.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h ecp_mont.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h @@ -183,6 +241,18 @@ ecp_nist.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h ecp_nist.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h ecp_nist.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h ecp_nist.o: ../../include/openssl/symhacks.h ec_lcl.h ecp_nist.c +ecp_nistp224.o: ../../include/openssl/opensslconf.h ecp_nistp224.c +ecp_nistp256.o: ../../include/openssl/opensslconf.h ecp_nistp256.c +ecp_nistp521.o: ../../include/openssl/opensslconf.h ecp_nistp521.c +ecp_nistputil.o: ../../include/openssl/opensslconf.h ecp_nistputil.c +ecp_oct.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h +ecp_oct.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h +ecp_oct.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h +ecp_oct.o: ../../include/openssl/err.h ../../include/openssl/lhash.h +ecp_oct.o: ../../include/openssl/obj_mac.h ../../include/openssl/opensslconf.h +ecp_oct.o: ../../include/openssl/opensslv.h ../../include/openssl/ossl_typ.h +ecp_oct.o: ../../include/openssl/safestack.h ../../include/openssl/stack.h +ecp_oct.o: ../../include/openssl/symhacks.h ec_lcl.h ecp_oct.c ecp_smpl.o: ../../include/openssl/asn1.h ../../include/openssl/bio.h ecp_smpl.o: ../../include/openssl/bn.h ../../include/openssl/crypto.h ecp_smpl.o: ../../include/openssl/e_os2.h ../../include/openssl/ec.h diff --git a/crypto/ec/ec.h b/crypto/ec/ec.h index 8bc2a235b1a75..9d01325af33b9 100644 --- a/crypto/ec/ec.h +++ b/crypto/ec/ec.h @@ -2,8 +2,12 @@ /* * Originally written by Bodo Moeller for the OpenSSL project. */ +/** + * \file crypto/ec/ec.h Include file for the OpenSSL EC functions + * \author Originally written by Bodo Moeller for the OpenSSL project + */ /* ==================================================================== - * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. + * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -92,15 +96,21 @@ extern "C" { # endif #endif - + #ifndef OPENSSL_ECC_MAX_FIELD_BITS # define OPENSSL_ECC_MAX_FIELD_BITS 661 #endif +/** Enum for the point conversion form as defined in X9.62 (ECDSA) + * for the encoding of a elliptic curve point (x,y) */ typedef enum { - /* values as defined in X9.62 (ECDSA) and elsewhere */ + /** the point is encoded as z||x, where the octet z specifies + * which solution of the quadratic equation y is */ POINT_CONVERSION_COMPRESSED = 2, + /** the point is encoded as z||x||y, where z is the octet 0x02 */ POINT_CONVERSION_UNCOMPRESSED = 4, + /** the point is encoded as z||x||y, where the octet z specifies + * which solution of the quadratic equation y is */ POINT_CONVERSION_HYBRID = 6 } point_conversion_form_t; @@ -121,37 +131,148 @@ typedef struct ec_group_st typedef struct ec_point_st EC_POINT; -/* EC_METHODs for curves over GF(p). - * EC_GFp_simple_method provides the basis for the optimized methods. +/********************************************************************/ +/* EC_METHODs for curves over GF(p) */ +/********************************************************************/ + +/** Returns the basic GFp ec methods which provides the basis for the + * optimized methods. + * \return EC_METHOD object */ const EC_METHOD *EC_GFp_simple_method(void); + +/** Returns GFp methods using montgomery multiplication. + * \return EC_METHOD object + */ const EC_METHOD *EC_GFp_mont_method(void); + +/** Returns GFp methods using optimized methods for NIST recommended curves + * \return EC_METHOD object + */ const EC_METHOD *EC_GFp_nist_method(void); -/* EC_METHOD for curves over GF(2^m). +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 +/** Returns 64-bit optimized methods for nistp224 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp224_method(void); + +/** Returns 64-bit optimized methods for nistp256 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp256_method(void); + +/** Returns 64-bit optimized methods for nistp521 + * \return EC_METHOD object + */ +const EC_METHOD *EC_GFp_nistp521_method(void); +#endif + +#ifndef OPENSSL_NO_EC2M +/********************************************************************/ +/* EC_METHOD for curves over GF(2^m) */ +/********************************************************************/ + +/** Returns the basic GF2m ec method + * \return EC_METHOD object */ const EC_METHOD *EC_GF2m_simple_method(void); +#endif + -EC_GROUP *EC_GROUP_new(const EC_METHOD *); -void EC_GROUP_free(EC_GROUP *); -void EC_GROUP_clear_free(EC_GROUP *); -int EC_GROUP_copy(EC_GROUP *, const EC_GROUP *); -EC_GROUP *EC_GROUP_dup(const EC_GROUP *); +/********************************************************************/ +/* EC_GROUP functions */ +/********************************************************************/ -const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *); -int EC_METHOD_get_field_type(const EC_METHOD *); +/** Creates a new EC_GROUP object + * \param meth EC_METHOD to use + * \return newly created EC_GROUP object or NULL in case of an error. + */ +EC_GROUP *EC_GROUP_new(const EC_METHOD *meth); -int EC_GROUP_set_generator(EC_GROUP *, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor); -const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *); -int EC_GROUP_get_order(const EC_GROUP *, BIGNUM *order, BN_CTX *); -int EC_GROUP_get_cofactor(const EC_GROUP *, BIGNUM *cofactor, BN_CTX *); +/** Frees a EC_GROUP object + * \param group EC_GROUP object to be freed. + */ +void EC_GROUP_free(EC_GROUP *group); -void EC_GROUP_set_curve_name(EC_GROUP *, int nid); -int EC_GROUP_get_curve_name(const EC_GROUP *); +/** Clears and frees a EC_GROUP object + * \param group EC_GROUP object to be cleared and freed. + */ +void EC_GROUP_clear_free(EC_GROUP *group); -void EC_GROUP_set_asn1_flag(EC_GROUP *, int flag); -int EC_GROUP_get_asn1_flag(const EC_GROUP *); +/** Copies EC_GROUP objects. Note: both EC_GROUPs must use the same EC_METHOD. + * \param dst destination EC_GROUP object + * \param src source EC_GROUP object + * \return 1 on success and 0 if an error occurred. + */ +int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src); + +/** Creates a new EC_GROUP object and copies the copies the content + * form src to the newly created EC_KEY object + * \param src source EC_GROUP object + * \return newly created EC_GROUP object or NULL in case of an error. + */ +EC_GROUP *EC_GROUP_dup(const EC_GROUP *src); + +/** Returns the EC_METHOD of the EC_GROUP object. + * \param group EC_GROUP object + * \return EC_METHOD used in this EC_GROUP object. + */ +const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group); + +/** Returns the field type of the EC_METHOD. + * \param meth EC_METHOD object + * \return NID of the underlying field type OID. + */ +int EC_METHOD_get_field_type(const EC_METHOD *meth); + +/** Sets the generator and it's order/cofactor of a EC_GROUP object. + * \param group EC_GROUP object + * \param generator EC_POINT object with the generator. + * \param order the order of the group generated by the generator. + * \param cofactor the index of the sub-group generated by the generator + * in the group of all points on the elliptic curve. + * \return 1 on success and 0 if an error occured + */ +int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor); + +/** Returns the generator of a EC_GROUP object. + * \param group EC_GROUP object + * \return the currently used generator (possibly NULL). + */ +const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group); + +/** Gets the order of a EC_GROUP + * \param group EC_GROUP object + * \param order BIGNUM to which the order is copied + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx); + +/** Gets the cofactor of a EC_GROUP + * \param group EC_GROUP object + * \param cofactor BIGNUM to which the cofactor is copied + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx); + +/** Sets the name of a EC_GROUP object + * \param group EC_GROUP object + * \param nid NID of the curve name OID + */ +void EC_GROUP_set_curve_name(EC_GROUP *group, int nid); + +/** Returns the curve name of a EC_GROUP object + * \param group EC_GROUP object + * \return NID of the curve name OID or 0 if not set. + */ +int EC_GROUP_get_curve_name(const EC_GROUP *group); + +void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag); +int EC_GROUP_get_asn1_flag(const EC_GROUP *group); void EC_GROUP_set_point_conversion_form(EC_GROUP *, point_conversion_form_t); point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *); @@ -160,36 +281,115 @@ unsigned char *EC_GROUP_get0_seed(const EC_GROUP *); size_t EC_GROUP_get_seed_len(const EC_GROUP *); size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len); -int EC_GROUP_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); -int EC_GROUP_get_curve_GFp(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); -int EC_GROUP_set_curve_GF2m(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); -int EC_GROUP_get_curve_GF2m(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *); - -/* returns the number of bits needed to represent a field element */ -int EC_GROUP_get_degree(const EC_GROUP *); +/** Sets the parameter of a ec over GFp defined by y^2 = x^3 + a*x + b + * \param group EC_GROUP object + * \param p BIGNUM with the prime number + * \param a BIGNUM with parameter a of the equation + * \param b BIGNUM with parameter b of the equation + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); + +/** Gets the parameter of the ec over GFp defined by y^2 = x^3 + a*x + b + * \param group EC_GROUP object + * \param p BIGNUM for the prime number + * \param a BIGNUM for parameter a of the equation + * \param b BIGNUM for parameter b of the equation + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); + +#ifndef OPENSSL_NO_EC2M +/** Sets the parameter of a ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b + * \param group EC_GROUP object + * \param p BIGNUM with the polynomial defining the underlying field + * \param a BIGNUM with parameter a of the equation + * \param b BIGNUM with parameter b of the equation + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); + +/** Gets the parameter of the ec over GF2m defined by y^2 + x*y = x^3 + a*x^2 + b + * \param group EC_GROUP object + * \param p BIGNUM for the polynomial defining the underlying field + * \param a BIGNUM for parameter a of the equation + * \param b BIGNUM for parameter b of the equation + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); +#endif +/** Returns the number of bits needed to represent a field element + * \param group EC_GROUP object + * \return number of bits needed to represent a field element + */ +int EC_GROUP_get_degree(const EC_GROUP *group); -/* EC_GROUP_check() returns 1 if 'group' defines a valid group, 0 otherwise */ +/** Checks whether the parameter in the EC_GROUP define a valid ec group + * \param group EC_GROUP object + * \param ctx BN_CTX object (optional) + * \return 1 if group is a valid ec group and 0 otherwise + */ int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx); -/* EC_GROUP_check_discriminant() returns 1 if the discriminant of the - * elliptic curve is not zero, 0 otherwise */ -int EC_GROUP_check_discriminant(const EC_GROUP *, BN_CTX *); -/* EC_GROUP_cmp() returns 0 if both groups are equal and 1 otherwise */ -int EC_GROUP_cmp(const EC_GROUP *, const EC_GROUP *, BN_CTX *); +/** Checks whether the discriminant of the elliptic curve is zero or not + * \param group EC_GROUP object + * \param ctx BN_CTX object (optional) + * \return 1 if the discriminant is not zero and 0 otherwise + */ +int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx); + +/** Compares two EC_GROUP objects + * \param a first EC_GROUP object + * \param b second EC_GROUP object + * \param ctx BN_CTX object (optional) + * \return 0 if both groups are equal and 1 otherwise + */ +int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx); /* EC_GROUP_new_GF*() calls EC_GROUP_new() and EC_GROUP_set_GF*() * after choosing an appropriate EC_METHOD */ -EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); -EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *); -/* EC_GROUP_new_by_curve_name() creates a EC_GROUP structure - * specified by a curve name (in form of a NID) */ +/** Creates a new EC_GROUP object with the specified parameters defined + * over GFp (defined by the equation y^2 = x^3 + a*x + b) + * \param p BIGNUM with the prime number + * \param a BIGNUM with the parameter a of the equation + * \param b BIGNUM with the parameter b of the equation + * \param ctx BN_CTX object (optional) + * \return newly created EC_GROUP object with the specified parameters + */ +EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); +#ifndef OPENSSL_NO_EC2M +/** Creates a new EC_GROUP object with the specified parameters defined + * over GF2m (defined by the equation y^2 + x*y = x^3 + a*x^2 + b) + * \param p BIGNUM with the polynomial defining the underlying field + * \param a BIGNUM with the parameter a of the equation + * \param b BIGNUM with the parameter b of the equation + * \param ctx BN_CTX object (optional) + * \return newly created EC_GROUP object with the specified parameters + */ +EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx); +#endif +/** Creates a EC_GROUP object with a curve specified by a NID + * \param nid NID of the OID of the curve name + * \return newly created EC_GROUP object with specified curve or NULL + * if an error occurred + */ EC_GROUP *EC_GROUP_new_by_curve_name(int nid); -/* handling of internal curves */ + + +/********************************************************************/ +/* handling of internal curves */ +/********************************************************************/ + typedef struct { int nid; const char *comment; } EC_builtin_curve; + /* EC_builtin_curves(EC_builtin_curve *r, size_t size) returns number * of all available curves or zero if a error occurred. * In case r ist not zero nitems EC_builtin_curve structures @@ -197,39 +397,168 @@ typedef struct { size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems); -/* EC_POINT functions */ +/********************************************************************/ +/* EC_POINT functions */ +/********************************************************************/ + +/** Creates a new EC_POINT object for the specified EC_GROUP + * \param group EC_GROUP the underlying EC_GROUP object + * \return newly created EC_POINT object or NULL if an error occurred + */ +EC_POINT *EC_POINT_new(const EC_GROUP *group); + +/** Frees a EC_POINT object + * \param point EC_POINT object to be freed + */ +void EC_POINT_free(EC_POINT *point); -EC_POINT *EC_POINT_new(const EC_GROUP *); -void EC_POINT_free(EC_POINT *); -void EC_POINT_clear_free(EC_POINT *); -int EC_POINT_copy(EC_POINT *, const EC_POINT *); -EC_POINT *EC_POINT_dup(const EC_POINT *, const EC_GROUP *); +/** Clears and frees a EC_POINT object + * \param point EC_POINT object to be cleared and freed + */ +void EC_POINT_clear_free(EC_POINT *point); + +/** Copies EC_POINT object + * \param dst destination EC_POINT object + * \param src source EC_POINT object + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src); + +/** Creates a new EC_POINT object and copies the content of the supplied + * EC_POINT + * \param src source EC_POINT object + * \param group underlying the EC_GROUP object + * \return newly created EC_POINT object or NULL if an error occurred + */ +EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group); -const EC_METHOD *EC_POINT_method_of(const EC_POINT *); - -int EC_POINT_set_to_infinity(const EC_GROUP *, EC_POINT *); -int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *, - const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *); -int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *, - BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *); -int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *, EC_POINT *, - const BIGNUM *x, const BIGNUM *y, BN_CTX *); -int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *, const EC_POINT *, - BIGNUM *x, BIGNUM *y, BN_CTX *); -int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *, EC_POINT *, - const BIGNUM *x, int y_bit, BN_CTX *); - -int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *, EC_POINT *, - const BIGNUM *x, const BIGNUM *y, BN_CTX *); -int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *, const EC_POINT *, - BIGNUM *x, BIGNUM *y, BN_CTX *); -int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *, EC_POINT *, - const BIGNUM *x, int y_bit, BN_CTX *); - -size_t EC_POINT_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *); -int EC_POINT_oct2point(const EC_GROUP *, EC_POINT *, - const unsigned char *buf, size_t len, BN_CTX *); +/** Returns the EC_METHOD used in EC_POINT object + * \param point EC_POINT object + * \return the EC_METHOD used + */ +const EC_METHOD *EC_POINT_method_of(const EC_POINT *point); + +/** Sets a point to infinity (neutral element) + * \param group underlying EC_GROUP object + * \param point EC_POINT to set to infinity + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point); + +/** Sets the jacobian projective coordinates of a EC_POINT over GFp + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param x BIGNUM with the x-coordinate + * \param y BIGNUM with the y-coordinate + * \param z BIGNUM with the z-coordinate + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, + const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx); + +/** Gets the jacobian projective coordinates of a EC_POINT over GFp + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param x BIGNUM for the x-coordinate + * \param y BIGNUM for the y-coordinate + * \param z BIGNUM for the z-coordinate + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group, + const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx); + +/** Sets the affine coordinates of a EC_POINT over GFp + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param x BIGNUM with the x-coordinate + * \param y BIGNUM with the y-coordinate + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, + const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx); + +/** Gets the affine coordinates of a EC_POINT over GFp + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param x BIGNUM for the x-coordinate + * \param y BIGNUM for the y-coordinate + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, + const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); + +/** Sets the x9.62 compressed coordinates of a EC_POINT over GFp + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param x BIGNUM with x-coordinate + * \param y_bit integer with the y-Bit (either 0 or 1) + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p, + const BIGNUM *x, int y_bit, BN_CTX *ctx); +#ifndef OPENSSL_NO_EC2M +/** Sets the affine coordinates of a EC_POINT over GF2m + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param x BIGNUM with the x-coordinate + * \param y BIGNUM with the y-coordinate + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p, + const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx); + +/** Gets the affine coordinates of a EC_POINT over GF2m + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param x BIGNUM for the x-coordinate + * \param y BIGNUM for the y-coordinate + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, + const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); + +/** Sets the x9.62 compressed coordinates of a EC_POINT over GF2m + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param x BIGNUM with x-coordinate + * \param y_bit integer with the y-Bit (either 0 or 1) + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p, + const BIGNUM *x, int y_bit, BN_CTX *ctx); +#endif +/** Encodes a EC_POINT object to a octet string + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param form point conversion form + * \param buf memory buffer for the result. If NULL the function returns + * required buffer size. + * \param len length of the memory buffer + * \param ctx BN_CTX object (optional) + * \return the length of the encoded octet string or 0 if an error occurred + */ +size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p, + point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx); + +/** Decodes a EC_POINT from a octet string + * \param group underlying EC_GROUP object + * \param p EC_POINT object + * \param buf memory buffer with the encoded ec point + * \param len length of the encoded ec point + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p, + const unsigned char *buf, size_t len, BN_CTX *ctx); /* other interfaces to point2oct/oct2point: */ BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *, @@ -241,36 +570,114 @@ char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *, EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *, EC_POINT *, BN_CTX *); -int EC_POINT_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *); -int EC_POINT_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *); -int EC_POINT_invert(const EC_GROUP *, EC_POINT *, BN_CTX *); -int EC_POINT_is_at_infinity(const EC_GROUP *, const EC_POINT *); -int EC_POINT_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *); -int EC_POINT_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *); +/********************************************************************/ +/* functions for doing EC_POINT arithmetic */ +/********************************************************************/ + +/** Computes the sum of two EC_POINT + * \param group underlying EC_GROUP object + * \param r EC_POINT object for the result (r = a + b) + * \param a EC_POINT object with the first summand + * \param b EC_POINT object with the second summand + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx); + +/** Computes the double of a EC_POINT + * \param group underlying EC_GROUP object + * \param r EC_POINT object for the result (r = 2 * a) + * \param a EC_POINT object + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx); + +/** Computes the inverse of a EC_POINT + * \param group underlying EC_GROUP object + * \param a EC_POINT object to be inverted (it's used for the result as well) + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx); + +/** Checks whether the point is the neutral element of the group + * \param group the underlying EC_GROUP object + * \param p EC_POINT object + * \return 1 if the point is the neutral element and 0 otherwise + */ +int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p); + +/** Checks whether the point is on the curve + * \param group underlying EC_GROUP object + * \param point EC_POINT object to check + * \param ctx BN_CTX object (optional) + * \return 1 if point if on the curve and 0 otherwise + */ +int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx); + +/** Compares two EC_POINTs + * \param group underlying EC_GROUP object + * \param a first EC_POINT object + * \param b second EC_POINT object + * \param ctx BN_CTX object (optional) + * \return 0 if both points are equal and a value != 0 otherwise + */ +int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx); int EC_POINT_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *); int EC_POINTs_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *); +/** Computes r = generator * n sum_{i=0}^num p[i] * m[i] + * \param group underlying EC_GROUP object + * \param r EC_POINT object for the result + * \param n BIGNUM with the multiplier for the group generator (optional) + * \param num number futher summands + * \param p array of size num of EC_POINT objects + * \param m array of size num of BIGNUM objects + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num, const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx); + +/** Computes r = generator * n + q * m + * \param group underlying EC_GROUP object + * \param r EC_POINT object for the result + * \param n BIGNUM with the multiplier for the group generator (optional) + * \param q EC_POINT object with the first factor of the second summand + * \param m BIGNUM with the second factor of the second summand + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx); -int EC_POINTs_mul(const EC_GROUP *, EC_POINT *r, const BIGNUM *, size_t num, const EC_POINT *[], const BIGNUM *[], BN_CTX *); -int EC_POINT_mul(const EC_GROUP *, EC_POINT *r, const BIGNUM *, const EC_POINT *, const BIGNUM *, BN_CTX *); - -/* EC_GROUP_precompute_mult() stores multiples of generator for faster point multiplication */ -int EC_GROUP_precompute_mult(EC_GROUP *, BN_CTX *); -/* EC_GROUP_have_precompute_mult() reports whether such precomputation has been done */ -int EC_GROUP_have_precompute_mult(const EC_GROUP *); +/** Stores multiples of generator for faster point multiplication + * \param group EC_GROUP object + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occured + */ +int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +/** Reports whether a precomputation has been done + * \param group EC_GROUP object + * \return 1 if a pre-computation has been done and 0 otherwise + */ +int EC_GROUP_have_precompute_mult(const EC_GROUP *group); -/* ASN1 stuff */ +/********************************************************************/ +/* ASN1 stuff */ +/********************************************************************/ /* EC_GROUP_get_basis_type() returns the NID of the basis type * used to represent the field elements */ int EC_GROUP_get_basis_type(const EC_GROUP *); +#ifndef OPENSSL_NO_EC2M int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k); int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1, unsigned int *k2, unsigned int *k3); +#endif #define OPENSSL_EC_NAMED_CURVE 0x001 @@ -293,28 +700,106 @@ int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off); int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off); #endif -/* the EC_KEY stuff */ + +/********************************************************************/ +/* EC_KEY functions */ +/********************************************************************/ + typedef struct ec_key_st EC_KEY; /* some values for the encoding_flag */ #define EC_PKEY_NO_PARAMETERS 0x001 #define EC_PKEY_NO_PUBKEY 0x002 +/* some values for the flags field */ +#define EC_FLAG_NON_FIPS_ALLOW 0x1 +#define EC_FLAG_FIPS_CHECKED 0x2 + +/** Creates a new EC_KEY object. + * \return EC_KEY object or NULL if an error occurred. + */ EC_KEY *EC_KEY_new(void); + +int EC_KEY_get_flags(const EC_KEY *key); + +void EC_KEY_set_flags(EC_KEY *key, int flags); + +void EC_KEY_clear_flags(EC_KEY *key, int flags); + +/** Creates a new EC_KEY object using a named curve as underlying + * EC_GROUP object. + * \param nid NID of the named curve. + * \return EC_KEY object or NULL if an error occurred. + */ EC_KEY *EC_KEY_new_by_curve_name(int nid); -void EC_KEY_free(EC_KEY *); -EC_KEY *EC_KEY_copy(EC_KEY *, const EC_KEY *); -EC_KEY *EC_KEY_dup(const EC_KEY *); - -int EC_KEY_up_ref(EC_KEY *); - -const EC_GROUP *EC_KEY_get0_group(const EC_KEY *); -int EC_KEY_set_group(EC_KEY *, const EC_GROUP *); -const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *); -int EC_KEY_set_private_key(EC_KEY *, const BIGNUM *); -const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *); -int EC_KEY_set_public_key(EC_KEY *, const EC_POINT *); -unsigned EC_KEY_get_enc_flags(const EC_KEY *); + +/** Frees a EC_KEY object. + * \param key EC_KEY object to be freed. + */ +void EC_KEY_free(EC_KEY *key); + +/** Copies a EC_KEY object. + * \param dst destination EC_KEY object + * \param src src EC_KEY object + * \return dst or NULL if an error occurred. + */ +EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src); + +/** Creates a new EC_KEY object and copies the content from src to it. + * \param src the source EC_KEY object + * \return newly created EC_KEY object or NULL if an error occurred. + */ +EC_KEY *EC_KEY_dup(const EC_KEY *src); + +/** Increases the internal reference count of a EC_KEY object. + * \param key EC_KEY object + * \return 1 on success and 0 if an error occurred. + */ +int EC_KEY_up_ref(EC_KEY *key); + +/** Returns the EC_GROUP object of a EC_KEY object + * \param key EC_KEY object + * \return the EC_GROUP object (possibly NULL). + */ +const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key); + +/** Sets the EC_GROUP of a EC_KEY object. + * \param key EC_KEY object + * \param group EC_GROUP to use in the EC_KEY object (note: the EC_KEY + * object will use an own copy of the EC_GROUP). + * \return 1 on success and 0 if an error occurred. + */ +int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group); + +/** Returns the private key of a EC_KEY object. + * \param key EC_KEY object + * \return a BIGNUM with the private key (possibly NULL). + */ +const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key); + +/** Sets the private key of a EC_KEY object. + * \param key EC_KEY object + * \param prv BIGNUM with the private key (note: the EC_KEY object + * will use an own copy of the BIGNUM). + * \return 1 on success and 0 if an error occurred. + */ +int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv); + +/** Returns the public key of a EC_KEY object. + * \param key the EC_KEY object + * \return a EC_POINT object with the public key (possibly NULL) + */ +const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key); + +/** Sets the public key of a EC_KEY object. + * \param key EC_KEY object + * \param pub EC_POINT object with the public key (note: the EC_KEY object + * will use an own copy of the EC_POINT object). + * \return 1 on success and 0 if an error occurred. + */ +int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub); + +unsigned EC_KEY_get_enc_flags(const EC_KEY *key); void EC_KEY_set_enc_flags(EC_KEY *, unsigned int); point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *); void EC_KEY_set_conv_form(EC_KEY *, point_conversion_form_t); @@ -325,31 +810,135 @@ void EC_KEY_insert_key_method_data(EC_KEY *, void *data, void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *)); /* wrapper functions for the underlying EC_GROUP object */ void EC_KEY_set_asn1_flag(EC_KEY *, int); -int EC_KEY_precompute_mult(EC_KEY *, BN_CTX *ctx); - -/* EC_KEY_generate_key() creates a ec private (public) key */ -int EC_KEY_generate_key(EC_KEY *); -/* EC_KEY_check_key() */ -int EC_KEY_check_key(const EC_KEY *); - -/* de- and encoding functions for SEC1 ECPrivateKey */ -EC_KEY *d2i_ECPrivateKey(EC_KEY **a, const unsigned char **in, long len); -int i2d_ECPrivateKey(EC_KEY *a, unsigned char **out); -/* de- and encoding functions for EC parameters */ -EC_KEY *d2i_ECParameters(EC_KEY **a, const unsigned char **in, long len); -int i2d_ECParameters(EC_KEY *a, unsigned char **out); -/* de- and encoding functions for EC public key - * (octet string, not DER -- hence 'o2i' and 'i2o') */ -EC_KEY *o2i_ECPublicKey(EC_KEY **a, const unsigned char **in, long len); -int i2o_ECPublicKey(EC_KEY *a, unsigned char **out); + +/** Creates a table of pre-computed multiples of the generator to + * accelerate further EC_KEY operations. + * \param key EC_KEY object + * \param ctx BN_CTX object (optional) + * \return 1 on success and 0 if an error occurred. + */ +int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx); + +/** Creates a new ec private (and optional a new public) key. + * \param key EC_KEY object + * \return 1 on success and 0 if an error occurred. + */ +int EC_KEY_generate_key(EC_KEY *key); + +/** Verifies that a private and/or public key is valid. + * \param key the EC_KEY object + * \return 1 on success and 0 otherwise. + */ +int EC_KEY_check_key(const EC_KEY *key); + +/** Sets a public key from affine coordindates performing + * neccessary NIST PKV tests. + * \param key the EC_KEY object + * \param x public key x coordinate + * \param y public key y coordinate + * \return 1 on success and 0 otherwise. + */ +int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y); + + +/********************************************************************/ +/* de- and encoding functions for SEC1 ECPrivateKey */ +/********************************************************************/ + +/** Decodes a private key from a memory buffer. + * \param key a pointer to a EC_KEY object which should be used (or NULL) + * \param in pointer to memory with the DER encoded private key + * \param len length of the DER encoded private key + * \return the decoded private key or NULL if an error occurred. + */ +EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len); + +/** Encodes a private key object and stores the result in a buffer. + * \param key the EC_KEY object to encode + * \param out the buffer for the result (if NULL the function returns number + * of bytes needed). + * \return 1 on success and 0 if an error occurred. + */ +int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out); + + +/********************************************************************/ +/* de- and encoding functions for EC parameters */ +/********************************************************************/ + +/** Decodes ec parameter from a memory buffer. + * \param key a pointer to a EC_KEY object which should be used (or NULL) + * \param in pointer to memory with the DER encoded ec parameters + * \param len length of the DER encoded ec parameters + * \return a EC_KEY object with the decoded parameters or NULL if an error + * occurred. + */ +EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len); + +/** Encodes ec parameter and stores the result in a buffer. + * \param key the EC_KEY object with ec paramters to encode + * \param out the buffer for the result (if NULL the function returns number + * of bytes needed). + * \return 1 on success and 0 if an error occurred. + */ +int i2d_ECParameters(EC_KEY *key, unsigned char **out); + + +/********************************************************************/ +/* de- and encoding functions for EC public key */ +/* (octet string, not DER -- hence 'o2i' and 'i2o') */ +/********************************************************************/ + +/** Decodes a ec public key from a octet string. + * \param key a pointer to a EC_KEY object which should be used + * \param in memory buffer with the encoded public key + * \param len length of the encoded public key + * \return EC_KEY object with decoded public key or NULL if an error + * occurred. + */ +EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len); + +/** Encodes a ec public key in an octet string. + * \param key the EC_KEY object with the public key + * \param out the buffer for the result (if NULL the function returns number + * of bytes needed). + * \return 1 on success and 0 if an error occurred + */ +int i2o_ECPublicKey(EC_KEY *key, unsigned char **out); #ifndef OPENSSL_NO_BIO -int ECParameters_print(BIO *bp, const EC_KEY *x); -int EC_KEY_print(BIO *bp, const EC_KEY *x, int off); +/** Prints out the ec parameters on human readable form. + * \param bp BIO object to which the information is printed + * \param key EC_KEY object + * \return 1 on success and 0 if an error occurred + */ +int ECParameters_print(BIO *bp, const EC_KEY *key); + +/** Prints out the contents of a EC_KEY object + * \param bp BIO object to which the information is printed + * \param key EC_KEY object + * \param off line offset + * \return 1 on success and 0 if an error occurred + */ +int EC_KEY_print(BIO *bp, const EC_KEY *key, int off); + #endif #ifndef OPENSSL_NO_FP_API -int ECParameters_print_fp(FILE *fp, const EC_KEY *x); -int EC_KEY_print_fp(FILE *fp, const EC_KEY *x, int off); +/** Prints out the ec parameters on human readable form. + * \param fp file descriptor to which the information is printed + * \param key EC_KEY object + * \return 1 on success and 0 if an error occurred + */ +int ECParameters_print_fp(FILE *fp, const EC_KEY *key); + +/** Prints out the contents of a EC_KEY object + * \param fp file descriptor to which the information is printed + * \param key EC_KEY object + * \param off line offset + * \return 1 on success and 0 if an error occurred + */ +int EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off); + #endif #define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x) @@ -362,6 +951,13 @@ int EC_KEY_print_fp(FILE *fp, const EC_KEY *x, int off); # endif #endif +#define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \ + EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, EVP_PKEY_OP_PARAMGEN, \ + EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL) + + +#define EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID (EVP_PKEY_ALG_CTRL + 1) + /* BEGIN ERROR CODES */ /* The following lines are auto generated by the script mkerr.pl. Any changes * made after this point may be overwritten when the script is next run. @@ -371,10 +967,19 @@ void ERR_load_EC_strings(void); /* Error codes for the EC functions. */ /* Function codes. */ +#define EC_F_BN_TO_FELEM 224 #define EC_F_COMPUTE_WNAF 143 #define EC_F_D2I_ECPARAMETERS 144 #define EC_F_D2I_ECPKPARAMETERS 145 #define EC_F_D2I_ECPRIVATEKEY 146 +#define EC_F_DO_EC_KEY_PRINT 221 +#define EC_F_ECKEY_PARAM2TYPE 223 +#define EC_F_ECKEY_PARAM_DECODE 212 +#define EC_F_ECKEY_PRIV_DECODE 213 +#define EC_F_ECKEY_PRIV_ENCODE 214 +#define EC_F_ECKEY_PUB_DECODE 215 +#define EC_F_ECKEY_PUB_ENCODE 216 +#define EC_F_ECKEY_TYPE2PARAM 220 #define EC_F_ECPARAMETERS_PRINT 147 #define EC_F_ECPARAMETERS_PRINT_FP 148 #define EC_F_ECPKPARAMETERS_PRINT 149 @@ -405,6 +1010,15 @@ void ERR_load_EC_strings(void); #define EC_F_EC_GFP_MONT_FIELD_SQR 132 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE 189 #define EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP 135 +#define EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE 225 +#define EC_F_EC_GFP_NISTP224_POINTS_MUL 228 +#define EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES 226 +#define EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE 230 +#define EC_F_EC_GFP_NISTP256_POINTS_MUL 231 +#define EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES 232 +#define EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE 233 +#define EC_F_EC_GFP_NISTP521_POINTS_MUL 234 +#define EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES 235 #define EC_F_EC_GFP_NIST_FIELD_MUL 200 #define EC_F_EC_GFP_NIST_FIELD_SQR 201 #define EC_F_EC_GFP_NIST_GROUP_SET_CURVE 202 @@ -447,8 +1061,8 @@ void ERR_load_EC_strings(void); #define EC_F_EC_KEY_NEW 182 #define EC_F_EC_KEY_PRINT 180 #define EC_F_EC_KEY_PRINT_FP 181 +#define EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES 229 #define EC_F_EC_POINTS_MAKE_AFFINE 136 -#define EC_F_EC_POINTS_MUL 138 #define EC_F_EC_POINT_ADD 112 #define EC_F_EC_POINT_CMP 113 #define EC_F_EC_POINT_COPY 114 @@ -478,22 +1092,38 @@ void ERR_load_EC_strings(void); #define EC_F_I2D_ECPKPARAMETERS 191 #define EC_F_I2D_ECPRIVATEKEY 192 #define EC_F_I2O_ECPUBLICKEY 151 +#define EC_F_NISTP224_PRE_COMP_NEW 227 +#define EC_F_NISTP256_PRE_COMP_NEW 236 +#define EC_F_NISTP521_PRE_COMP_NEW 237 #define EC_F_O2I_ECPUBLICKEY 152 +#define EC_F_OLD_EC_PRIV_DECODE 222 +#define EC_F_PKEY_EC_CTRL 197 +#define EC_F_PKEY_EC_CTRL_STR 198 +#define EC_F_PKEY_EC_DERIVE 217 +#define EC_F_PKEY_EC_KEYGEN 199 +#define EC_F_PKEY_EC_PARAMGEN 219 +#define EC_F_PKEY_EC_SIGN 218 /* Reason codes. */ #define EC_R_ASN1_ERROR 115 #define EC_R_ASN1_UNKNOWN_FIELD 116 +#define EC_R_BIGNUM_OUT_OF_RANGE 144 #define EC_R_BUFFER_TOO_SMALL 100 +#define EC_R_COORDINATES_OUT_OF_RANGE 146 #define EC_R_D2I_ECPKPARAMETERS_FAILURE 117 +#define EC_R_DECODE_ERROR 142 #define EC_R_DISCRIMINANT_IS_ZERO 118 #define EC_R_EC_GROUP_NEW_BY_NAME_FAILURE 119 -#define EC_R_FIELD_TOO_LARGE 138 +#define EC_R_FIELD_TOO_LARGE 143 +#define EC_R_GF2M_NOT_SUPPORTED 147 #define EC_R_GROUP2PKPARAMETERS_FAILURE 120 #define EC_R_I2D_ECPKPARAMETERS_FAILURE 121 #define EC_R_INCOMPATIBLE_OBJECTS 101 #define EC_R_INVALID_ARGUMENT 112 #define EC_R_INVALID_COMPRESSED_POINT 110 #define EC_R_INVALID_COMPRESSION_BIT 109 +#define EC_R_INVALID_CURVE 141 +#define EC_R_INVALID_DIGEST_TYPE 138 #define EC_R_INVALID_ENCODING 102 #define EC_R_INVALID_FIELD 103 #define EC_R_INVALID_FORM 104 @@ -501,6 +1131,7 @@ void ERR_load_EC_strings(void); #define EC_R_INVALID_PENTANOMIAL_BASIS 132 #define EC_R_INVALID_PRIVATE_KEY 123 #define EC_R_INVALID_TRINOMIAL_BASIS 137 +#define EC_R_KEYS_NOT_SET 140 #define EC_R_MISSING_PARAMETERS 124 #define EC_R_MISSING_PRIVATE_KEY 125 #define EC_R_NOT_A_NIST_PRIME 135 @@ -508,6 +1139,7 @@ void ERR_load_EC_strings(void); #define EC_R_NOT_IMPLEMENTED 126 #define EC_R_NOT_INITIALIZED 111 #define EC_R_NO_FIELD_MOD 133 +#define EC_R_NO_PARAMETERS_SET 139 #define EC_R_PASSED_NULL_PARAMETER 134 #define EC_R_PKPARAMETERS2GROUP_FAILURE 127 #define EC_R_POINT_AT_INFINITY 106 @@ -518,6 +1150,7 @@ void ERR_load_EC_strings(void); #define EC_R_UNKNOWN_GROUP 129 #define EC_R_UNKNOWN_ORDER 114 #define EC_R_UNSUPPORTED_FIELD 131 +#define EC_R_WRONG_CURVE_PARAMETERS 145 #define EC_R_WRONG_ORDER 130 #ifdef __cplusplus diff --git a/crypto/ec/ec2_mult.c b/crypto/ec/ec2_mult.c index 7dca5e4bcd436..26f4a783fcc1e 100644 --- a/crypto/ec/ec2_mult.c +++ b/crypto/ec/ec2_mult.c @@ -71,12 +71,14 @@ #include "ec_lcl.h" +#ifndef OPENSSL_NO_EC2M + /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective * coordinates. * Uses algorithm Mdouble in appendix of * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over - * GF(2^m) without precomputation". + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * modified to not require precomputation of c=b^{2^{m-1}}. */ static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) @@ -107,8 +109,8 @@ static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery * projective coordinates. * Uses algorithm Madd in appendix of - * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over - * GF(2^m) without precomputation". + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). */ static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) @@ -140,8 +142,8 @@ static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) * using Montgomery point multiplication algorithm Mxy() in appendix of - * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over - * GF(2^m) without precomputation". + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * Returns: * 0 on error * 1 if return value should be the point at infinity @@ -209,15 +211,15 @@ static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIG /* Computes scalar*point and stores the result in r. * point can not equal r. * Uses algorithm 2P of - * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over - * GF(2^m) without precomputation". + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). */ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx) { BIGNUM *x1, *x2, *z1, *z2; - int ret = 0, i, j; - BN_ULONG mask; + int ret = 0, i; + BN_ULONG mask,word; if (r == point) { @@ -251,22 +253,24 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */ /* find top most bit and go one past it */ - i = scalar->top - 1; j = BN_BITS2 - 1; + i = scalar->top - 1; mask = BN_TBIT; - while (!(scalar->d[i] & mask)) { mask >>= 1; j--; } - mask >>= 1; j--; + word = scalar->d[i]; + while (!(word & mask)) mask >>= 1; + mask >>= 1; /* if top most bit was at word break, go to next word */ if (!mask) { - i--; j = BN_BITS2 - 1; + i--; mask = BN_TBIT; } for (; i >= 0; i--) { - for (; j >= 0; j--) + word = scalar->d[i]; + while (mask) { - if (scalar->d[i] & mask) + if (word & mask) { if (!gf2m_Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err; if (!gf2m_Mdouble(group, x2, z2, ctx)) goto err; @@ -278,7 +282,6 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, } mask >>= 1; } - j = BN_BITS2 - 1; mask = BN_TBIT; } @@ -383,3 +386,5 @@ int ec_GF2m_have_precompute_mult(const EC_GROUP *group) { return ec_wNAF_have_precompute_mult(group); } + +#endif diff --git a/crypto/ec/ec2_oct.c b/crypto/ec/ec2_oct.c new file mode 100644 index 0000000000000..f1d75e5ddf66a --- /dev/null +++ b/crypto/ec/ec2_oct.c @@ -0,0 +1,407 @@ +/* crypto/ec/ec2_oct.c */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * + * The Elliptic Curve Public-Key Crypto Library (ECC Code) included + * herein is developed by SUN MICROSYSTEMS, INC., and is contributed + * to the OpenSSL project. + * + * The ECC Code is licensed pursuant to the OpenSSL open source + * license provided below. + * + * The software is originally written by Sheueling Chang Shantz and + * Douglas Stebila of Sun Microsystems Laboratories. + * + */ +/* ==================================================================== + * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ + +#include <openssl/err.h> + +#include "ec_lcl.h" + +#ifndef OPENSSL_NO_EC2M + +/* Calculates and sets the affine coordinates of an EC_POINT from the given + * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. + * Note that the simple implementation only uses affine coordinates. + * + * The method is from the following publication: + * + * Harper, Menezes, Vanstone: + * "Public-Key Cryptosystems with Very Small Key Lengths", + * EUROCRYPT '92, Springer-Verlag LNCS 658, + * published February 1993 + * + * US Patents 6,141,420 and 6,618,483 (Vanstone, Mullin, Agnew) describe + * the same method, but claim no priority date earlier than July 29, 1994 + * (and additionally fail to cite the EUROCRYPT '92 publication as prior art). + */ +int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x_, int y_bit, BN_CTX *ctx) + { + BN_CTX *new_ctx = NULL; + BIGNUM *tmp, *x, *y, *z; + int ret = 0, z0; + + /* clear error queue */ + ERR_clear_error(); + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + y_bit = (y_bit != 0) ? 1 : 0; + + BN_CTX_start(ctx); + tmp = BN_CTX_get(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + z = BN_CTX_get(ctx); + if (z == NULL) goto err; + + if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; + if (BN_is_zero(x)) + { + if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; + } + else + { + if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; + if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; + if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; + if (!BN_GF2m_add(tmp, x, tmp)) goto err; + if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) + { + unsigned long err = ERR_peek_last_error(); + + if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) + { + ERR_clear_error(); + ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); + } + else + ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); + goto err; + } + z0 = (BN_is_odd(z)) ? 1 : 0; + if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; + if (z0 != y_bit) + { + if (!BN_GF2m_add(y, y, x)) goto err; + } + } + + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + + +/* Converts an EC_POINT to an octet string. + * If buf is NULL, the encoded length will be returned. + * If the length len of buf is smaller than required an error will be returned. + */ +size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) + { + size_t ret; + BN_CTX *new_ctx = NULL; + int used_ctx = 0; + BIGNUM *x, *y, *yxi; + size_t field_len, i, skip; + + if ((form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); + goto err; + } + + if (EC_POINT_is_at_infinity(group, point)) + { + /* encodes to a single 0 octet */ + if (buf != NULL) + { + if (len < 1) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + buf[0] = 0; + } + return 1; + } + + + /* ret := required output buffer length */ + field_len = (EC_GROUP_get_degree(group) + 7) / 8; + ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + + /* if 'buf' is NULL, just return required length */ + if (buf != NULL) + { + if (len < ret) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + goto err; + } + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + used_ctx = 1; + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + yxi = BN_CTX_get(ctx); + if (yxi == NULL) goto err; + + if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + + buf[0] = form; + if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) + { + if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; + if (BN_is_odd(yxi)) buf[0]++; + } + + i = 1; + + skip = field_len - BN_num_bytes(x); + if (skip > field_len) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) + { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(x, buf + i); + i += skip; + if (i != 1 + field_len) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) + { + skip = field_len - BN_num_bytes(y); + if (skip > field_len) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) + { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(y, buf + i); + i += skip; + } + + if (i != ret) + { + ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + } + + if (used_ctx) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + + err: + if (used_ctx) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return 0; + } + + +/* Converts an octet string representation to an EC_POINT. + * Note that the simple implementation only uses affine coordinates. + */ +int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) + { + point_conversion_form_t form; + int y_bit; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *yxi; + size_t field_len, enc_len; + int ret = 0; + + if (len == 0) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + form = buf[0]; + y_bit = form & 1; + form = form & ~1U; + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (form == 0) + { + if (len != 1) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + return EC_POINT_set_to_infinity(group, point); + } + + field_len = (EC_GROUP_get_degree(group) + 7) / 8; + enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + + if (len != enc_len) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + yxi = BN_CTX_get(ctx); + if (yxi == NULL) goto err; + + if (!BN_bin2bn(buf + 1, field_len, x)) goto err; + if (BN_ucmp(x, &group->field) >= 0) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + + if (form == POINT_CONVERSION_COMPRESSED) + { + if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; + } + else + { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; + if (BN_ucmp(y, &group->field) >= 0) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + if (form == POINT_CONVERSION_HYBRID) + { + if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; + if (y_bit != BN_is_odd(yxi)) + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + } + + if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; + } + + if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ + { + ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); + goto err; + } + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } +#endif diff --git a/crypto/ec/ec2_smpl.c b/crypto/ec/ec2_smpl.c index c06b3b667f0bf..e0e59c7d8299b 100644 --- a/crypto/ec/ec2_smpl.c +++ b/crypto/ec/ec2_smpl.c @@ -14,7 +14,7 @@ * */ /* ==================================================================== - * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. + * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -71,10 +71,20 @@ #include "ec_lcl.h" +#ifndef OPENSSL_NO_EC2M + +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif + const EC_METHOD *EC_GF2m_simple_method(void) { +#ifdef OPENSSL_FIPS + return fips_ec_gf2m_simple_method(); +#else static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_characteristic_two_field, ec_GF2m_simple_group_init, ec_GF2m_simple_group_finish, @@ -93,9 +103,7 @@ const EC_METHOD *EC_GF2m_simple_method(void) 0 /* get_Jprojective_coordinates_GFp */, ec_GF2m_simple_point_set_affine_coordinates, ec_GF2m_simple_point_get_affine_coordinates, - ec_GF2m_simple_set_compressed_coordinates, - ec_GF2m_simple_point2oct, - ec_GF2m_simple_oct2point, + 0,0,0, ec_GF2m_simple_add, ec_GF2m_simple_dbl, ec_GF2m_simple_invert, @@ -118,6 +126,7 @@ const EC_METHOD *EC_GF2m_simple_method(void) 0 /* field_set_to_one */ }; return &ret; +#endif } @@ -157,6 +166,7 @@ void ec_GF2m_simple_group_clear_finish(EC_GROUP *group) group->poly[2] = 0; group->poly[3] = 0; group->poly[4] = 0; + group->poly[5] = -1; } @@ -174,10 +184,9 @@ int ec_GF2m_simple_group_copy(EC_GROUP *dest, const EC_GROUP *src) dest->poly[2] = src->poly[2]; dest->poly[3] = src->poly[3]; dest->poly[4] = src->poly[4]; - if(bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) - return 0; - if(bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) - return 0; + dest->poly[5] = src->poly[5]; + if (bn_wexpand(&dest->a, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; + if (bn_wexpand(&dest->b, (int)(dest->poly[0] + BN_BITS2 - 1) / BN_BITS2) == NULL) return 0; for (i = dest->a.top; i < dest->a.dmax; i++) dest->a.d[i] = 0; for (i = dest->b.top; i < dest->b.dmax; i++) dest->b.d[i] = 0; return 1; @@ -192,7 +201,7 @@ int ec_GF2m_simple_group_set_curve(EC_GROUP *group, /* group->field */ if (!BN_copy(&group->field, p)) goto err; - i = BN_GF2m_poly2arr(&group->field, group->poly, 5); + i = BN_GF2m_poly2arr(&group->field, group->poly, 6) - 1; if ((i != 5) && (i != 3)) { ECerr(EC_F_EC_GF2M_SIMPLE_GROUP_SET_CURVE, EC_R_UNSUPPORTED_FIELD); @@ -405,274 +414,6 @@ int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_ return ret; } - -/* Include patented algorithms. */ -#include "ec2_smpt.c" - - -/* Converts an EC_POINT to an octet string. - * If buf is NULL, the encoded length will be returned. - * If the length len of buf is smaller than required an error will be returned. - * - * The point compression section of this function is patented by Certicom Corp. - * under US Patent 6,141,420. Point compression is disabled by default and can - * be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at - * Configure-time. - */ -size_t ec_GF2m_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { - size_t ret; - BN_CTX *new_ctx = NULL; - int used_ctx = 0; - BIGNUM *x, *y, *yxi; - size_t field_len, i, skip; - -#ifndef OPENSSL_EC_BIN_PT_COMP - if ((form == POINT_CONVERSION_COMPRESSED) || (form == POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_DISABLED); - goto err; - } -#endif - - if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); - goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { - /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - buf[0] = 0; - } - return 1; - } - - - /* ret := required output buffer length */ - field_len = (EC_GROUP_get_degree(group) + 7) / 8; - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - goto err; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - used_ctx = 1; - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - yxi = BN_CTX_get(ctx); - if (yxi == NULL) goto err; - - if (!EC_POINT_get_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; - - buf[0] = form; -#ifdef OPENSSL_EC_BIN_PT_COMP - if ((form != POINT_CONVERSION_UNCOMPRESSED) && !BN_is_zero(x)) - { - if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; - if (BN_is_odd(yxi)) buf[0]++; - } -#endif - - i = 1; - - skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(x, buf + i); - i += skip; - if (i != 1 + field_len) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { - skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(y, buf + i); - i += skip; - } - - if (i != ret) - { - ECerr(EC_F_EC_GF2M_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - } - - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - - err: - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return 0; - } - - -/* Converts an octet string representation to an EC_POINT. - * Note that the simple implementation only uses affine coordinates. - */ -int ec_GF2m_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - point_conversion_form_t form; - int y_bit; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y, *yxi; - size_t field_len, enc_len; - int ret = 0; - - if (len == 0) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - form = buf[0]; - y_bit = form & 1; - form = form & ~1U; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (form == 0) - { - if (len != 1) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - return EC_POINT_set_to_infinity(group, point); - } - - field_len = (EC_GROUP_get_degree(group) + 7) / 8; - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - if (len != enc_len) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - yxi = BN_CTX_get(ctx); - if (yxi == NULL) goto err; - - if (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - if (!EC_POINT_set_compressed_coordinates_GF2m(group, point, x, y_bit, ctx)) goto err; - } - else - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (!group->meth->field_div(group, yxi, y, x, ctx)) goto err; - if (y_bit != BN_is_odd(yxi)) - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - } - - if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; - } - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { - ECerr(EC_F_EC_GF2M_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); - goto err; - } - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - /* Computes a + b and stores the result in r. r could be a or b, a could be b. * Uses algorithm A.10.2 of IEEE P1363. */ @@ -974,3 +715,5 @@ int ec_GF2m_simple_field_div(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a, { return BN_GF2m_mod_div(r, a, b, &group->field, ctx); } + +#endif diff --git a/crypto/ec/ec2_smpt.c b/crypto/ec/ec2_smpt.c deleted file mode 100644 index 72a8d570517f3..0000000000000 --- a/crypto/ec/ec2_smpt.c +++ /dev/null @@ -1,141 +0,0 @@ -/* crypto/ec/ec2_smpt.c */ -/* This code was originally written by Douglas Stebila - * <dstebila@student.math.uwaterloo.ca> for the OpenSSL project. - */ -/* ==================================================================== - * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in - * the documentation and/or other materials provided with the - * distribution. - * - * 3. All advertising materials mentioning features or use of this - * software must display the following acknowledgment: - * "This product includes software developed by the OpenSSL Project - * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" - * - * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to - * endorse or promote products derived from this software without - * prior written permission. For written permission, please contact - * openssl-core@openssl.org. - * - * 5. Products derived from this software may not be called "OpenSSL" - * nor may "OpenSSL" appear in their names without prior written - * permission of the OpenSSL Project. - * - * 6. Redistributions of any form whatsoever must retain the following - * acknowledgment: - * "This product includes software developed by the OpenSSL Project - * for use in the OpenSSL Toolkit (http://www.openssl.org/)" - * - * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY - * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR - * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR - * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, - * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT - * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; - * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, - * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) - * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED - * OF THE POSSIBILITY OF SUCH DAMAGE. - * ==================================================================== - * - * This product includes cryptographic software written by Eric Young - * (eay@cryptsoft.com). This product includes software written by Tim - * Hudson (tjh@cryptsoft.com). - * - */ - - -/* Calaculates and sets the affine coordinates of an EC_POINT from the given - * compressed coordinates. Uses algorithm 2.3.4 of SEC 1. - * Note that the simple implementation only uses affine coordinates. - * - * This algorithm is patented by Certicom Corp. under US Patent 6,141,420 - * (for licensing information, contact licensing@certicom.com). - * This function is disabled by default and can be enabled by defining the - * preprocessor macro OPENSSL_EC_BIN_PT_COMP at Configure-time. - */ -int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x_, int y_bit, BN_CTX *ctx) - { -#ifndef OPENSSL_EC_BIN_PT_COMP - ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_DISABLED); - return 0; -#else - BN_CTX *new_ctx = NULL; - BIGNUM *tmp, *x, *y, *z; - int ret = 0, z0; - - /* clear error queue */ - ERR_clear_error(); - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - y_bit = (y_bit != 0) ? 1 : 0; - - BN_CTX_start(ctx); - tmp = BN_CTX_get(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - z = BN_CTX_get(ctx); - if (z == NULL) goto err; - - if (!BN_GF2m_mod_arr(x, x_, group->poly)) goto err; - if (BN_is_zero(x)) - { - if (!BN_GF2m_mod_sqrt_arr(y, &group->b, group->poly, ctx)) goto err; - } - else - { - if (!group->meth->field_sqr(group, tmp, x, ctx)) goto err; - if (!group->meth->field_div(group, tmp, &group->b, tmp, ctx)) goto err; - if (!BN_GF2m_add(tmp, &group->a, tmp)) goto err; - if (!BN_GF2m_add(tmp, x, tmp)) goto err; - if (!BN_GF2m_mod_solve_quad_arr(z, tmp, group->poly, ctx)) - { - unsigned long err = ERR_peek_last_error(); - - if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NO_SOLUTION) - { - ERR_clear_error(); - ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - } - else - ECerr(EC_F_EC_GF2M_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); - goto err; - } - z0 = (BN_is_odd(z)) ? 1 : 0; - if (!group->meth->field_mul(group, y, x, z, ctx)) goto err; - if (z0 != y_bit) - { - if (!BN_GF2m_add(y, y, x)) goto err; - } - } - - if (!EC_POINT_set_affine_coordinates_GF2m(group, point, x, y, ctx)) goto err; - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; -#endif - } diff --git a/crypto/ec/ec_ameth.c b/crypto/ec/ec_ameth.c new file mode 100644 index 0000000000000..83909c185359a --- /dev/null +++ b/crypto/ec/ec_ameth.c @@ -0,0 +1,660 @@ +/* Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL + * project 2006. + */ +/* ==================================================================== + * Copyright (c) 2006 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * licensing@OpenSSL.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ + +#include <stdio.h> +#include "cryptlib.h" +#include <openssl/x509.h> +#include <openssl/ec.h> +#include <openssl/bn.h> +#ifndef OPENSSL_NO_CMS +#include <openssl/cms.h> +#endif +#include "asn1_locl.h" + +static int eckey_param2type(int *pptype, void **ppval, EC_KEY *ec_key) + { + const EC_GROUP *group; + int nid; + if (ec_key == NULL || (group = EC_KEY_get0_group(ec_key)) == NULL) + { + ECerr(EC_F_ECKEY_PARAM2TYPE, EC_R_MISSING_PARAMETERS); + return 0; + } + if (EC_GROUP_get_asn1_flag(group) + && (nid = EC_GROUP_get_curve_name(group))) + /* we have a 'named curve' => just set the OID */ + { + *ppval = OBJ_nid2obj(nid); + *pptype = V_ASN1_OBJECT; + } + else /* explicit parameters */ + { + ASN1_STRING *pstr = NULL; + pstr = ASN1_STRING_new(); + if (!pstr) + return 0; + pstr->length = i2d_ECParameters(ec_key, &pstr->data); + if (pstr->length < 0) + { + ASN1_STRING_free(pstr); + ECerr(EC_F_ECKEY_PARAM2TYPE, ERR_R_EC_LIB); + return 0; + } + *ppval = pstr; + *pptype = V_ASN1_SEQUENCE; + } + return 1; + } + +static int eckey_pub_encode(X509_PUBKEY *pk, const EVP_PKEY *pkey) + { + EC_KEY *ec_key = pkey->pkey.ec; + void *pval = NULL; + int ptype; + unsigned char *penc = NULL, *p; + int penclen; + + if (!eckey_param2type(&ptype, &pval, ec_key)) + { + ECerr(EC_F_ECKEY_PUB_ENCODE, ERR_R_EC_LIB); + return 0; + } + penclen = i2o_ECPublicKey(ec_key, NULL); + if (penclen <= 0) + goto err; + penc = OPENSSL_malloc(penclen); + if (!penc) + goto err; + p = penc; + penclen = i2o_ECPublicKey(ec_key, &p); + if (penclen <= 0) + goto err; + if (X509_PUBKEY_set0_param(pk, OBJ_nid2obj(EVP_PKEY_EC), + ptype, pval, penc, penclen)) + return 1; + err: + if (ptype == V_ASN1_OBJECT) + ASN1_OBJECT_free(pval); + else + ASN1_STRING_free(pval); + if (penc) + OPENSSL_free(penc); + return 0; + } + +static EC_KEY *eckey_type2param(int ptype, void *pval) + { + EC_KEY *eckey = NULL; + if (ptype == V_ASN1_SEQUENCE) + { + ASN1_STRING *pstr = pval; + const unsigned char *pm = NULL; + int pmlen; + pm = pstr->data; + pmlen = pstr->length; + if (!(eckey = d2i_ECParameters(NULL, &pm, pmlen))) + { + ECerr(EC_F_ECKEY_TYPE2PARAM, EC_R_DECODE_ERROR); + goto ecerr; + } + } + else if (ptype == V_ASN1_OBJECT) + { + ASN1_OBJECT *poid = pval; + EC_GROUP *group; + + /* type == V_ASN1_OBJECT => the parameters are given + * by an asn1 OID + */ + if ((eckey = EC_KEY_new()) == NULL) + { + ECerr(EC_F_ECKEY_TYPE2PARAM, ERR_R_MALLOC_FAILURE); + goto ecerr; + } + group = EC_GROUP_new_by_curve_name(OBJ_obj2nid(poid)); + if (group == NULL) + goto ecerr; + EC_GROUP_set_asn1_flag(group, OPENSSL_EC_NAMED_CURVE); + if (EC_KEY_set_group(eckey, group) == 0) + goto ecerr; + EC_GROUP_free(group); + } + else + { + ECerr(EC_F_ECKEY_TYPE2PARAM, EC_R_DECODE_ERROR); + goto ecerr; + } + + return eckey; + + ecerr: + if (eckey) + EC_KEY_free(eckey); + return NULL; + } + +static int eckey_pub_decode(EVP_PKEY *pkey, X509_PUBKEY *pubkey) + { + const unsigned char *p = NULL; + void *pval; + int ptype, pklen; + EC_KEY *eckey = NULL; + X509_ALGOR *palg; + + if (!X509_PUBKEY_get0_param(NULL, &p, &pklen, &palg, pubkey)) + return 0; + X509_ALGOR_get0(NULL, &ptype, &pval, palg); + + eckey = eckey_type2param(ptype, pval); + + if (!eckey) + { + ECerr(EC_F_ECKEY_PUB_DECODE, ERR_R_EC_LIB); + return 0; + } + + /* We have parameters now set public key */ + if (!o2i_ECPublicKey(&eckey, &p, pklen)) + { + ECerr(EC_F_ECKEY_PUB_DECODE, EC_R_DECODE_ERROR); + goto ecerr; + } + + EVP_PKEY_assign_EC_KEY(pkey, eckey); + return 1; + + ecerr: + if (eckey) + EC_KEY_free(eckey); + return 0; + } + +static int eckey_pub_cmp(const EVP_PKEY *a, const EVP_PKEY *b) + { + int r; + const EC_GROUP *group = EC_KEY_get0_group(b->pkey.ec); + const EC_POINT *pa = EC_KEY_get0_public_key(a->pkey.ec), + *pb = EC_KEY_get0_public_key(b->pkey.ec); + r = EC_POINT_cmp(group, pa, pb, NULL); + if (r == 0) + return 1; + if (r == 1) + return 0; + return -2; + } + +static int eckey_priv_decode(EVP_PKEY *pkey, PKCS8_PRIV_KEY_INFO *p8) + { + const unsigned char *p = NULL; + void *pval; + int ptype, pklen; + EC_KEY *eckey = NULL; + X509_ALGOR *palg; + + if (!PKCS8_pkey_get0(NULL, &p, &pklen, &palg, p8)) + return 0; + X509_ALGOR_get0(NULL, &ptype, &pval, palg); + + eckey = eckey_type2param(ptype, pval); + + if (!eckey) + goto ecliberr; + + /* We have parameters now set private key */ + if (!d2i_ECPrivateKey(&eckey, &p, pklen)) + { + ECerr(EC_F_ECKEY_PRIV_DECODE, EC_R_DECODE_ERROR); + goto ecerr; + } + + /* calculate public key (if necessary) */ + if (EC_KEY_get0_public_key(eckey) == NULL) + { + const BIGNUM *priv_key; + const EC_GROUP *group; + EC_POINT *pub_key; + /* the public key was not included in the SEC1 private + * key => calculate the public key */ + group = EC_KEY_get0_group(eckey); + pub_key = EC_POINT_new(group); + if (pub_key == NULL) + { + ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); + goto ecliberr; + } + if (!EC_POINT_copy(pub_key, EC_GROUP_get0_generator(group))) + { + EC_POINT_free(pub_key); + ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); + goto ecliberr; + } + priv_key = EC_KEY_get0_private_key(eckey); + if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, NULL)) + { + EC_POINT_free(pub_key); + ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); + goto ecliberr; + } + if (EC_KEY_set_public_key(eckey, pub_key) == 0) + { + EC_POINT_free(pub_key); + ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); + goto ecliberr; + } + EC_POINT_free(pub_key); + } + + EVP_PKEY_assign_EC_KEY(pkey, eckey); + return 1; + + ecliberr: + ECerr(EC_F_ECKEY_PRIV_DECODE, ERR_R_EC_LIB); + ecerr: + if (eckey) + EC_KEY_free(eckey); + return 0; + } + +static int eckey_priv_encode(PKCS8_PRIV_KEY_INFO *p8, const EVP_PKEY *pkey) +{ + EC_KEY *ec_key; + unsigned char *ep, *p; + int eplen, ptype; + void *pval; + unsigned int tmp_flags, old_flags; + + ec_key = pkey->pkey.ec; + + if (!eckey_param2type(&ptype, &pval, ec_key)) + { + ECerr(EC_F_ECKEY_PRIV_ENCODE, EC_R_DECODE_ERROR); + return 0; + } + + /* set the private key */ + + /* do not include the parameters in the SEC1 private key + * see PKCS#11 12.11 */ + old_flags = EC_KEY_get_enc_flags(ec_key); + tmp_flags = old_flags | EC_PKEY_NO_PARAMETERS; + EC_KEY_set_enc_flags(ec_key, tmp_flags); + eplen = i2d_ECPrivateKey(ec_key, NULL); + if (!eplen) + { + EC_KEY_set_enc_flags(ec_key, old_flags); + ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_EC_LIB); + return 0; + } + ep = (unsigned char *) OPENSSL_malloc(eplen); + if (!ep) + { + EC_KEY_set_enc_flags(ec_key, old_flags); + ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_MALLOC_FAILURE); + return 0; + } + p = ep; + if (!i2d_ECPrivateKey(ec_key, &p)) + { + EC_KEY_set_enc_flags(ec_key, old_flags); + OPENSSL_free(ep); + ECerr(EC_F_ECKEY_PRIV_ENCODE, ERR_R_EC_LIB); + } + /* restore old encoding flags */ + EC_KEY_set_enc_flags(ec_key, old_flags); + + if (!PKCS8_pkey_set0(p8, OBJ_nid2obj(NID_X9_62_id_ecPublicKey), 0, + ptype, pval, ep, eplen)) + return 0; + + return 1; +} + +static int int_ec_size(const EVP_PKEY *pkey) + { + return ECDSA_size(pkey->pkey.ec); + } + +static int ec_bits(const EVP_PKEY *pkey) + { + BIGNUM *order = BN_new(); + const EC_GROUP *group; + int ret; + + if (!order) + { + ERR_clear_error(); + return 0; + } + group = EC_KEY_get0_group(pkey->pkey.ec); + if (!EC_GROUP_get_order(group, order, NULL)) + { + ERR_clear_error(); + return 0; + } + + ret = BN_num_bits(order); + BN_free(order); + return ret; + } + +static int ec_missing_parameters(const EVP_PKEY *pkey) + { + if (EC_KEY_get0_group(pkey->pkey.ec) == NULL) + return 1; + return 0; + } + +static int ec_copy_parameters(EVP_PKEY *to, const EVP_PKEY *from) + { + EC_GROUP *group = EC_GROUP_dup(EC_KEY_get0_group(from->pkey.ec)); + if (group == NULL) + return 0; + if (EC_KEY_set_group(to->pkey.ec, group) == 0) + return 0; + EC_GROUP_free(group); + return 1; + } + +static int ec_cmp_parameters(const EVP_PKEY *a, const EVP_PKEY *b) + { + const EC_GROUP *group_a = EC_KEY_get0_group(a->pkey.ec), + *group_b = EC_KEY_get0_group(b->pkey.ec); + if (EC_GROUP_cmp(group_a, group_b, NULL)) + return 0; + else + return 1; + } + +static void int_ec_free(EVP_PKEY *pkey) + { + EC_KEY_free(pkey->pkey.ec); + } + +static int do_EC_KEY_print(BIO *bp, const EC_KEY *x, int off, int ktype) + { + unsigned char *buffer=NULL; + const char *ecstr; + size_t buf_len=0, i; + int ret=0, reason=ERR_R_BIO_LIB; + BIGNUM *pub_key=NULL, *order=NULL; + BN_CTX *ctx=NULL; + const EC_GROUP *group; + const EC_POINT *public_key; + const BIGNUM *priv_key; + + if (x == NULL || (group = EC_KEY_get0_group(x)) == NULL) + { + reason = ERR_R_PASSED_NULL_PARAMETER; + goto err; + } + + ctx = BN_CTX_new(); + if (ctx == NULL) + { + reason = ERR_R_MALLOC_FAILURE; + goto err; + } + + if (ktype > 0) + { + public_key = EC_KEY_get0_public_key(x); + if ((pub_key = EC_POINT_point2bn(group, public_key, + EC_KEY_get_conv_form(x), NULL, ctx)) == NULL) + { + reason = ERR_R_EC_LIB; + goto err; + } + if (pub_key) + buf_len = (size_t)BN_num_bytes(pub_key); + } + + if (ktype == 2) + { + priv_key = EC_KEY_get0_private_key(x); + if (priv_key && (i = (size_t)BN_num_bytes(priv_key)) > buf_len) + buf_len = i; + } + else + priv_key = NULL; + + if (ktype > 0) + { + buf_len += 10; + if ((buffer = OPENSSL_malloc(buf_len)) == NULL) + { + reason = ERR_R_MALLOC_FAILURE; + goto err; + } + } + if (ktype == 2) + ecstr = "Private-Key"; + else if (ktype == 1) + ecstr = "Public-Key"; + else + ecstr = "ECDSA-Parameters"; + + if (!BIO_indent(bp, off, 128)) + goto err; + if ((order = BN_new()) == NULL) + goto err; + if (!EC_GROUP_get_order(group, order, NULL)) + goto err; + if (BIO_printf(bp, "%s: (%d bit)\n", ecstr, + BN_num_bits(order)) <= 0) goto err; + + if ((priv_key != NULL) && !ASN1_bn_print(bp, "priv:", priv_key, + buffer, off)) + goto err; + if ((pub_key != NULL) && !ASN1_bn_print(bp, "pub: ", pub_key, + buffer, off)) + goto err; + if (!ECPKParameters_print(bp, group, off)) + goto err; + ret=1; +err: + if (!ret) + ECerr(EC_F_DO_EC_KEY_PRINT, reason); + if (pub_key) + BN_free(pub_key); + if (order) + BN_free(order); + if (ctx) + BN_CTX_free(ctx); + if (buffer != NULL) + OPENSSL_free(buffer); + return(ret); + } + +static int eckey_param_decode(EVP_PKEY *pkey, + const unsigned char **pder, int derlen) + { + EC_KEY *eckey; + if (!(eckey = d2i_ECParameters(NULL, pder, derlen))) + { + ECerr(EC_F_ECKEY_PARAM_DECODE, ERR_R_EC_LIB); + return 0; + } + EVP_PKEY_assign_EC_KEY(pkey, eckey); + return 1; + } + +static int eckey_param_encode(const EVP_PKEY *pkey, unsigned char **pder) + { + return i2d_ECParameters(pkey->pkey.ec, pder); + } + +static int eckey_param_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx) + { + return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 0); + } + +static int eckey_pub_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx) + { + return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 1); + } + + +static int eckey_priv_print(BIO *bp, const EVP_PKEY *pkey, int indent, + ASN1_PCTX *ctx) + { + return do_EC_KEY_print(bp, pkey->pkey.ec, indent, 2); + } + +static int old_ec_priv_decode(EVP_PKEY *pkey, + const unsigned char **pder, int derlen) + { + EC_KEY *ec; + if (!(ec = d2i_ECPrivateKey (NULL, pder, derlen))) + { + ECerr(EC_F_OLD_EC_PRIV_DECODE, EC_R_DECODE_ERROR); + return 0; + } + EVP_PKEY_assign_EC_KEY(pkey, ec); + return 1; + } + +static int old_ec_priv_encode(const EVP_PKEY *pkey, unsigned char **pder) + { + return i2d_ECPrivateKey(pkey->pkey.ec, pder); + } + +static int ec_pkey_ctrl(EVP_PKEY *pkey, int op, long arg1, void *arg2) + { + switch (op) + { + case ASN1_PKEY_CTRL_PKCS7_SIGN: + if (arg1 == 0) + { + int snid, hnid; + X509_ALGOR *alg1, *alg2; + PKCS7_SIGNER_INFO_get0_algs(arg2, NULL, &alg1, &alg2); + if (alg1 == NULL || alg1->algorithm == NULL) + return -1; + hnid = OBJ_obj2nid(alg1->algorithm); + if (hnid == NID_undef) + return -1; + if (!OBJ_find_sigid_by_algs(&snid, hnid, EVP_PKEY_id(pkey))) + return -1; + X509_ALGOR_set0(alg2, OBJ_nid2obj(snid), V_ASN1_UNDEF, 0); + } + return 1; +#ifndef OPENSSL_NO_CMS + case ASN1_PKEY_CTRL_CMS_SIGN: + if (arg1 == 0) + { + int snid, hnid; + X509_ALGOR *alg1, *alg2; + CMS_SignerInfo_get0_algs(arg2, NULL, NULL, + &alg1, &alg2); + if (alg1 == NULL || alg1->algorithm == NULL) + return -1; + hnid = OBJ_obj2nid(alg1->algorithm); + if (hnid == NID_undef) + return -1; + if (!OBJ_find_sigid_by_algs(&snid, hnid, EVP_PKEY_id(pkey))) + return -1; + X509_ALGOR_set0(alg2, OBJ_nid2obj(snid), V_ASN1_UNDEF, 0); + } + return 1; +#endif + + case ASN1_PKEY_CTRL_DEFAULT_MD_NID: + *(int *)arg2 = NID_sha1; + return 2; + + default: + return -2; + + } + + } + +const EVP_PKEY_ASN1_METHOD eckey_asn1_meth = + { + EVP_PKEY_EC, + EVP_PKEY_EC, + 0, + "EC", + "OpenSSL EC algorithm", + + eckey_pub_decode, + eckey_pub_encode, + eckey_pub_cmp, + eckey_pub_print, + + eckey_priv_decode, + eckey_priv_encode, + eckey_priv_print, + + int_ec_size, + ec_bits, + + eckey_param_decode, + eckey_param_encode, + ec_missing_parameters, + ec_copy_parameters, + ec_cmp_parameters, + eckey_param_print, + 0, + + int_ec_free, + ec_pkey_ctrl, + old_ec_priv_decode, + old_ec_priv_encode + }; diff --git a/crypto/ec/ec_asn1.c b/crypto/ec/ec_asn1.c index ae555398594b8..175eec53428ba 100644 --- a/crypto/ec/ec_asn1.c +++ b/crypto/ec/ec_asn1.c @@ -83,7 +83,7 @@ int EC_GROUP_get_basis_type(const EC_GROUP *group) /* everything else is currently not supported */ return 0; } - +#ifndef OPENSSL_NO_EC2M int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k) { if (group == NULL) @@ -101,7 +101,6 @@ int EC_GROUP_get_trinomial_basis(const EC_GROUP *group, unsigned int *k) return 1; } - int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, unsigned int *k2, unsigned int *k3) { @@ -124,7 +123,7 @@ int EC_GROUP_get_pentanomial_basis(const EC_GROUP *group, unsigned int *k1, return 1; } - +#endif /* some structures needed for the asn1 encoding */ @@ -340,6 +339,12 @@ static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) } } else /* nid == NID_X9_62_characteristic_two_field */ +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_ASN1_GROUP2FIELDID, EC_R_GF2M_NOT_SUPPORTED); + goto err; + } +#else { int field_type; X9_62_CHARACTERISTIC_TWO *char_two; @@ -419,6 +424,7 @@ static int ec_asn1_group2fieldid(const EC_GROUP *group, X9_62_FIELDID *field) } } } +#endif ok = 1; @@ -456,6 +462,7 @@ static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve) goto err; } } +#ifndef OPENSSL_NO_EC2M else /* nid == NID_X9_62_characteristic_two_field */ { if (!EC_GROUP_get_curve_GF2m(group, NULL, tmp_1, tmp_2, NULL)) @@ -464,7 +471,7 @@ static int ec_asn1_group2curve(const EC_GROUP *group, X9_62_CURVE *curve) goto err; } } - +#endif len_1 = (size_t)BN_num_bytes(tmp_1); len_2 = (size_t)BN_num_bytes(tmp_2); @@ -775,8 +782,13 @@ static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *params) /* get the field parameters */ tmp = OBJ_obj2nid(params->fieldID->fieldType); - if (tmp == NID_X9_62_characteristic_two_field) +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_ASN1_PARAMETERS2GROUP, EC_R_GF2M_NOT_SUPPORTED); + goto err; + } +#else { X9_62_CHARACTERISTIC_TWO *char_two; @@ -862,6 +874,7 @@ static EC_GROUP *ec_asn1_parameters2group(const ECPARAMETERS *params) /* create the EC_GROUP structure */ ret = EC_GROUP_new_curve_GF2m(p, a, b, NULL); } +#endif else if (tmp == NID_X9_62_prime_field) { /* we have a curve over a prime field */ @@ -1065,6 +1078,7 @@ EC_GROUP *d2i_ECPKParameters(EC_GROUP **a, const unsigned char **in, long len) if ((group = ec_asn1_pkparameters2group(params)) == NULL) { ECerr(EC_F_D2I_ECPKPARAMETERS, EC_R_PKPARAMETERS2GROUP_FAILURE); + ECPKPARAMETERS_free(params); return NULL; } diff --git a/crypto/ec/ec_curve.c b/crypto/ec/ec_curve.c index beac20969b753..c72fb2697ca28 100644 --- a/crypto/ec/ec_curve.c +++ b/crypto/ec/ec_curve.c @@ -3,7 +3,7 @@ * Written by Nils Larsch for the OpenSSL project. */ /* ==================================================================== - * Copyright (c) 1998-2004 The OpenSSL Project. All rights reserved. + * Copyright (c) 1998-2010 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -72,927 +72,1694 @@ #include "ec_lcl.h" #include <openssl/err.h> #include <openssl/obj_mac.h> +#include <openssl/opensslconf.h> -typedef struct ec_curve_data_st { - int field_type; /* either NID_X9_62_prime_field or +typedef struct { + int field_type, /* either NID_X9_62_prime_field or * NID_X9_62_characteristic_two_field */ - const char *p; /* either a prime number or a polynomial */ - const char *a; - const char *b; - const char *x; /* the x coordinate of the generator */ - const char *y; /* the y coordinate of the generator */ - const char *order; /* the order of the group generated by the - * generator */ - const BN_ULONG cofactor;/* the cofactor */ - const unsigned char *seed;/* the seed (optional) */ - size_t seed_len; - const char *comment; /* a short description of the curve */ + seed_len, + param_len; + unsigned int cofactor; /* promoted to BN_ULONG */ } EC_CURVE_DATA; /* the nist prime curves */ -static const unsigned char _EC_NIST_PRIME_192_SEED[] = { - 0x30,0x45,0xAE,0x6F,0xC8,0x42,0x2F,0x64,0xED,0x57, - 0x95,0x28,0xD3,0x81,0x20,0xEA,0xE1,0x21,0x96,0xD5}; -static const EC_CURVE_DATA _EC_NIST_PRIME_192 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC", - "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1", - "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012", - "07192b95ffc8da78631011ed6b24cdd573f977a11e794811", - "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",1, - _EC_NIST_PRIME_192_SEED, 20, - "NIST/X9.62/SECG curve over a 192 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } + _EC_NIST_PRIME_192 = { + { NID_X9_62_prime_field,20,24,1 }, + { 0x30,0x45,0xAE,0x6F,0xC8,0x42,0x2F,0x64,0xED,0x57, /* seed */ + 0x95,0x28,0xD3,0x81,0x20,0xEA,0xE1,0x21,0x96,0xD5, + + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFC, + 0x64,0x21,0x05,0x19,0xE5,0x9C,0x80,0xE7,0x0F,0xA7, /* b */ + 0xE9,0xAB,0x72,0x24,0x30,0x49,0xFE,0xB8,0xDE,0xEC, + 0xC1,0x46,0xB9,0xB1, + 0x18,0x8D,0xA8,0x0E,0xB0,0x30,0x90,0xF6,0x7C,0xBF, /* x */ + 0x20,0xEB,0x43,0xA1,0x88,0x00,0xF4,0xFF,0x0A,0xFD, + 0x82,0xFF,0x10,0x12, + 0x07,0x19,0x2b,0x95,0xff,0xc8,0xda,0x78,0x63,0x10, /* y */ + 0x11,0xed,0x6b,0x24,0xcd,0xd5,0x73,0xf9,0x77,0xa1, + 0x1e,0x79,0x48,0x11, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0x99,0xDE,0xF8,0x36,0x14,0x6B,0xC9,0xB1, + 0xB4,0xD2,0x28,0x31 } }; -static const unsigned char _EC_NIST_PRIME_224_SEED[] = { - 0xBD,0x71,0x34,0x47,0x99,0xD5,0xC7,0xFC,0xDC,0x45, - 0xB5,0x9F,0xA3,0xB9,0xAB,0x8F,0x6A,0x94,0x8B,0xC5}; -static const EC_CURVE_DATA _EC_NIST_PRIME_224 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", - "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", - "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", - "bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",1, - _EC_NIST_PRIME_224_SEED, 20, - "NIST/SECG curve over a 224 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+28*6]; } + _EC_NIST_PRIME_224 = { + { NID_X9_62_prime_field,20,28,1 }, + { 0xBD,0x71,0x34,0x47,0x99,0xD5,0xC7,0xFC,0xDC,0x45, /* seed */ + 0xB5,0x9F,0xA3,0xB9,0xAB,0x8F,0x6A,0x94,0x8B,0xC5, + + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ + 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, + 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4, + 0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ + 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, + 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21, + 0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ + 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, + 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0x16,0xA2,0xE0,0xB8,0xF0,0x3E, + 0x13,0xDD,0x29,0x45,0x5C,0x5C,0x2A,0x3D } }; -static const unsigned char _EC_NIST_PRIME_384_SEED[] = { - 0xA3,0x35,0x92,0x6A,0xA3,0x19,0xA2,0x7A,0x1D,0x00, - 0x89,0x6A,0x67,0x73,0xA4,0x82,0x7A,0xCD,0xAC,0x73}; -static const EC_CURVE_DATA _EC_NIST_PRIME_384 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFF" - "FFF0000000000000000FFFFFFFF", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFF" - "FFF0000000000000000FFFFFFFC", - "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC6563" - "98D8A2ED19D2A85C8EDD3EC2AEF", - "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F" - "25DBF55296C3A545E3872760AB7", - "3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b" - "1ce1d7e819d7a431d7c90ea0e5f", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0" - "DB248B0A77AECEC196ACCC52973",1, - _EC_NIST_PRIME_384_SEED, 20, - "NIST/SECG curve over a 384 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+48*6]; } + _EC_NIST_PRIME_384 = { + { NID_X9_62_prime_field,20,48,1 }, + { 0xA3,0x35,0x92,0x6A,0xA3,0x19,0xA2,0x7A,0x1D,0x00, /* seed */ + 0x89,0x6A,0x67,0x73,0xA4,0x82,0x7A,0xCD,0xAC,0x73, + + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFE,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0xFF,0xFF,0xFF,0xFC, + 0xB3,0x31,0x2F,0xA7,0xE2,0x3E,0xE7,0xE4,0x98,0x8E, /* b */ + 0x05,0x6B,0xE3,0xF8,0x2D,0x19,0x18,0x1D,0x9C,0x6E, + 0xFE,0x81,0x41,0x12,0x03,0x14,0x08,0x8F,0x50,0x13, + 0x87,0x5A,0xC6,0x56,0x39,0x8D,0x8A,0x2E,0xD1,0x9D, + 0x2A,0x85,0xC8,0xED,0xD3,0xEC,0x2A,0xEF, + 0xAA,0x87,0xCA,0x22,0xBE,0x8B,0x05,0x37,0x8E,0xB1, /* x */ + 0xC7,0x1E,0xF3,0x20,0xAD,0x74,0x6E,0x1D,0x3B,0x62, + 0x8B,0xA7,0x9B,0x98,0x59,0xF7,0x41,0xE0,0x82,0x54, + 0x2A,0x38,0x55,0x02,0xF2,0x5D,0xBF,0x55,0x29,0x6C, + 0x3A,0x54,0x5E,0x38,0x72,0x76,0x0A,0xB7, + 0x36,0x17,0xde,0x4a,0x96,0x26,0x2c,0x6f,0x5d,0x9e, /* y */ + 0x98,0xbf,0x92,0x92,0xdc,0x29,0xf8,0xf4,0x1d,0xbd, + 0x28,0x9a,0x14,0x7c,0xe9,0xda,0x31,0x13,0xb5,0xf0, + 0xb8,0xc0,0x0a,0x60,0xb1,0xce,0x1d,0x7e,0x81,0x9d, + 0x7a,0x43,0x1d,0x7c,0x90,0xea,0x0e,0x5f, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xC7,0x63,0x4D,0x81,0xF4,0x37, + 0x2D,0xDF,0x58,0x1A,0x0D,0xB2,0x48,0xB0,0xA7,0x7A, + 0xEC,0xEC,0x19,0x6A,0xCC,0xC5,0x29,0x73 } }; -static const unsigned char _EC_NIST_PRIME_521_SEED[] = { - 0xD0,0x9E,0x88,0x00,0x29,0x1C,0xB8,0x53,0x96,0xCC, - 0x67,0x17,0x39,0x32,0x84,0xAA,0xA0,0xDA,0x64,0xBA}; -static const EC_CURVE_DATA _EC_NIST_PRIME_521 = { - NID_X9_62_prime_field, - "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", - "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC", - "051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156" - "193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00", - "C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14" - "B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66", - "011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c9" - "7ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", - "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51" - "868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",1, - _EC_NIST_PRIME_521_SEED, 20, - "NIST/SECG curve over a 521 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+66*6]; } + _EC_NIST_PRIME_521 = { + { NID_X9_62_prime_field,20,66,1 }, + { 0xD0,0x9E,0x88,0x00,0x29,0x1C,0xB8,0x53,0x96,0xCC, /* seed */ + 0x67,0x17,0x39,0x32,0x84,0xAA,0xA0,0xDA,0x64,0xBA, + + 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFC, + 0x00,0x51,0x95,0x3E,0xB9,0x61,0x8E,0x1C,0x9A,0x1F, /* b */ + 0x92,0x9A,0x21,0xA0,0xB6,0x85,0x40,0xEE,0xA2,0xDA, + 0x72,0x5B,0x99,0xB3,0x15,0xF3,0xB8,0xB4,0x89,0x91, + 0x8E,0xF1,0x09,0xE1,0x56,0x19,0x39,0x51,0xEC,0x7E, + 0x93,0x7B,0x16,0x52,0xC0,0xBD,0x3B,0xB1,0xBF,0x07, + 0x35,0x73,0xDF,0x88,0x3D,0x2C,0x34,0xF1,0xEF,0x45, + 0x1F,0xD4,0x6B,0x50,0x3F,0x00, + 0x00,0xC6,0x85,0x8E,0x06,0xB7,0x04,0x04,0xE9,0xCD, /* x */ + 0x9E,0x3E,0xCB,0x66,0x23,0x95,0xB4,0x42,0x9C,0x64, + 0x81,0x39,0x05,0x3F,0xB5,0x21,0xF8,0x28,0xAF,0x60, + 0x6B,0x4D,0x3D,0xBA,0xA1,0x4B,0x5E,0x77,0xEF,0xE7, + 0x59,0x28,0xFE,0x1D,0xC1,0x27,0xA2,0xFF,0xA8,0xDE, + 0x33,0x48,0xB3,0xC1,0x85,0x6A,0x42,0x9B,0xF9,0x7E, + 0x7E,0x31,0xC2,0xE5,0xBD,0x66, + 0x01,0x18,0x39,0x29,0x6a,0x78,0x9a,0x3b,0xc0,0x04, /* y */ + 0x5c,0x8a,0x5f,0xb4,0x2c,0x7d,0x1b,0xd9,0x98,0xf5, + 0x44,0x49,0x57,0x9b,0x44,0x68,0x17,0xaf,0xbd,0x17, + 0x27,0x3e,0x66,0x2c,0x97,0xee,0x72,0x99,0x5e,0xf4, + 0x26,0x40,0xc5,0x50,0xb9,0x01,0x3f,0xad,0x07,0x61, + 0x35,0x3c,0x70,0x86,0xa2,0x72,0xc2,0x40,0x88,0xbe, + 0x94,0x76,0x9f,0xd1,0x66,0x50, + 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFA,0x51,0x86,0x87,0x83,0xBF,0x2F, + 0x96,0x6B,0x7F,0xCC,0x01,0x48,0xF7,0x09,0xA5,0xD0, + 0x3B,0xB5,0xC9,0xB8,0x89,0x9C,0x47,0xAE,0xBB,0x6F, + 0xB7,0x1E,0x91,0x38,0x64,0x09 } }; + /* the x9.62 prime curves (minus the nist prime curves) */ -static const unsigned char _EC_X9_62_PRIME_192V2_SEED[] = { - 0x31,0xA9,0x2E,0xE2,0x02,0x9F,0xD1,0x0D,0x90,0x1B, - 0x11,0x3E,0x99,0x07,0x10,0xF0,0xD2,0x1A,0xC6,0xB6}; -static const EC_CURVE_DATA _EC_X9_62_PRIME_192V2 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC", - "CC22D6DFB95C6B25E49C0D6364A4E5980C393AA21668D953", - "EEA2BAE7E1497842F2DE7769CFE9C989C072AD696F48034A", - "6574d11d69b6ec7a672bb82a083df2f2b0847de970b2de15", - "FFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31",1, - _EC_X9_62_PRIME_192V2_SEED, 20, - "X9.62 curve over a 192 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } + _EC_X9_62_PRIME_192V2 = { + { NID_X9_62_prime_field,20,24,1 }, + { 0x31,0xA9,0x2E,0xE2,0x02,0x9F,0xD1,0x0D,0x90,0x1B, /* seed */ + 0x11,0x3E,0x99,0x07,0x10,0xF0,0xD2,0x1A,0xC6,0xB6, + + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFC, + 0xCC,0x22,0xD6,0xDF,0xB9,0x5C,0x6B,0x25,0xE4,0x9C, /* b */ + 0x0D,0x63,0x64,0xA4,0xE5,0x98,0x0C,0x39,0x3A,0xA2, + 0x16,0x68,0xD9,0x53, + 0xEE,0xA2,0xBA,0xE7,0xE1,0x49,0x78,0x42,0xF2,0xDE, /* x */ + 0x77,0x69,0xCF,0xE9,0xC9,0x89,0xC0,0x72,0xAD,0x69, + 0x6F,0x48,0x03,0x4A, + 0x65,0x74,0xd1,0x1d,0x69,0xb6,0xec,0x7a,0x67,0x2b, /* y */ + 0xb8,0x2a,0x08,0x3d,0xf2,0xf2,0xb0,0x84,0x7d,0xe9, + 0x70,0xb2,0xde,0x15, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFE,0x5F,0xB1,0xA7,0x24,0xDC,0x80,0x41,0x86, + 0x48,0xD8,0xDD,0x31 } }; -static const unsigned char _EC_X9_62_PRIME_192V3_SEED[] = { - 0xC4,0x69,0x68,0x44,0x35,0xDE,0xB3,0x78,0xC4,0xB6, - 0x5C,0xA9,0x59,0x1E,0x2A,0x57,0x63,0x05,0x9A,0x2E}; -static const EC_CURVE_DATA _EC_X9_62_PRIME_192V3 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC", - "22123DC2395A05CAA7423DAECCC94760A7D462256BD56916", - "7D29778100C65A1DA1783716588DCE2B8B4AEE8E228F1896", - "38a90f22637337334b49dcb66a6dc8f9978aca7648a943b0", - "FFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13",1, - _EC_X9_62_PRIME_192V3_SEED, 20, - "X9.62 curve over a 192 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } + _EC_X9_62_PRIME_192V3 = { + { NID_X9_62_prime_field,20,24,1 }, + { 0xC4,0x69,0x68,0x44,0x35,0xDE,0xB3,0x78,0xC4,0xB6, /* seed */ + 0x5C,0xA9,0x59,0x1E,0x2A,0x57,0x63,0x05,0x9A,0x2E, + + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFC, + 0x22,0x12,0x3D,0xC2,0x39,0x5A,0x05,0xCA,0xA7,0x42, /* b */ + 0x3D,0xAE,0xCC,0xC9,0x47,0x60,0xA7,0xD4,0x62,0x25, + 0x6B,0xD5,0x69,0x16, + 0x7D,0x29,0x77,0x81,0x00,0xC6,0x5A,0x1D,0xA1,0x78, /* x */ + 0x37,0x16,0x58,0x8D,0xCE,0x2B,0x8B,0x4A,0xEE,0x8E, + 0x22,0x8F,0x18,0x96, + 0x38,0xa9,0x0f,0x22,0x63,0x73,0x37,0x33,0x4b,0x49, /* y */ + 0xdc,0xb6,0x6a,0x6d,0xc8,0xf9,0x97,0x8a,0xca,0x76, + 0x48,0xa9,0x43,0xb0, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0x7A,0x62,0xD0,0x31,0xC8,0x3F,0x42,0x94, + 0xF6,0x40,0xEC,0x13 } }; -static const unsigned char _EC_X9_62_PRIME_239V1_SEED[] = { - 0xE4,0x3B,0xB4,0x60,0xF0,0xB8,0x0C,0xC0,0xC0,0xB0, - 0x75,0x79,0x8E,0x94,0x80,0x60,0xF8,0x32,0x1B,0x7D}; -static const EC_CURVE_DATA _EC_X9_62_PRIME_239V1 = { - NID_X9_62_prime_field, - "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF", - "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC", - "6B016C3BDCF18941D0D654921475CA71A9DB2FB27D1D37796185C2942C0A", - "0FFA963CDCA8816CCC33B8642BEDF905C3D358573D3F27FBBD3B3CB9AAAF", - "7debe8e4e90a5dae6e4054ca530ba04654b36818ce226b39fccb7b02f1ae", - "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B",1, - _EC_X9_62_PRIME_239V1_SEED, 20, - "X9.62 curve over a 239 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } + _EC_X9_62_PRIME_239V1 = { + { NID_X9_62_prime_field,20,30,1 }, + { 0xE4,0x3B,0xB4,0x60,0xF0,0xB8,0x0C,0xC0,0xC0,0xB0, /* seed */ + 0x75,0x79,0x8E,0x94,0x80,0x60,0xF8,0x32,0x1B,0x7D, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, + 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, + 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, + + 0x6B,0x01,0x6C,0x3B,0xDC,0xF1,0x89,0x41,0xD0,0xD6, /* b */ + 0x54,0x92,0x14,0x75,0xCA,0x71,0xA9,0xDB,0x2F,0xB2, + 0x7D,0x1D,0x37,0x79,0x61,0x85,0xC2,0x94,0x2C,0x0A, + + 0x0F,0xFA,0x96,0x3C,0xDC,0xA8,0x81,0x6C,0xCC,0x33, /* x */ + 0xB8,0x64,0x2B,0xED,0xF9,0x05,0xC3,0xD3,0x58,0x57, + 0x3D,0x3F,0x27,0xFB,0xBD,0x3B,0x3C,0xB9,0xAA,0xAF, + + 0x7d,0xeb,0xe8,0xe4,0xe9,0x0a,0x5d,0xae,0x6e,0x40, /* y */ + 0x54,0xca,0x53,0x0b,0xa0,0x46,0x54,0xb3,0x68,0x18, + 0xce,0x22,0x6b,0x39,0xfc,0xcb,0x7b,0x02,0xf1,0xae, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0x7F,0xFF,0xFF,0x9E,0x5E,0x9A,0x9F,0x5D, + 0x90,0x71,0xFB,0xD1,0x52,0x26,0x88,0x90,0x9D,0x0B } }; -static const unsigned char _EC_X9_62_PRIME_239V2_SEED[] = { - 0xE8,0xB4,0x01,0x16,0x04,0x09,0x53,0x03,0xCA,0x3B, - 0x80,0x99,0x98,0x2B,0xE0,0x9F,0xCB,0x9A,0xE6,0x16}; -static const EC_CURVE_DATA _EC_X9_62_PRIME_239V2 = { - NID_X9_62_prime_field, - "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF", - "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC", - "617FAB6832576CBBFED50D99F0249C3FEE58B94BA0038C7AE84C8C832F2C", - "38AF09D98727705120C921BB5E9E26296A3CDCF2F35757A0EAFD87B830E7", - "5b0125e4dbea0ec7206da0fc01d9b081329fb555de6ef460237dff8be4ba", - "7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063",1, - _EC_X9_62_PRIME_239V2_SEED, 20, - "X9.62 curve over a 239 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } + _EC_X9_62_PRIME_239V2 = { + { NID_X9_62_prime_field,20,30,1 }, + { 0xE8,0xB4,0x01,0x16,0x04,0x09,0x53,0x03,0xCA,0x3B, /* seed */ + 0x80,0x99,0x98,0x2B,0xE0,0x9F,0xCB,0x9A,0xE6,0x16, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, + 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, + 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, + + 0x61,0x7F,0xAB,0x68,0x32,0x57,0x6C,0xBB,0xFE,0xD5, /* b */ + 0x0D,0x99,0xF0,0x24,0x9C,0x3F,0xEE,0x58,0xB9,0x4B, + 0xA0,0x03,0x8C,0x7A,0xE8,0x4C,0x8C,0x83,0x2F,0x2C, + + 0x38,0xAF,0x09,0xD9,0x87,0x27,0x70,0x51,0x20,0xC9, /* x */ + 0x21,0xBB,0x5E,0x9E,0x26,0x29,0x6A,0x3C,0xDC,0xF2, + 0xF3,0x57,0x57,0xA0,0xEA,0xFD,0x87,0xB8,0x30,0xE7, + + 0x5b,0x01,0x25,0xe4,0xdb,0xea,0x0e,0xc7,0x20,0x6d, /* y */ + 0xa0,0xfc,0x01,0xd9,0xb0,0x81,0x32,0x9f,0xb5,0x55, + 0xde,0x6e,0xf4,0x60,0x23,0x7d,0xff,0x8b,0xe4,0xba, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0x80,0x00,0x00,0xCF,0xA7,0xE8,0x59,0x43, + 0x77,0xD4,0x14,0xC0,0x38,0x21,0xBC,0x58,0x20,0x63 } }; -static const unsigned char _EC_X9_62_PRIME_239V3_SEED[] = { - 0x7D,0x73,0x74,0x16,0x8F,0xFE,0x34,0x71,0xB6,0x0A, - 0x85,0x76,0x86,0xA1,0x94,0x75,0xD3,0xBF,0xA2,0xFF}; -static const EC_CURVE_DATA _EC_X9_62_PRIME_239V3 = { - NID_X9_62_prime_field, - "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF", - "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC", - "255705FA2A306654B1F4CB03D6A750A30C250102D4988717D9BA15AB6D3E", - "6768AE8E18BB92CFCF005C949AA2C6D94853D0E660BBF854B1C9505FE95A", - "1607e6898f390c06bc1d552bad226f3b6fcfe48b6e818499af18e3ed6cf3", - "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551",1, - _EC_X9_62_PRIME_239V3_SEED, 20, - "X9.62 curve over a 239 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } + _EC_X9_62_PRIME_239V3 = { + { NID_X9_62_prime_field,20,30,1 }, + { 0x7D,0x73,0x74,0x16,0x8F,0xFE,0x34,0x71,0xB6,0x0A, /* seed */ + 0x85,0x76,0x86,0xA1,0x94,0x75,0xD3,0xBF,0xA2,0xFF, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, + 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0x80,0x00, + 0x00,0x00,0x00,0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFC, + + 0x25,0x57,0x05,0xFA,0x2A,0x30,0x66,0x54,0xB1,0xF4, /* b */ + 0xCB,0x03,0xD6,0xA7,0x50,0xA3,0x0C,0x25,0x01,0x02, + 0xD4,0x98,0x87,0x17,0xD9,0xBA,0x15,0xAB,0x6D,0x3E, + + 0x67,0x68,0xAE,0x8E,0x18,0xBB,0x92,0xCF,0xCF,0x00, /* x */ + 0x5C,0x94,0x9A,0xA2,0xC6,0xD9,0x48,0x53,0xD0,0xE6, + 0x60,0xBB,0xF8,0x54,0xB1,0xC9,0x50,0x5F,0xE9,0x5A, + + 0x16,0x07,0xe6,0x89,0x8f,0x39,0x0c,0x06,0xbc,0x1d, /* y */ + 0x55,0x2b,0xad,0x22,0x6f,0x3b,0x6f,0xcf,0xe4,0x8b, + 0x6e,0x81,0x84,0x99,0xaf,0x18,0xe3,0xed,0x6c,0xf3, + + 0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0x7F,0xFF,0xFF,0x97,0x5D,0xEB,0x41,0xB3, + 0xA6,0x05,0x7C,0x3C,0x43,0x21,0x46,0x52,0x65,0x51 } }; -static const unsigned char _EC_X9_62_PRIME_256V1_SEED[] = { - 0xC4,0x9D,0x36,0x08,0x86,0xE7,0x04,0x93,0x6A,0x66, - 0x78,0xE1,0x13,0x9D,0x26,0xB7,0x81,0x9F,0x7E,0x90}; -static const EC_CURVE_DATA _EC_X9_62_PRIME_256V1 = { - NID_X9_62_prime_field, - "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF", - "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC", - "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B", - "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296", - "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", - "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",1, - _EC_X9_62_PRIME_256V1_SEED, 20, - "X9.62/SECG curve over a 256 bit prime field" + +static const struct { EC_CURVE_DATA h; unsigned char data[20+32*6]; } + _EC_X9_62_PRIME_256V1 = { + { NID_X9_62_prime_field,20,32,1 }, + { 0xC4,0x9D,0x36,0x08,0x86,0xE7,0x04,0x93,0x6A,0x66, /* seed */ + 0x78,0xE1,0x13,0x9D,0x26,0xB7,0x81,0x9F,0x7E,0x90, + + 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x01,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x01,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFC, + 0x5A,0xC6,0x35,0xD8,0xAA,0x3A,0x93,0xE7,0xB3,0xEB, /* b */ + 0xBD,0x55,0x76,0x98,0x86,0xBC,0x65,0x1D,0x06,0xB0, + 0xCC,0x53,0xB0,0xF6,0x3B,0xCE,0x3C,0x3E,0x27,0xD2, + 0x60,0x4B, + 0x6B,0x17,0xD1,0xF2,0xE1,0x2C,0x42,0x47,0xF8,0xBC, /* x */ + 0xE6,0xE5,0x63,0xA4,0x40,0xF2,0x77,0x03,0x7D,0x81, + 0x2D,0xEB,0x33,0xA0,0xF4,0xA1,0x39,0x45,0xD8,0x98, + 0xC2,0x96, + 0x4f,0xe3,0x42,0xe2,0xfe,0x1a,0x7f,0x9b,0x8e,0xe7, /* y */ + 0xeb,0x4a,0x7c,0x0f,0x9e,0x16,0x2b,0xce,0x33,0x57, + 0x6b,0x31,0x5e,0xce,0xcb,0xb6,0x40,0x68,0x37,0xbf, + 0x51,0xf5, + 0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xBC,0xE6,0xFA,0xAD, + 0xA7,0x17,0x9E,0x84,0xF3,0xB9,0xCA,0xC2,0xFC,0x63, + 0x25,0x51 } }; + /* the secg prime curves (minus the nist and x9.62 prime curves) */ -static const unsigned char _EC_SECG_PRIME_112R1_SEED[] = { - 0x00,0xF5,0x0B,0x02,0x8E,0x4D,0x69,0x6E,0x67,0x68, - 0x75,0x61,0x51,0x75,0x29,0x04,0x72,0x78,0x3F,0xB1}; -static const EC_CURVE_DATA _EC_SECG_PRIME_112R1 = { - NID_X9_62_prime_field, - "DB7C2ABF62E35E668076BEAD208B", - "DB7C2ABF62E35E668076BEAD2088", - "659EF8BA043916EEDE8911702B22", - "09487239995A5EE76B55F9C2F098", - "a89ce5af8724c0a23e0e0ff77500", - "DB7C2ABF62E35E7628DFAC6561C5",1, - _EC_SECG_PRIME_112R1_SEED, 20, - "SECG/WTLS curve over a 112 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+14*6]; } + _EC_SECG_PRIME_112R1 = { + { NID_X9_62_prime_field,20,14,1 }, + { 0x00,0xF5,0x0B,0x02,0x8E,0x4D,0x69,0x6E,0x67,0x68, /* seed */ + 0x75,0x61,0x51,0x75,0x29,0x04,0x72,0x78,0x3F,0xB1, + + 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* p */ + 0xBE,0xAD,0x20,0x8B, + 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* a */ + 0xBE,0xAD,0x20,0x88, + 0x65,0x9E,0xF8,0xBA,0x04,0x39,0x16,0xEE,0xDE,0x89, /* b */ + 0x11,0x70,0x2B,0x22, + 0x09,0x48,0x72,0x39,0x99,0x5A,0x5E,0xE7,0x6B,0x55, /* x */ + 0xF9,0xC2,0xF0,0x98, + 0xa8,0x9c,0xe5,0xaf,0x87,0x24,0xc0,0xa2,0x3e,0x0e, /* y */ + 0x0f,0xf7,0x75,0x00, + 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x76,0x28,0xDF, /* order */ + 0xAC,0x65,0x61,0xC5 } }; -static const unsigned char _EC_SECG_PRIME_112R2_SEED[] = { - 0x00,0x27,0x57,0xA1,0x11,0x4D,0x69,0x6E,0x67,0x68, - 0x75,0x61,0x51,0x75,0x53,0x16,0xC0,0x5E,0x0B,0xD4}; -static const EC_CURVE_DATA _EC_SECG_PRIME_112R2 = { - NID_X9_62_prime_field, - "DB7C2ABF62E35E668076BEAD208B", - "6127C24C05F38A0AAAF65C0EF02C", - "51DEF1815DB5ED74FCC34C85D709", - "4BA30AB5E892B4E1649DD0928643", - "adcd46f5882e3747def36e956e97", - "36DF0AAFD8B8D7597CA10520D04B",4, - _EC_SECG_PRIME_112R2_SEED, 20, - "SECG curve over a 112 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+14*6]; } + _EC_SECG_PRIME_112R2 = { + { NID_X9_62_prime_field,20,14,4 }, + { 0x00,0x27,0x57,0xA1,0x11,0x4D,0x69,0x6E,0x67,0x68, /* seed */ + 0x75,0x61,0x51,0x75,0x53,0x16,0xC0,0x5E,0x0B,0xD4, + + 0xDB,0x7C,0x2A,0xBF,0x62,0xE3,0x5E,0x66,0x80,0x76, /* p */ + 0xBE,0xAD,0x20,0x8B, + 0x61,0x27,0xC2,0x4C,0x05,0xF3,0x8A,0x0A,0xAA,0xF6, /* a */ + 0x5C,0x0E,0xF0,0x2C, + 0x51,0xDE,0xF1,0x81,0x5D,0xB5,0xED,0x74,0xFC,0xC3, /* b */ + 0x4C,0x85,0xD7,0x09, + 0x4B,0xA3,0x0A,0xB5,0xE8,0x92,0xB4,0xE1,0x64,0x9D, /* x */ + 0xD0,0x92,0x86,0x43, + 0xad,0xcd,0x46,0xf5,0x88,0x2e,0x37,0x47,0xde,0xf3, /* y */ + 0x6e,0x95,0x6e,0x97, + 0x36,0xDF,0x0A,0xAF,0xD8,0xB8,0xD7,0x59,0x7C,0xA1, /* order */ + 0x05,0x20,0xD0,0x4B } }; -static const unsigned char _EC_SECG_PRIME_128R1_SEED[] = { - 0x00,0x0E,0x0D,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, - 0x51,0x75,0x0C,0xC0,0x3A,0x44,0x73,0xD0,0x36,0x79}; -static const EC_CURVE_DATA _EC_SECG_PRIME_128R1 = { - NID_X9_62_prime_field, - "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF", - "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC", - "E87579C11079F43DD824993C2CEE5ED3", - "161FF7528B899B2D0C28607CA52C5B86", - "cf5ac8395bafeb13c02da292dded7a83", - "FFFFFFFE0000000075A30D1B9038A115",1, - _EC_SECG_PRIME_128R1_SEED, 20, - "SECG curve over a 128 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+16*6]; } + _EC_SECG_PRIME_128R1 = { + { NID_X9_62_prime_field,20,16,1 }, + { 0x00,0x0E,0x0D,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ + 0x51,0x75,0x0C,0xC0,0x3A,0x44,0x73,0xD0,0x36,0x79, + + 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFC, + 0xE8,0x75,0x79,0xC1,0x10,0x79,0xF4,0x3D,0xD8,0x24, /* b */ + 0x99,0x3C,0x2C,0xEE,0x5E,0xD3, + 0x16,0x1F,0xF7,0x52,0x8B,0x89,0x9B,0x2D,0x0C,0x28, /* x */ + 0x60,0x7C,0xA5,0x2C,0x5B,0x86, + 0xcf,0x5a,0xc8,0x39,0x5b,0xaf,0xeb,0x13,0xc0,0x2d, /* y */ + 0xa2,0x92,0xdd,0xed,0x7a,0x83, + 0xFF,0xFF,0xFF,0xFE,0x00,0x00,0x00,0x00,0x75,0xA3, /* order */ + 0x0D,0x1B,0x90,0x38,0xA1,0x15 } }; -static const unsigned char _EC_SECG_PRIME_128R2_SEED[] = { - 0x00,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75, - 0x12,0xD8,0xF0,0x34,0x31,0xFC,0xE6,0x3B,0x88,0xF4}; -static const EC_CURVE_DATA _EC_SECG_PRIME_128R2 = { - NID_X9_62_prime_field, - "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF", - "D6031998D1B3BBFEBF59CC9BBFF9AEE1", - "5EEEFCA380D02919DC2C6558BB6D8A5D", - "7B6AA5D85E572983E6FB32A7CDEBC140", - "27b6916a894d3aee7106fe805fc34b44", - "3FFFFFFF7FFFFFFFBE0024720613B5A3",4, - _EC_SECG_PRIME_128R2_SEED, 20, - "SECG curve over a 128 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+16*6]; } + _EC_SECG_PRIME_128R2 = { + { NID_X9_62_prime_field,20,16,4 }, + { 0x00,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75, /* seed */ + 0x12,0xD8,0xF0,0x34,0x31,0xFC,0xE6,0x3B,0x88,0xF4, + + 0xFF,0xFF,0xFF,0xFD,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xD6,0x03,0x19,0x98,0xD1,0xB3,0xBB,0xFE,0xBF,0x59, /* a */ + 0xCC,0x9B,0xBF,0xF9,0xAE,0xE1, + 0x5E,0xEE,0xFC,0xA3,0x80,0xD0,0x29,0x19,0xDC,0x2C, /* b */ + 0x65,0x58,0xBB,0x6D,0x8A,0x5D, + 0x7B,0x6A,0xA5,0xD8,0x5E,0x57,0x29,0x83,0xE6,0xFB, /* x */ + 0x32,0xA7,0xCD,0xEB,0xC1,0x40, + 0x27,0xb6,0x91,0x6a,0x89,0x4d,0x3a,0xee,0x71,0x06, /* y */ + 0xfe,0x80,0x5f,0xc3,0x4b,0x44, + 0x3F,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF,0xFF,0xBE,0x00, /* order */ + 0x24,0x72,0x06,0x13,0xB5,0xA3 } }; -static const EC_CURVE_DATA _EC_SECG_PRIME_160K1 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73", - "0", - "7", - "3B4C382CE37AA192A4019E763036F4F5DD4D7EBB", - "938cf935318fdced6bc28286531733c3f03c4fee", - "0100000000000000000001B8FA16DFAB9ACA16B6B3",1, - NULL, 0, - "SECG curve over a 160 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } + _EC_SECG_PRIME_160K1 = { + { NID_X9_62_prime_field,0,21,1 }, + { /* no seed */ + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, + 0x73, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x07, + 0x00,0x3B,0x4C,0x38,0x2C,0xE3,0x7A,0xA1,0x92,0xA4, /* x */ + 0x01,0x9E,0x76,0x30,0x36,0xF4,0xF5,0xDD,0x4D,0x7E, + 0xBB, + 0x00,0x93,0x8c,0xf9,0x35,0x31,0x8f,0xdc,0xed,0x6b, /* y */ + 0xc2,0x82,0x86,0x53,0x17,0x33,0xc3,0xf0,0x3c,0x4f, + 0xee, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x01,0xB8,0xFA,0x16,0xDF,0xAB,0x9A,0xCA,0x16,0xB6, + 0xB3 } }; -static const unsigned char _EC_SECG_PRIME_160R1_SEED[] = { - 0x10,0x53,0xCD,0xE4,0x2C,0x14,0xD6,0x96,0xE6,0x76, - 0x87,0x56,0x15,0x17,0x53,0x3B,0xF3,0xF8,0x33,0x45}; -static const EC_CURVE_DATA _EC_SECG_PRIME_160R1 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC", - "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45", - "4A96B5688EF573284664698968C38BB913CBFC82", - "23a628553168947d59dcc912042351377ac5fb32", - "0100000000000000000001F4C8F927AED3CA752257",1, - _EC_SECG_PRIME_160R1_SEED, 20, - "SECG curve over a 160 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } + _EC_SECG_PRIME_160R1 = { + { NID_X9_62_prime_field,20,21,1 }, + { 0x10,0x53,0xCD,0xE4,0x2C,0x14,0xD6,0x96,0xE6,0x76, /* seed */ + 0x87,0x56,0x15,0x17,0x53,0x3B,0xF3,0xF8,0x33,0x45, + + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF, + 0xFF, + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x7F,0xFF,0xFF, + 0xFC, + 0x00,0x1C,0x97,0xBE,0xFC,0x54,0xBD,0x7A,0x8B,0x65, /* b */ + 0xAC,0xF8,0x9F,0x81,0xD4,0xD4,0xAD,0xC5,0x65,0xFA, + 0x45, + 0x00,0x4A,0x96,0xB5,0x68,0x8E,0xF5,0x73,0x28,0x46, /* x */ + 0x64,0x69,0x89,0x68,0xC3,0x8B,0xB9,0x13,0xCB,0xFC, + 0x82, + 0x00,0x23,0xa6,0x28,0x55,0x31,0x68,0x94,0x7d,0x59, /* y */ + 0xdc,0xc9,0x12,0x04,0x23,0x51,0x37,0x7a,0xc5,0xfb, + 0x32, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x01,0xF4,0xC8,0xF9,0x27,0xAE,0xD3,0xCA,0x75,0x22, + 0x57 } }; -static const unsigned char _EC_SECG_PRIME_160R2_SEED[] = { - 0xB9,0x9B,0x99,0xB0,0x99,0xB3,0x23,0xE0,0x27,0x09, - 0xA4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x51}; -static const EC_CURVE_DATA _EC_SECG_PRIME_160R2 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70", - "B4E134D3FB59EB8BAB57274904664D5AF50388BA", - "52DCB034293A117E1F4FF11B30F7199D3144CE6D", - "feaffef2e331f296e071fa0df9982cfea7d43f2e", - "0100000000000000000000351EE786A818F3A1A16B",1, - _EC_SECG_PRIME_160R2_SEED, 20, - "SECG/WTLS curve over a 160 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } + _EC_SECG_PRIME_160R2 = { + { NID_X9_62_prime_field,20,21,1 }, + { 0xB9,0x9B,0x99,0xB0,0x99,0xB3,0x23,0xE0,0x27,0x09, /* seed */ + 0xA4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x51, + + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, + 0x73, + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xAC, + 0x70, + 0x00,0xB4,0xE1,0x34,0xD3,0xFB,0x59,0xEB,0x8B,0xAB, /* b */ + 0x57,0x27,0x49,0x04,0x66,0x4D,0x5A,0xF5,0x03,0x88, + 0xBA, + 0x00,0x52,0xDC,0xB0,0x34,0x29,0x3A,0x11,0x7E,0x1F, /* x */ + 0x4F,0xF1,0x1B,0x30,0xF7,0x19,0x9D,0x31,0x44,0xCE, + 0x6D, + 0x00,0xfe,0xaf,0xfe,0xf2,0xe3,0x31,0xf2,0x96,0xe0, /* y */ + 0x71,0xfa,0x0d,0xf9,0x98,0x2c,0xfe,0xa7,0xd4,0x3f, + 0x2e, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x35,0x1E,0xE7,0x86,0xA8,0x18,0xF3,0xA1,0xA1, + 0x6B } }; -static const EC_CURVE_DATA _EC_SECG_PRIME_192K1 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37", - "0", - "3", - "DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D", - "9b2f2f6d9c5628a7844163d015be86344082aa88d95e2f9d", - "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D",1, - NULL, 20, - "SECG curve over a 192 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } + _EC_SECG_PRIME_192K1 = { + { NID_X9_62_prime_field,0,24,1 }, + { /* no seed */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xFF,0xFF,0xEE,0x37, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x03, + 0xDB,0x4F,0xF1,0x0E,0xC0,0x57,0xE9,0xAE,0x26,0xB0, /* x */ + 0x7D,0x02,0x80,0xB7,0xF4,0x34,0x1D,0xA5,0xD1,0xB1, + 0xEA,0xE0,0x6C,0x7D, + 0x9b,0x2f,0x2f,0x6d,0x9c,0x56,0x28,0xa7,0x84,0x41, /* y */ + 0x63,0xd0,0x15,0xbe,0x86,0x34,0x40,0x82,0xaa,0x88, + 0xd9,0x5e,0x2f,0x9d, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFE,0x26,0xF2,0xFC,0x17,0x0F,0x69,0x46,0x6A, + 0x74,0xDE,0xFD,0x8D } }; -static const EC_CURVE_DATA _EC_SECG_PRIME_224K1 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D", - "0", - "5", - "A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C", - "7e089fed7fba344282cafbd6f7e319f7c0b0bd59e2ca4bdb556d61a5", - "010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7",1, - NULL, 20, - "SECG curve over a 224 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+29*6]; } + _EC_SECG_PRIME_224K1 = { + { NID_X9_62_prime_field,0,29,1 }, + { /* no seed */ + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xE5,0x6D, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x05, + 0x00,0xA1,0x45,0x5B,0x33,0x4D,0xF0,0x99,0xDF,0x30, /* x */ + 0xFC,0x28,0xA1,0x69,0xA4,0x67,0xE9,0xE4,0x70,0x75, + 0xA9,0x0F,0x7E,0x65,0x0E,0xB6,0xB7,0xA4,0x5C, + 0x00,0x7e,0x08,0x9f,0xed,0x7f,0xba,0x34,0x42,0x82, /* y */ + 0xca,0xfb,0xd6,0xf7,0xe3,0x19,0xf7,0xc0,0xb0,0xbd, + 0x59,0xe2,0xca,0x4b,0xdb,0x55,0x6d,0x61,0xa5, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x00,0x00,0x01,0xDC,0xE8,0xD2,0xEC,0x61, + 0x84,0xCA,0xF0,0xA9,0x71,0x76,0x9F,0xB1,0xF7 } }; -static const EC_CURVE_DATA _EC_SECG_PRIME_256K1 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", - "0", - "7", - "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", - "483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141",1, - NULL, 20, - "SECG curve over a 256 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+32*6]; } + _EC_SECG_PRIME_256K1 = { + { NID_X9_62_prime_field,0,32,1 }, + { /* no seed */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF, + 0xFC,0x2F, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x07, + 0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,0x55,0xA0, /* x */ + 0x62,0x95,0xCE,0x87,0x0B,0x07,0x02,0x9B,0xFC,0xDB, + 0x2D,0xCE,0x28,0xD9,0x59,0xF2,0x81,0x5B,0x16,0xF8, + 0x17,0x98, + 0x48,0x3a,0xda,0x77,0x26,0xa3,0xc4,0x65,0x5d,0xa4, /* y */ + 0xfb,0xfc,0x0e,0x11,0x08,0xa8,0xfd,0x17,0xb4,0x48, + 0xa6,0x85,0x54,0x19,0x9c,0x47,0xd0,0x8f,0xfb,0x10, + 0xd4,0xb8, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xBA,0xAE,0xDC,0xE6, + 0xAF,0x48,0xA0,0x3B,0xBF,0xD2,0x5E,0x8C,0xD0,0x36, + 0x41,0x41 } }; /* some wap/wtls curves */ -static const EC_CURVE_DATA _EC_WTLS_8 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFDE7", - "0", - "3", - "1", - "2", - "0100000000000001ECEA551AD837E9",1, - NULL, 20, - "WTLS curve over a 112 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+15*6]; } + _EC_WTLS_8 = { + { NID_X9_62_prime_field,0,15,1 }, + { /* no seed */ + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFD,0xE7, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x03, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ + 0x00,0x00,0x00,0x00,0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ + 0x00,0x00,0x00,0x00,0x02, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xEC,0xEA, /* order */ + 0x55,0x1A,0xD8,0x37,0xE9 } }; -static const EC_CURVE_DATA _EC_WTLS_9 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC808F", - "0", - "3", - "1", - "2", - "0100000000000000000001CDC98AE0E2DE574ABF33",1, - NULL, 20, - "WTLS curve over a 160 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } + _EC_WTLS_9 = { + { NID_X9_62_prime_field,0,21,1 }, + { /* no seed */ + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFC,0x80, + 0x8F, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x03, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x02, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x01,0xCD,0xC9,0x8A,0xE0,0xE2,0xDE,0x57,0x4A,0xBF, + 0x33 } }; -static const EC_CURVE_DATA _EC_WTLS_12 = { - NID_X9_62_prime_field, - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", - "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", - "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", - "bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", - "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", 1, - NULL, 0, - "WTLS curvs over a 224 bit prime field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+28*6]; } + _EC_WTLS_12 = { + { NID_X9_62_prime_field,0,28,1 }, + { /* no seed */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, + 0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ + 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, + 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4, + 0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ + 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, + 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21, + 0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ + 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, + 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0x16,0xA2,0xE0,0xB8,0xF0,0x3E, + 0x13,0xDD,0x29,0x45,0x5C,0x5C,0x2A,0x3D } }; +#ifndef OPENSSL_NO_EC2M + /* characteristic two curves */ -static const unsigned char _EC_SECG_CHAR2_113R1_SEED[] = { - 0x10,0xE7,0x23,0xAB,0x14,0xD6,0x96,0xE6,0x76,0x87, - 0x56,0x15,0x17,0x56,0xFE,0xBF,0x8F,0xCB,0x49,0xA9}; -static const EC_CURVE_DATA _EC_SECG_CHAR2_113R1 = { - NID_X9_62_characteristic_two_field, - "020000000000000000000000000201", - "003088250CA6E7C7FE649CE85820F7", - "00E8BEE4D3E2260744188BE0E9C723", - "009D73616F35F4AB1407D73562C10F", - "00A52830277958EE84D1315ED31886", - "0100000000000000D9CCEC8A39E56F", 2, - _EC_SECG_CHAR2_113R1_SEED, 20, - "SECG curve over a 113 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+15*6]; } + _EC_SECG_CHAR2_113R1 = { + { NID_X9_62_characteristic_two_field,20,15,2 }, + { 0x10,0xE7,0x23,0xAB,0x14,0xD6,0x96,0xE6,0x76,0x87, /* seed */ + 0x56,0x15,0x17,0x56,0xFE,0xBF,0x8F,0xCB,0x49,0xA9, + + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x02,0x01, + 0x00,0x30,0x88,0x25,0x0C,0xA6,0xE7,0xC7,0xFE,0x64, /* a */ + 0x9C,0xE8,0x58,0x20,0xF7, + 0x00,0xE8,0xBE,0xE4,0xD3,0xE2,0x26,0x07,0x44,0x18, /* b */ + 0x8B,0xE0,0xE9,0xC7,0x23, + 0x00,0x9D,0x73,0x61,0x6F,0x35,0xF4,0xAB,0x14,0x07, /* x */ + 0xD7,0x35,0x62,0xC1,0x0F, + 0x00,0xA5,0x28,0x30,0x27,0x79,0x58,0xEE,0x84,0xD1, /* y */ + 0x31,0x5E,0xD3,0x18,0x86, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0xD9,0xCC, /* order */ + 0xEC,0x8A,0x39,0xE5,0x6F } }; -static const unsigned char _EC_SECG_CHAR2_113R2_SEED[] = { - 0x10,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE, - 0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x5D}; -static const EC_CURVE_DATA _EC_SECG_CHAR2_113R2 = { - NID_X9_62_characteristic_two_field, - "020000000000000000000000000201", - "00689918DBEC7E5A0DD6DFC0AA55C7", - "0095E9A9EC9B297BD4BF36E059184F", - "01A57A6A7B26CA5EF52FCDB8164797", - "00B3ADC94ED1FE674C06E695BABA1D", - "010000000000000108789B2496AF93", 2, - _EC_SECG_CHAR2_113R2_SEED, 20, - "SECG curve over a 113 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+15*6]; } + _EC_SECG_CHAR2_113R2 = { + { NID_X9_62_characteristic_two_field,20,15,2 }, + { 0x10,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE, /* seed */ + 0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x5D, + + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x02,0x01, + 0x00,0x68,0x99,0x18,0xDB,0xEC,0x7E,0x5A,0x0D,0xD6, /* a */ + 0xDF,0xC0,0xAA,0x55,0xC7, + 0x00,0x95,0xE9,0xA9,0xEC,0x9B,0x29,0x7B,0xD4,0xBF, /* b */ + 0x36,0xE0,0x59,0x18,0x4F, + 0x01,0xA5,0x7A,0x6A,0x7B,0x26,0xCA,0x5E,0xF5,0x2F, /* x */ + 0xCD,0xB8,0x16,0x47,0x97, + 0x00,0xB3,0xAD,0xC9,0x4E,0xD1,0xFE,0x67,0x4C,0x06, /* y */ + 0xE6,0x95,0xBA,0xBA,0x1D, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x08,0x78, /* order */ + 0x9B,0x24,0x96,0xAF,0x93 } }; -static const unsigned char _EC_SECG_CHAR2_131R1_SEED[] = { - 0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75,0x98, - 0x5B,0xD3,0xAD,0xBA,0xDA,0x21,0xB4,0x3A,0x97,0xE2}; -static const EC_CURVE_DATA _EC_SECG_CHAR2_131R1 = { - NID_X9_62_characteristic_two_field, - "080000000000000000000000000000010D", - "07A11B09A76B562144418FF3FF8C2570B8", - "0217C05610884B63B9C6C7291678F9D341", - "0081BAF91FDF9833C40F9C181343638399", - "078C6E7EA38C001F73C8134B1B4EF9E150", - "0400000000000000023123953A9464B54D", 2, - _EC_SECG_CHAR2_131R1_SEED, 20, - "SECG/WTLS curve over a 131 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+17*6]; } + _EC_SECG_CHAR2_131R1 = { + { NID_X9_62_characteristic_two_field,20,17,2 }, + { 0x4D,0x69,0x6E,0x67,0x68,0x75,0x61,0x51,0x75,0x98, /* seed */ + 0x5B,0xD3,0xAD,0xBA,0xDA,0x21,0xB4,0x3A,0x97,0xE2, + + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x01,0x0D, + 0x07,0xA1,0x1B,0x09,0xA7,0x6B,0x56,0x21,0x44,0x41, /* a */ + 0x8F,0xF3,0xFF,0x8C,0x25,0x70,0xB8, + 0x02,0x17,0xC0,0x56,0x10,0x88,0x4B,0x63,0xB9,0xC6, /* b */ + 0xC7,0x29,0x16,0x78,0xF9,0xD3,0x41, + 0x00,0x81,0xBA,0xF9,0x1F,0xDF,0x98,0x33,0xC4,0x0F, /* x */ + 0x9C,0x18,0x13,0x43,0x63,0x83,0x99, + 0x07,0x8C,0x6E,0x7E,0xA3,0x8C,0x00,0x1F,0x73,0xC8, /* y */ + 0x13,0x4B,0x1B,0x4E,0xF9,0xE1,0x50, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x02,0x31, /* order */ + 0x23,0x95,0x3A,0x94,0x64,0xB5,0x4D } }; -static const unsigned char _EC_SECG_CHAR2_131R2_SEED[] = { - 0x98,0x5B,0xD3,0xAD,0xBA,0xD4,0xD6,0x96,0xE6,0x76, - 0x87,0x56,0x15,0x17,0x5A,0x21,0xB4,0x3A,0x97,0xE3}; -static const EC_CURVE_DATA _EC_SECG_CHAR2_131R2 = { - NID_X9_62_characteristic_two_field, - "080000000000000000000000000000010D", - "03E5A88919D7CAFCBF415F07C2176573B2", - "04B8266A46C55657AC734CE38F018F2192", - "0356DCD8F2F95031AD652D23951BB366A8", - "0648F06D867940A5366D9E265DE9EB240F", - "0400000000000000016954A233049BA98F", 2, - _EC_SECG_CHAR2_131R2_SEED, 20, - "SECG curve over a 131 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+17*6]; } + _EC_SECG_CHAR2_131R2 = { + { NID_X9_62_characteristic_two_field,20,17,2 }, + { 0x98,0x5B,0xD3,0xAD,0xBA,0xD4,0xD6,0x96,0xE6,0x76, /* seed */ + 0x87,0x56,0x15,0x17,0x5A,0x21,0xB4,0x3A,0x97,0xE3, + + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x01,0x0D, + 0x03,0xE5,0xA8,0x89,0x19,0xD7,0xCA,0xFC,0xBF,0x41, /* a */ + 0x5F,0x07,0xC2,0x17,0x65,0x73,0xB2, + 0x04,0xB8,0x26,0x6A,0x46,0xC5,0x56,0x57,0xAC,0x73, /* b */ + 0x4C,0xE3,0x8F,0x01,0x8F,0x21,0x92, + 0x03,0x56,0xDC,0xD8,0xF2,0xF9,0x50,0x31,0xAD,0x65, /* x */ + 0x2D,0x23,0x95,0x1B,0xB3,0x66,0xA8, + 0x06,0x48,0xF0,0x6D,0x86,0x79,0x40,0xA5,0x36,0x6D, /* y */ + 0x9E,0x26,0x5D,0xE9,0xEB,0x24,0x0F, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x69, /* order */ + 0x54,0xA2,0x33,0x04,0x9B,0xA9,0x8F } }; -static const EC_CURVE_DATA _EC_NIST_CHAR2_163K = { - NID_X9_62_characteristic_two_field, - "0800000000000000000000000000000000000000C9", - "1", - "1", - "02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8", - "0289070FB05D38FF58321F2E800536D538CCDAA3D9", - "04000000000000000000020108A2E0CC0D99F8A5EF", 2, - NULL, 0, - "NIST/SECG/WTLS curve over a 163 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } + _EC_NIST_CHAR2_163K = { + { NID_X9_62_characteristic_two_field,0,21,2 }, + { /* no seed */ + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0xC9, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x01, + 0x02,0xFE,0x13,0xC0,0x53,0x7B,0xBC,0x11,0xAC,0xAA, /* x */ + 0x07,0xD7,0x93,0xDE,0x4E,0x6D,0x5E,0x5C,0x94,0xEE, + 0xE8, + 0x02,0x89,0x07,0x0F,0xB0,0x5D,0x38,0xFF,0x58,0x32, /* y */ + 0x1F,0x2E,0x80,0x05,0x36,0xD5,0x38,0xCC,0xDA,0xA3, + 0xD9, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x02,0x01,0x08,0xA2,0xE0,0xCC,0x0D,0x99,0xF8,0xA5, + 0xEF } }; -static const unsigned char _EC_SECG_CHAR2_163R1_SEED[] = { - 0x24,0xB7,0xB1,0x37,0xC8,0xA1,0x4D,0x69,0x6E,0x67, - 0x68,0x75,0x61,0x51,0x75,0x6F,0xD0,0xDA,0x2E,0x5C}; -static const EC_CURVE_DATA _EC_SECG_CHAR2_163R1 = { - NID_X9_62_characteristic_two_field, - "0800000000000000000000000000000000000000C9", - "07B6882CAAEFA84F9554FF8428BD88E246D2782AE2", - "0713612DCDDCB40AAB946BDA29CA91F73AF958AFD9", - "0369979697AB43897789566789567F787A7876A654", - "00435EDB42EFAFB2989D51FEFCE3C80988F41FF883", - "03FFFFFFFFFFFFFFFFFFFF48AAB689C29CA710279B", 2, +static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } + _EC_SECG_CHAR2_163R1 = { + { NID_X9_62_characteristic_two_field,0,21,2 }, + { /* no seed */ +#if 0 /* The algorithm used to derive the curve parameters from * the seed used here is slightly different than the - * algorithm described in X9.62 . - */ -#if 0 - _EC_SECG_CHAR2_163R1_SEED, 20, -#else - NULL, 0, + * algorithm described in X9.62 . */ + 0x24,0xB7,0xB1,0x37,0xC8,0xA1,0x4D,0x69,0x6E,0x67, + 0x68,0x75,0x61,0x51,0x75,0x6F,0xD0,0xDA,0x2E,0x5C, #endif - "SECG curve over a 163 bit binary field" + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0xC9, + 0x07,0xB6,0x88,0x2C,0xAA,0xEF,0xA8,0x4F,0x95,0x54, /* a */ + 0xFF,0x84,0x28,0xBD,0x88,0xE2,0x46,0xD2,0x78,0x2A, + 0xE2, + 0x07,0x13,0x61,0x2D,0xCD,0xDC,0xB4,0x0A,0xAB,0x94, /* b */ + 0x6B,0xDA,0x29,0xCA,0x91,0xF7,0x3A,0xF9,0x58,0xAF, + 0xD9, + 0x03,0x69,0x97,0x96,0x97,0xAB,0x43,0x89,0x77,0x89, /* x */ + 0x56,0x67,0x89,0x56,0x7F,0x78,0x7A,0x78,0x76,0xA6, + 0x54, + 0x00,0x43,0x5E,0xDB,0x42,0xEF,0xAF,0xB2,0x98,0x9D, /* y */ + 0x51,0xFE,0xFC,0xE3,0xC8,0x09,0x88,0xF4,0x1F,0xF8, + 0x83, + 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0x48,0xAA,0xB6,0x89,0xC2,0x9C,0xA7,0x10,0x27, + 0x9B } }; -static const unsigned char _EC_NIST_CHAR2_163B_SEED[] = { - 0x85,0xE2,0x5B,0xFE,0x5C,0x86,0x22,0x6C,0xDB,0x12, - 0x01,0x6F,0x75,0x53,0xF9,0xD0,0xE6,0x93,0xA2,0x68}; -static const EC_CURVE_DATA _EC_NIST_CHAR2_163B ={ - NID_X9_62_characteristic_two_field, - "0800000000000000000000000000000000000000C9", - "1", - "020A601907B8C953CA1481EB10512F78744A3205FD", - "03F0EBA16286A2D57EA0991168D4994637E8343E36", - "00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1", - "040000000000000000000292FE77E70C12A4234C33", 2, -/* The seed here was used to created the curve parameters in normal - * basis representation (and not the polynomial representation used here) - */ +static const struct { EC_CURVE_DATA h; unsigned char data[0+21*6]; } + _EC_NIST_CHAR2_163B = { + { NID_X9_62_characteristic_two_field,0,21,2 }, + { /* no seed */ #if 0 - _EC_NIST_CHAR2_163B_SEED, 20, -#else - NULL, 0, +/* The seed here was used to created the curve parameters in normal + * basis representation (and not the polynomial representation used here) */ + 0x85,0xE2,0x5B,0xFE,0x5C,0x86,0x22,0x6C,0xDB,0x12, + 0x01,0x6F,0x75,0x53,0xF9,0xD0,0xE6,0x93,0xA2,0x68, #endif - "NIST/SECG curve over a 163 bit binary field" + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0xC9, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x01, + 0x02,0x0A,0x60,0x19,0x07,0xB8,0xC9,0x53,0xCA,0x14, /* b */ + 0x81,0xEB,0x10,0x51,0x2F,0x78,0x74,0x4A,0x32,0x05, + 0xFD, + 0x03,0xF0,0xEB,0xA1,0x62,0x86,0xA2,0xD5,0x7E,0xA0, /* x */ + 0x99,0x11,0x68,0xD4,0x99,0x46,0x37,0xE8,0x34,0x3E, + 0x36, + 0x00,0xD5,0x1F,0xBC,0x6C,0x71,0xA0,0x09,0x4F,0xA2, /* y */ + 0xCD,0xD5,0x45,0xB1,0x1C,0x5C,0x0C,0x79,0x73,0x24, + 0xF1, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x02,0x92,0xFE,0x77,0xE7,0x0C,0x12,0xA4,0x23,0x4C, + 0x33 } }; -static const unsigned char _EC_SECG_CHAR2_193R1_SEED[] = { - 0x10,0x3F,0xAE,0xC7,0x4D,0x69,0x6E,0x67,0x68,0x75, - 0x61,0x51,0x75,0x77,0x7F,0xC5,0xB1,0x91,0xEF,0x30}; -static const EC_CURVE_DATA _EC_SECG_CHAR2_193R1 = { - NID_X9_62_characteristic_two_field, - "02000000000000000000000000000000000000000000008001", - "0017858FEB7A98975169E171F77B4087DE098AC8A911DF7B01", - "00FDFB49BFE6C3A89FACADAA7A1E5BBC7CC1C2E5D831478814", - "01F481BC5F0FF84A74AD6CDF6FDEF4BF6179625372D8C0C5E1", - "0025E399F2903712CCF3EA9E3A1AD17FB0B3201B6AF7CE1B05", - "01000000000000000000000000C7F34A778F443ACC920EBA49", 2, - _EC_SECG_CHAR2_193R1_SEED, 20, - "SECG curve over a 193 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+25*6]; } + _EC_SECG_CHAR2_193R1 = { + { NID_X9_62_characteristic_two_field,20,25,2 }, + { 0x10,0x3F,0xAE,0xC7,0x4D,0x69,0x6E,0x67,0x68,0x75, /* seed */ + 0x61,0x51,0x75,0x77,0x7F,0xC5,0xB1,0x91,0xEF,0x30, + + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x80,0x01, + 0x00,0x17,0x85,0x8F,0xEB,0x7A,0x98,0x97,0x51,0x69, /* a */ + 0xE1,0x71,0xF7,0x7B,0x40,0x87,0xDE,0x09,0x8A,0xC8, + 0xA9,0x11,0xDF,0x7B,0x01, + 0x00,0xFD,0xFB,0x49,0xBF,0xE6,0xC3,0xA8,0x9F,0xAC, /* b */ + 0xAD,0xAA,0x7A,0x1E,0x5B,0xBC,0x7C,0xC1,0xC2,0xE5, + 0xD8,0x31,0x47,0x88,0x14, + 0x01,0xF4,0x81,0xBC,0x5F,0x0F,0xF8,0x4A,0x74,0xAD, /* x */ + 0x6C,0xDF,0x6F,0xDE,0xF4,0xBF,0x61,0x79,0x62,0x53, + 0x72,0xD8,0xC0,0xC5,0xE1, + 0x00,0x25,0xE3,0x99,0xF2,0x90,0x37,0x12,0xCC,0xF3, /* y */ + 0xEA,0x9E,0x3A,0x1A,0xD1,0x7F,0xB0,0xB3,0x20,0x1B, + 0x6A,0xF7,0xCE,0x1B,0x05, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x00,0xC7,0xF3,0x4A,0x77,0x8F,0x44,0x3A, + 0xCC,0x92,0x0E,0xBA,0x49 } }; -static const unsigned char _EC_SECG_CHAR2_193R2_SEED[] = { - 0x10,0xB7,0xB4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15, - 0x17,0x51,0x37,0xC8,0xA1,0x6F,0xD0,0xDA,0x22,0x11}; -static const EC_CURVE_DATA _EC_SECG_CHAR2_193R2 = { - NID_X9_62_characteristic_two_field, - "02000000000000000000000000000000000000000000008001", - "0163F35A5137C2CE3EA6ED8667190B0BC43ECD69977702709B", - "00C9BB9E8927D4D64C377E2AB2856A5B16E3EFB7F61D4316AE", - "00D9B67D192E0367C803F39E1A7E82CA14A651350AAE617E8F", - "01CE94335607C304AC29E7DEFBD9CA01F596F927224CDECF6C", - "010000000000000000000000015AAB561B005413CCD4EE99D5", 2, - _EC_SECG_CHAR2_193R2_SEED, 20, - "SECG curve over a 193 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+25*6]; } + _EC_SECG_CHAR2_193R2 = { + { NID_X9_62_characteristic_two_field,20,25,2 }, + { 0x10,0xB7,0xB4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15, /* seed */ + 0x17,0x51,0x37,0xC8,0xA1,0x6F,0xD0,0xDA,0x22,0x11, + + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x80,0x01, + 0x01,0x63,0xF3,0x5A,0x51,0x37,0xC2,0xCE,0x3E,0xA6, /* a */ + 0xED,0x86,0x67,0x19,0x0B,0x0B,0xC4,0x3E,0xCD,0x69, + 0x97,0x77,0x02,0x70,0x9B, + 0x00,0xC9,0xBB,0x9E,0x89,0x27,0xD4,0xD6,0x4C,0x37, /* b */ + 0x7E,0x2A,0xB2,0x85,0x6A,0x5B,0x16,0xE3,0xEF,0xB7, + 0xF6,0x1D,0x43,0x16,0xAE, + 0x00,0xD9,0xB6,0x7D,0x19,0x2E,0x03,0x67,0xC8,0x03, /* x */ + 0xF3,0x9E,0x1A,0x7E,0x82,0xCA,0x14,0xA6,0x51,0x35, + 0x0A,0xAE,0x61,0x7E,0x8F, + 0x01,0xCE,0x94,0x33,0x56,0x07,0xC3,0x04,0xAC,0x29, /* y */ + 0xE7,0xDE,0xFB,0xD9,0xCA,0x01,0xF5,0x96,0xF9,0x27, + 0x22,0x4C,0xDE,0xCF,0x6C, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x01,0x5A,0xAB,0x56,0x1B,0x00,0x54,0x13, + 0xCC,0xD4,0xEE,0x99,0xD5 } }; -static const EC_CURVE_DATA _EC_NIST_CHAR2_233K = { - NID_X9_62_characteristic_two_field, - "020000000000000000000000000000000000000004000000000000000001", - "0", - "1", - "017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126", - "01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3", - "008000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF", 4, - NULL, 0, - "NIST/SECG/WTLS curve over a 233 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+30*6]; } + _EC_NIST_CHAR2_233K = { + { NID_X9_62_characteristic_two_field,0,30,4 }, + { /* no seed */ + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + + 0x01,0x72,0x32,0xBA,0x85,0x3A,0x7E,0x73,0x1A,0xF1, /* x */ + 0x29,0xF2,0x2F,0xF4,0x14,0x95,0x63,0xA4,0x19,0xC2, + 0x6B,0xF5,0x0A,0x4C,0x9D,0x6E,0xEF,0xAD,0x61,0x26, + + 0x01,0xDB,0x53,0x7D,0xEC,0xE8,0x19,0xB7,0xF7,0x0F, /* y */ + 0x55,0x5A,0x67,0xC4,0x27,0xA8,0xCD,0x9B,0xF1,0x8A, + 0xEB,0x9B,0x56,0xE0,0xC1,0x10,0x56,0xFA,0xE6,0xA3, + + 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x00,0x00,0x00,0x06,0x9D,0x5B,0xB9,0x15, + 0xBC,0xD4,0x6E,0xFB,0x1A,0xD5,0xF1,0x73,0xAB,0xDF } }; -static const unsigned char _EC_NIST_CHAR2_233B_SEED[] = { - 0x74,0xD5,0x9F,0xF0,0x7F,0x6B,0x41,0x3D,0x0E,0xA1, - 0x4B,0x34,0x4B,0x20,0xA2,0xDB,0x04,0x9B,0x50,0xC3}; -static const EC_CURVE_DATA _EC_NIST_CHAR2_233B = { - NID_X9_62_characteristic_two_field, - "020000000000000000000000000000000000000004000000000000000001", - "000000000000000000000000000000000000000000000000000000000001", - "0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD", - "00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B", - "01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052", - "01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7", 2, - _EC_NIST_CHAR2_233B_SEED, 20, - "NIST/SECG/WTLS curve over a 233 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } + _EC_NIST_CHAR2_233B = { + { NID_X9_62_characteristic_two_field,20,30,2 }, + { 0x74,0xD5,0x9F,0xF0,0x7F,0x6B,0x41,0x3D,0x0E,0xA1, /* seed */ + 0x4B,0x34,0x4B,0x20,0xA2,0xDB,0x04,0x9B,0x50,0xC3, + + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + + 0x00,0x66,0x64,0x7E,0xDE,0x6C,0x33,0x2C,0x7F,0x8C, /* b */ + 0x09,0x23,0xBB,0x58,0x21,0x3B,0x33,0x3B,0x20,0xE9, + 0xCE,0x42,0x81,0xFE,0x11,0x5F,0x7D,0x8F,0x90,0xAD, + + 0x00,0xFA,0xC9,0xDF,0xCB,0xAC,0x83,0x13,0xBB,0x21, /* x */ + 0x39,0xF1,0xBB,0x75,0x5F,0xEF,0x65,0xBC,0x39,0x1F, + 0x8B,0x36,0xF8,0xF8,0xEB,0x73,0x71,0xFD,0x55,0x8B, + + 0x01,0x00,0x6A,0x08,0xA4,0x19,0x03,0x35,0x06,0x78, /* y */ + 0xE5,0x85,0x28,0xBE,0xBF,0x8A,0x0B,0xEF,0xF8,0x67, + 0xA7,0xCA,0x36,0x71,0x6F,0x7E,0x01,0xF8,0x10,0x52, + + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x00,0x00,0x00,0x13,0xE9,0x74,0xE7,0x2F, + 0x8A,0x69,0x22,0x03,0x1D,0x26,0x03,0xCF,0xE0,0xD7 } }; -static const EC_CURVE_DATA _EC_SECG_CHAR2_239K1 = { - NID_X9_62_characteristic_two_field, - "800000000000000000004000000000000000000000000000000000000001", - "0", - "1", - "29A0B6A887A983E9730988A68727A8B2D126C44CC2CC7B2A6555193035DC", - "76310804F12E549BDB011C103089E73510ACB275FC312A5DC6B76553F0CA", - "2000000000000000000000000000005A79FEC67CB6E91F1C1DA800E478A5", 4, - NULL, 0, - "SECG curve over a 239 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+30*6]; } + _EC_SECG_CHAR2_239K1 = { + { NID_X9_62_characteristic_two_field,0,30,4 }, + { /* no seed */ + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + + 0x29,0xA0,0xB6,0xA8,0x87,0xA9,0x83,0xE9,0x73,0x09, /* x */ + 0x88,0xA6,0x87,0x27,0xA8,0xB2,0xD1,0x26,0xC4,0x4C, + 0xC2,0xCC,0x7B,0x2A,0x65,0x55,0x19,0x30,0x35,0xDC, + + 0x76,0x31,0x08,0x04,0xF1,0x2E,0x54,0x9B,0xDB,0x01, /* y */ + 0x1C,0x10,0x30,0x89,0xE7,0x35,0x10,0xAC,0xB2,0x75, + 0xFC,0x31,0x2A,0x5D,0xC6,0xB7,0x65,0x53,0xF0,0xCA, + + 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x00,0x00,0x00,0x5A,0x79,0xFE,0xC6,0x7C, + 0xB6,0xE9,0x1F,0x1C,0x1D,0xA8,0x00,0xE4,0x78,0xA5 } }; -static const EC_CURVE_DATA _EC_NIST_CHAR2_283K = { - NID_X9_62_characteristic_two_field, - "080000000000000000000000000000000000000000000000000000000000000000001" - "0A1", - "0", - "1", - "0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492" - "836", - "01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2" - "259", - "01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163" - "C61", 4, - NULL, 20, - "NIST/SECG curve over a 283 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+36*6]; } + _EC_NIST_CHAR2_283K = { + { NID_X9_62_characteristic_two_field,0,36,4 }, + { /* no seed */ + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x10,0xA1, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x01, + 0x05,0x03,0x21,0x3F,0x78,0xCA,0x44,0x88,0x3F,0x1A, /* x */ + 0x3B,0x81,0x62,0xF1,0x88,0xE5,0x53,0xCD,0x26,0x5F, + 0x23,0xC1,0x56,0x7A,0x16,0x87,0x69,0x13,0xB0,0xC2, + 0xAC,0x24,0x58,0x49,0x28,0x36, + 0x01,0xCC,0xDA,0x38,0x0F,0x1C,0x9E,0x31,0x8D,0x90, /* y */ + 0xF9,0x5D,0x07,0xE5,0x42,0x6F,0xE8,0x7E,0x45,0xC0, + 0xE8,0x18,0x46,0x98,0xE4,0x59,0x62,0x36,0x4E,0x34, + 0x11,0x61,0x77,0xDD,0x22,0x59, + 0x01,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xE9,0xAE, + 0x2E,0xD0,0x75,0x77,0x26,0x5D,0xFF,0x7F,0x94,0x45, + 0x1E,0x06,0x1E,0x16,0x3C,0x61 } }; -static const unsigned char _EC_NIST_CHAR2_283B_SEED[] = { - 0x77,0xE2,0xB0,0x73,0x70,0xEB,0x0F,0x83,0x2A,0x6D, - 0xD5,0xB6,0x2D,0xFC,0x88,0xCD,0x06,0xBB,0x84,0xBE}; -static const EC_CURVE_DATA _EC_NIST_CHAR2_283B = { - NID_X9_62_characteristic_two_field, - "080000000000000000000000000000000000000000000000000000000000000000001" - "0A1", - "000000000000000000000000000000000000000000000000000000000000000000000" - "001", - "027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A" - "2F5", - "05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12" - "053", - "03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE811" - "2F4", - "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB" - "307", 2, - _EC_NIST_CHAR2_283B_SEED, 20, - "NIST/SECG curve over a 283 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+36*6]; } + _EC_NIST_CHAR2_283B = { + { NID_X9_62_characteristic_two_field,20,36,2 }, + { 0x77,0xE2,0xB0,0x73,0x70,0xEB,0x0F,0x83,0x2A,0x6D, /* no seed */ + 0xD5,0xB6,0x2D,0xFC,0x88,0xCD,0x06,0xBB,0x84,0xBE, + + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x10,0xA1, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x01, + 0x02,0x7B,0x68,0x0A,0xC8,0xB8,0x59,0x6D,0xA5,0xA4, /* b */ + 0xAF,0x8A,0x19,0xA0,0x30,0x3F,0xCA,0x97,0xFD,0x76, + 0x45,0x30,0x9F,0xA2,0xA5,0x81,0x48,0x5A,0xF6,0x26, + 0x3E,0x31,0x3B,0x79,0xA2,0xF5, + 0x05,0xF9,0x39,0x25,0x8D,0xB7,0xDD,0x90,0xE1,0x93, /* x */ + 0x4F,0x8C,0x70,0xB0,0xDF,0xEC,0x2E,0xED,0x25,0xB8, + 0x55,0x7E,0xAC,0x9C,0x80,0xE2,0xE1,0x98,0xF8,0xCD, + 0xBE,0xCD,0x86,0xB1,0x20,0x53, + 0x03,0x67,0x68,0x54,0xFE,0x24,0x14,0x1C,0xB9,0x8F, /* y */ + 0xE6,0xD4,0xB2,0x0D,0x02,0xB4,0x51,0x6F,0xF7,0x02, + 0x35,0x0E,0xDD,0xB0,0x82,0x67,0x79,0xC8,0x13,0xF0, + 0xDF,0x45,0xBE,0x81,0x12,0xF4, + 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xEF,0x90, + 0x39,0x96,0x60,0xFC,0x93,0x8A,0x90,0x16,0x5B,0x04, + 0x2A,0x7C,0xEF,0xAD,0xB3,0x07 } }; -static const EC_CURVE_DATA _EC_NIST_CHAR2_409K = { - NID_X9_62_characteristic_two_field, - "020000000000000000000000000000000000000000000000000000000000000000000" - "00000000000008000000000000000000001", - "0", - "1", - "0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C4601" - "89EB5AAAA62EE222EB1B35540CFE9023746", - "01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6" - "C42E9C55215AA9CA27A5863EC48D8E0286B", - "007FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F83B2D4EA20400" - "EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF", 4, - NULL, 0, - "NIST/SECG curve over a 409 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+52*6]; } + _EC_NIST_CHAR2_409K = { + { NID_X9_62_characteristic_two_field,0,52,4 }, + { /* no seed */ + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x01, + 0x00,0x60,0xF0,0x5F,0x65,0x8F,0x49,0xC1,0xAD,0x3A, /* x */ + 0xB1,0x89,0x0F,0x71,0x84,0x21,0x0E,0xFD,0x09,0x87, + 0xE3,0x07,0xC8,0x4C,0x27,0xAC,0xCF,0xB8,0xF9,0xF6, + 0x7C,0xC2,0xC4,0x60,0x18,0x9E,0xB5,0xAA,0xAA,0x62, + 0xEE,0x22,0x2E,0xB1,0xB3,0x55,0x40,0xCF,0xE9,0x02, + 0x37,0x46, + 0x01,0xE3,0x69,0x05,0x0B,0x7C,0x4E,0x42,0xAC,0xBA, /* y */ + 0x1D,0xAC,0xBF,0x04,0x29,0x9C,0x34,0x60,0x78,0x2F, + 0x91,0x8E,0xA4,0x27,0xE6,0x32,0x51,0x65,0xE9,0xEA, + 0x10,0xE3,0xDA,0x5F,0x6C,0x42,0xE9,0xC5,0x52,0x15, + 0xAA,0x9C,0xA2,0x7A,0x58,0x63,0xEC,0x48,0xD8,0xE0, + 0x28,0x6B, + 0x00,0x7F,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0x5F,0x83,0xB2, + 0xD4,0xEA,0x20,0x40,0x0E,0xC4,0x55,0x7D,0x5E,0xD3, + 0xE3,0xE7,0xCA,0x5B,0x4B,0x5C,0x83,0xB8,0xE0,0x1E, + 0x5F,0xCF } }; -static const unsigned char _EC_NIST_CHAR2_409B_SEED[] = { - 0x40,0x99,0xB5,0xA4,0x57,0xF9,0xD6,0x9F,0x79,0x21, - 0x3D,0x09,0x4C,0x4B,0xCD,0x4D,0x42,0x62,0x21,0x0B}; -static const EC_CURVE_DATA _EC_NIST_CHAR2_409B = { - NID_X9_62_characteristic_two_field, - "020000000000000000000000000000000000000000000000000000000000000000000" - "00000000000008000000000000000000001", - "000000000000000000000000000000000000000000000000000000000000000000000" - "00000000000000000000000000000000001", - "0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A19" - "7B272822F6CD57A55AA4F50AE317B13545F", - "015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255" - "A868A1180515603AEAB60794E54BB7996A7", - "0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514" - "F1FDF4B4F40D2181B3681C364BA0273C706", - "010000000000000000000000000000000000000000000000000001E2AAD6A612F3330" - "7BE5FA47C3C9E052F838164CD37D9A21173", 2, - _EC_NIST_CHAR2_409B_SEED, 20, - "NIST/SECG curve over a 409 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+52*6]; } + _EC_NIST_CHAR2_409B = { + { NID_X9_62_characteristic_two_field,20,52,2 }, + { 0x40,0x99,0xB5,0xA4,0x57,0xF9,0xD6,0x9F,0x79,0x21, /* seed */ + 0x3D,0x09,0x4C,0x4B,0xCD,0x4D,0x42,0x62,0x21,0x0B, + + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x01, + 0x00,0x21,0xA5,0xC2,0xC8,0xEE,0x9F,0xEB,0x5C,0x4B, /* b */ + 0x9A,0x75,0x3B,0x7B,0x47,0x6B,0x7F,0xD6,0x42,0x2E, + 0xF1,0xF3,0xDD,0x67,0x47,0x61,0xFA,0x99,0xD6,0xAC, + 0x27,0xC8,0xA9,0xA1,0x97,0xB2,0x72,0x82,0x2F,0x6C, + 0xD5,0x7A,0x55,0xAA,0x4F,0x50,0xAE,0x31,0x7B,0x13, + 0x54,0x5F, + 0x01,0x5D,0x48,0x60,0xD0,0x88,0xDD,0xB3,0x49,0x6B, /* x */ + 0x0C,0x60,0x64,0x75,0x62,0x60,0x44,0x1C,0xDE,0x4A, + 0xF1,0x77,0x1D,0x4D,0xB0,0x1F,0xFE,0x5B,0x34,0xE5, + 0x97,0x03,0xDC,0x25,0x5A,0x86,0x8A,0x11,0x80,0x51, + 0x56,0x03,0xAE,0xAB,0x60,0x79,0x4E,0x54,0xBB,0x79, + 0x96,0xA7, + 0x00,0x61,0xB1,0xCF,0xAB,0x6B,0xE5,0xF3,0x2B,0xBF, /* y */ + 0xA7,0x83,0x24,0xED,0x10,0x6A,0x76,0x36,0xB9,0xC5, + 0xA7,0xBD,0x19,0x8D,0x01,0x58,0xAA,0x4F,0x54,0x88, + 0xD0,0x8F,0x38,0x51,0x4F,0x1F,0xDF,0x4B,0x4F,0x40, + 0xD2,0x18,0x1B,0x36,0x81,0xC3,0x64,0xBA,0x02,0x73, + 0xC7,0x06, + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xE2,0xAA,0xD6, + 0xA6,0x12,0xF3,0x33,0x07,0xBE,0x5F,0xA4,0x7C,0x3C, + 0x9E,0x05,0x2F,0x83,0x81,0x64,0xCD,0x37,0xD9,0xA2, + 0x11,0x73 } }; -static const EC_CURVE_DATA _EC_NIST_CHAR2_571K = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000000000000000000000000000" - "000000000000000000000000000000000000000000000000000000000000000000000" - "00425", - "0", - "1", - "026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA443709" - "58493B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A0" - "1C8972", - "0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D497" - "9C0AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143E" - "F1C7A3", - "020000000000000000000000000000000000000000000000000000000000000000000" - "000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F63" - "7C1001", 4, - NULL, 0, - "NIST/SECG curve over a 571 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+72*6]; } + _EC_NIST_CHAR2_571K = { + { NID_X9_62_characteristic_two_field,0,72,4 }, + { /* no seed */ + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0x25, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x01, + 0x02,0x6E,0xB7,0xA8,0x59,0x92,0x3F,0xBC,0x82,0x18, /* x */ + 0x96,0x31,0xF8,0x10,0x3F,0xE4,0xAC,0x9C,0xA2,0x97, + 0x00,0x12,0xD5,0xD4,0x60,0x24,0x80,0x48,0x01,0x84, + 0x1C,0xA4,0x43,0x70,0x95,0x84,0x93,0xB2,0x05,0xE6, + 0x47,0xDA,0x30,0x4D,0xB4,0xCE,0xB0,0x8C,0xBB,0xD1, + 0xBA,0x39,0x49,0x47,0x76,0xFB,0x98,0x8B,0x47,0x17, + 0x4D,0xCA,0x88,0xC7,0xE2,0x94,0x52,0x83,0xA0,0x1C, + 0x89,0x72, + 0x03,0x49,0xDC,0x80,0x7F,0x4F,0xBF,0x37,0x4F,0x4A, /* y */ + 0xEA,0xDE,0x3B,0xCA,0x95,0x31,0x4D,0xD5,0x8C,0xEC, + 0x9F,0x30,0x7A,0x54,0xFF,0xC6,0x1E,0xFC,0x00,0x6D, + 0x8A,0x2C,0x9D,0x49,0x79,0xC0,0xAC,0x44,0xAE,0xA7, + 0x4F,0xBE,0xBB,0xB9,0xF7,0x72,0xAE,0xDC,0xB6,0x20, + 0xB0,0x1A,0x7B,0xA7,0xAF,0x1B,0x32,0x04,0x30,0xC8, + 0x59,0x19,0x84,0xF6,0x01,0xCD,0x4C,0x14,0x3E,0xF1, + 0xC7,0xA3, + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x13,0x18,0x50,0xE1, + 0xF1,0x9A,0x63,0xE4,0xB3,0x91,0xA8,0xDB,0x91,0x7F, + 0x41,0x38,0xB6,0x30,0xD8,0x4B,0xE5,0xD6,0x39,0x38, + 0x1E,0x91,0xDE,0xB4,0x5C,0xFE,0x77,0x8F,0x63,0x7C, + 0x10,0x01 } }; -static const unsigned char _EC_NIST_CHAR2_571B_SEED[] = { - 0x2A,0xA0,0x58,0xF7,0x3A,0x0E,0x33,0xAB,0x48,0x6B, - 0x0F,0x61,0x04,0x10,0xC5,0x3A,0x7F,0x13,0x23,0x10}; -static const EC_CURVE_DATA _EC_NIST_CHAR2_571B = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000000000000000000000000000" - "000000000000000000000000000000000000000000000000000000000000000000000" - "00425", - "000000000000000000000000000000000000000000000000000000000000000000000" - "000000000000000000000000000000000000000000000000000000000000000000000" - "000001", - "02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFA" - "BBD8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F29" - "55727A", - "0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53" - "950F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8E" - "EC2D19", - "037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423" - "E43BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B" - "8AC15B", - "03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" - "FFFE661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2F" - "E84E47", 2, - _EC_NIST_CHAR2_571B_SEED, 20, - "NIST/SECG curve over a 571 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+72*6]; } + _EC_NIST_CHAR2_571B = { + { NID_X9_62_characteristic_two_field,20,72,2 }, + { 0x2A,0xA0,0x58,0xF7,0x3A,0x0E,0x33,0xAB,0x48,0x6B, /* seed */ + 0x0F,0x61,0x04,0x10,0xC5,0x3A,0x7F,0x13,0x23,0x10, + + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x04,0x25, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x01, + 0x02,0xF4,0x0E,0x7E,0x22,0x21,0xF2,0x95,0xDE,0x29, /* b */ + 0x71,0x17,0xB7,0xF3,0xD6,0x2F,0x5C,0x6A,0x97,0xFF, + 0xCB,0x8C,0xEF,0xF1,0xCD,0x6B,0xA8,0xCE,0x4A,0x9A, + 0x18,0xAD,0x84,0xFF,0xAB,0xBD,0x8E,0xFA,0x59,0x33, + 0x2B,0xE7,0xAD,0x67,0x56,0xA6,0x6E,0x29,0x4A,0xFD, + 0x18,0x5A,0x78,0xFF,0x12,0xAA,0x52,0x0E,0x4D,0xE7, + 0x39,0xBA,0xCA,0x0C,0x7F,0xFE,0xFF,0x7F,0x29,0x55, + 0x72,0x7A, + 0x03,0x03,0x00,0x1D,0x34,0xB8,0x56,0x29,0x6C,0x16, /* x */ + 0xC0,0xD4,0x0D,0x3C,0xD7,0x75,0x0A,0x93,0xD1,0xD2, + 0x95,0x5F,0xA8,0x0A,0xA5,0xF4,0x0F,0xC8,0xDB,0x7B, + 0x2A,0xBD,0xBD,0xE5,0x39,0x50,0xF4,0xC0,0xD2,0x93, + 0xCD,0xD7,0x11,0xA3,0x5B,0x67,0xFB,0x14,0x99,0xAE, + 0x60,0x03,0x86,0x14,0xF1,0x39,0x4A,0xBF,0xA3,0xB4, + 0xC8,0x50,0xD9,0x27,0xE1,0xE7,0x76,0x9C,0x8E,0xEC, + 0x2D,0x19, + 0x03,0x7B,0xF2,0x73,0x42,0xDA,0x63,0x9B,0x6D,0xCC, /* y */ + 0xFF,0xFE,0xB7,0x3D,0x69,0xD7,0x8C,0x6C,0x27,0xA6, + 0x00,0x9C,0xBB,0xCA,0x19,0x80,0xF8,0x53,0x39,0x21, + 0xE8,0xA6,0x84,0x42,0x3E,0x43,0xBA,0xB0,0x8A,0x57, + 0x62,0x91,0xAF,0x8F,0x46,0x1B,0xB2,0xA8,0xB3,0x53, + 0x1D,0x2F,0x04,0x85,0xC1,0x9B,0x16,0xE2,0xF1,0x51, + 0x6E,0x23,0xDD,0x3C,0x1A,0x48,0x27,0xAF,0x1B,0x8A, + 0xC1,0x5B, + 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xE6,0x61,0xCE,0x18, + 0xFF,0x55,0x98,0x73,0x08,0x05,0x9B,0x18,0x68,0x23, + 0x85,0x1E,0xC7,0xDD,0x9C,0xA1,0x16,0x1D,0xE9,0x3D, + 0x51,0x74,0xD6,0x6E,0x83,0x82,0xE9,0xBB,0x2F,0xE8, + 0x4E,0x47 } }; -static const unsigned char _EC_X9_62_CHAR2_163V1_SEED[] = { - 0xD2,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE, - 0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x54}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_163V1 = { - NID_X9_62_characteristic_two_field, - "080000000000000000000000000000000000000107", - "072546B5435234A422E0789675F432C89435DE5242", - "00C9517D06D5240D3CFF38C74B20B6CD4D6F9DD4D9", - "07AF69989546103D79329FCC3D74880F33BBE803CB", - "01EC23211B5966ADEA1D3F87F7EA5848AEF0B7CA9F", - "0400000000000000000001E60FC8821CC74DAEAFC1", 2, - _EC_X9_62_CHAR2_163V1_SEED, 20, - "X9.62 curve over a 163 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } + _EC_X9_62_CHAR2_163V1 = { + { NID_X9_62_characteristic_two_field,20,21,2 }, + { 0xD2,0xC0,0xFB,0x15,0x76,0x08,0x60,0xDE,0xF1,0xEE, + 0xF4,0xD6,0x96,0xE6,0x76,0x87,0x56,0x15,0x17,0x54, /* seed */ + + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x07, + 0x07,0x25,0x46,0xB5,0x43,0x52,0x34,0xA4,0x22,0xE0, /* a */ + 0x78,0x96,0x75,0xF4,0x32,0xC8,0x94,0x35,0xDE,0x52, + 0x42, + 0x00,0xC9,0x51,0x7D,0x06,0xD5,0x24,0x0D,0x3C,0xFF, /* b */ + 0x38,0xC7,0x4B,0x20,0xB6,0xCD,0x4D,0x6F,0x9D,0xD4, + 0xD9, + 0x07,0xAF,0x69,0x98,0x95,0x46,0x10,0x3D,0x79,0x32, /* x */ + 0x9F,0xCC,0x3D,0x74,0x88,0x0F,0x33,0xBB,0xE8,0x03, + 0xCB, + 0x01,0xEC,0x23,0x21,0x1B,0x59,0x66,0xAD,0xEA,0x1D, /* y */ + 0x3F,0x87,0xF7,0xEA,0x58,0x48,0xAE,0xF0,0xB7,0xCA, + 0x9F, + 0x04,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x01,0xE6,0x0F,0xC8,0x82,0x1C,0xC7,0x4D,0xAE,0xAF, + 0xC1 } }; -static const unsigned char _EC_X9_62_CHAR2_163V2_SEED[] = { - 0x53,0x81,0x4C,0x05,0x0D,0x44,0xD6,0x96,0xE6,0x76, - 0x87,0x56,0x15,0x17,0x58,0x0C,0xA4,0xE2,0x9F,0xFD}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_163V2 = { - NID_X9_62_characteristic_two_field, - "080000000000000000000000000000000000000107", - "0108B39E77C4B108BED981ED0E890E117C511CF072", - "0667ACEB38AF4E488C407433FFAE4F1C811638DF20", - "0024266E4EB5106D0A964D92C4860E2671DB9B6CC5", - "079F684DDF6684C5CD258B3890021B2386DFD19FC5", - "03FFFFFFFFFFFFFFFFFFFDF64DE1151ADBB78F10A7", 2, - _EC_X9_62_CHAR2_163V2_SEED, 20, - "X9.62 curve over a 163 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } + _EC_X9_62_CHAR2_163V2 = { + { NID_X9_62_characteristic_two_field,20,21,2 }, + { 0x53,0x81,0x4C,0x05,0x0D,0x44,0xD6,0x96,0xE6,0x76, /* seed */ + 0x87,0x56,0x15,0x17,0x58,0x0C,0xA4,0xE2,0x9F,0xFD, + + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x07, + 0x01,0x08,0xB3,0x9E,0x77,0xC4,0xB1,0x08,0xBE,0xD9, /* a */ + 0x81,0xED,0x0E,0x89,0x0E,0x11,0x7C,0x51,0x1C,0xF0, + 0x72, + 0x06,0x67,0xAC,0xEB,0x38,0xAF,0x4E,0x48,0x8C,0x40, /* b */ + 0x74,0x33,0xFF,0xAE,0x4F,0x1C,0x81,0x16,0x38,0xDF, + 0x20, + 0x00,0x24,0x26,0x6E,0x4E,0xB5,0x10,0x6D,0x0A,0x96, /* x */ + 0x4D,0x92,0xC4,0x86,0x0E,0x26,0x71,0xDB,0x9B,0x6C, + 0xC5, + 0x07,0x9F,0x68,0x4D,0xDF,0x66,0x84,0xC5,0xCD,0x25, /* y */ + 0x8B,0x38,0x90,0x02,0x1B,0x23,0x86,0xDF,0xD1,0x9F, + 0xC5, + 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFD,0xF6,0x4D,0xE1,0x15,0x1A,0xDB,0xB7,0x8F,0x10, + 0xA7 } }; -static const unsigned char _EC_X9_62_CHAR2_163V3_SEED[] = { - 0x50,0xCB,0xF1,0xD9,0x5C,0xA9,0x4D,0x69,0x6E,0x67, - 0x68,0x75,0x61,0x51,0x75,0xF1,0x6A,0x36,0xA3,0xB8}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_163V3 = { - NID_X9_62_characteristic_two_field, - "080000000000000000000000000000000000000107", - "07A526C63D3E25A256A007699F5447E32AE456B50E", - "03F7061798EB99E238FD6F1BF95B48FEEB4854252B", - "02F9F87B7C574D0BDECF8A22E6524775F98CDEBDCB", - "05B935590C155E17EA48EB3FF3718B893DF59A05D0", - "03FFFFFFFFFFFFFFFFFFFE1AEE140F110AFF961309", 2, - _EC_X9_62_CHAR2_163V3_SEED, 20, - "X9.62 curve over a 163 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+21*6]; } + _EC_X9_62_CHAR2_163V3 = { + { NID_X9_62_characteristic_two_field,20,21,2 }, + { 0x50,0xCB,0xF1,0xD9,0x5C,0xA9,0x4D,0x69,0x6E,0x67, /* seed */ + 0x68,0x75,0x61,0x51,0x75,0xF1,0x6A,0x36,0xA3,0xB8, + + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + 0x07, + 0x07,0xA5,0x26,0xC6,0x3D,0x3E,0x25,0xA2,0x56,0xA0, /* a */ + 0x07,0x69,0x9F,0x54,0x47,0xE3,0x2A,0xE4,0x56,0xB5, + 0x0E, + 0x03,0xF7,0x06,0x17,0x98,0xEB,0x99,0xE2,0x38,0xFD, /* b */ + 0x6F,0x1B,0xF9,0x5B,0x48,0xFE,0xEB,0x48,0x54,0x25, + 0x2B, + 0x02,0xF9,0xF8,0x7B,0x7C,0x57,0x4D,0x0B,0xDE,0xCF, /* x */ + 0x8A,0x22,0xE6,0x52,0x47,0x75,0xF9,0x8C,0xDE,0xBD, + 0xCB, + 0x05,0xB9,0x35,0x59,0x0C,0x15,0x5E,0x17,0xEA,0x48, /* y */ + 0xEB,0x3F,0xF3,0x71,0x8B,0x89,0x3D,0xF5,0x9A,0x05, + 0xD0, + 0x03,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFE,0x1A,0xEE,0x14,0x0F,0x11,0x0A,0xFF,0x96,0x13, + 0x09 } }; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_176V1 = { - NID_X9_62_characteristic_two_field, - "0100000000000000000000000000000000080000000007", - "E4E6DB2995065C407D9D39B8D0967B96704BA8E9C90B", - "5DDA470ABE6414DE8EC133AE28E9BBD7FCEC0AE0FFF2", - "8D16C2866798B600F9F08BB4A8E860F3298CE04A5798", - "6FA4539C2DADDDD6BAB5167D61B436E1D92BB16A562C", - "00010092537397ECA4F6145799D62B0A19CE06FE26AD", 0xFF6E, - NULL, 0, - "X9.62 curve over a 176 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+23*6]; } + _EC_X9_62_CHAR2_176V1 = { + { NID_X9_62_characteristic_two_field,0,23,0xFF6E }, + { /* no seed */ + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x00,0x00, + 0x00,0x00,0x07, + 0x00,0xE4,0xE6,0xDB,0x29,0x95,0x06,0x5C,0x40,0x7D, /* a */ + 0x9D,0x39,0xB8,0xD0,0x96,0x7B,0x96,0x70,0x4B,0xA8, + 0xE9,0xC9,0x0B, + 0x00,0x5D,0xDA,0x47,0x0A,0xBE,0x64,0x14,0xDE,0x8E, /* b */ + 0xC1,0x33,0xAE,0x28,0xE9,0xBB,0xD7,0xFC,0xEC,0x0A, + 0xE0,0xFF,0xF2, + 0x00,0x8D,0x16,0xC2,0x86,0x67,0x98,0xB6,0x00,0xF9, /* x */ + 0xF0,0x8B,0xB4,0xA8,0xE8,0x60,0xF3,0x29,0x8C,0xE0, + 0x4A,0x57,0x98, + 0x00,0x6F,0xA4,0x53,0x9C,0x2D,0xAD,0xDD,0xD6,0xBA, /* y */ + 0xB5,0x16,0x7D,0x61,0xB4,0x36,0xE1,0xD9,0x2B,0xB1, + 0x6A,0x56,0x2C, + 0x00,0x00,0x01,0x00,0x92,0x53,0x73,0x97,0xEC,0xA4, /* order */ + 0xF6,0x14,0x57,0x99,0xD6,0x2B,0x0A,0x19,0xCE,0x06, + 0xFE,0x26,0xAD } }; -static const unsigned char _EC_X9_62_CHAR2_191V1_SEED[] = { - 0x4E,0x13,0xCA,0x54,0x27,0x44,0xD6,0x96,0xE6,0x76, - 0x87,0x56,0x15,0x17,0x55,0x2F,0x27,0x9A,0x8C,0x84}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_191V1 = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000201", - "2866537B676752636A68F56554E12640276B649EF7526267", - "2E45EF571F00786F67B0081B9495A3D95462F5DE0AA185EC", - "36B3DAF8A23206F9C4F299D7B21A9C369137F2C84AE1AA0D", - "765BE73433B3F95E332932E70EA245CA2418EA0EF98018FB", - "40000000000000000000000004A20E90C39067C893BBB9A5", 2, - _EC_X9_62_CHAR2_191V1_SEED, 20, - "X9.62 curve over a 191 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } + _EC_X9_62_CHAR2_191V1 = { + { NID_X9_62_characteristic_two_field,20,24,2 }, + { 0x4E,0x13,0xCA,0x54,0x27,0x44,0xD6,0x96,0xE6,0x76, /* seed */ + 0x87,0x56,0x15,0x17,0x55,0x2F,0x27,0x9A,0x8C,0x84, + + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x02,0x01, + 0x28,0x66,0x53,0x7B,0x67,0x67,0x52,0x63,0x6A,0x68, /* a */ + 0xF5,0x65,0x54,0xE1,0x26,0x40,0x27,0x6B,0x64,0x9E, + 0xF7,0x52,0x62,0x67, + 0x2E,0x45,0xEF,0x57,0x1F,0x00,0x78,0x6F,0x67,0xB0, /* b */ + 0x08,0x1B,0x94,0x95,0xA3,0xD9,0x54,0x62,0xF5,0xDE, + 0x0A,0xA1,0x85,0xEC, + 0x36,0xB3,0xDA,0xF8,0xA2,0x32,0x06,0xF9,0xC4,0xF2, /* x */ + 0x99,0xD7,0xB2,0x1A,0x9C,0x36,0x91,0x37,0xF2,0xC8, + 0x4A,0xE1,0xAA,0x0D, + 0x76,0x5B,0xE7,0x34,0x33,0xB3,0xF9,0x5E,0x33,0x29, /* y */ + 0x32,0xE7,0x0E,0xA2,0x45,0xCA,0x24,0x18,0xEA,0x0E, + 0xF9,0x80,0x18,0xFB, + 0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x04,0xA2,0x0E,0x90,0xC3,0x90,0x67,0xC8, + 0x93,0xBB,0xB9,0xA5 } }; -static const unsigned char _EC_X9_62_CHAR2_191V2_SEED[] = { - 0x08,0x71,0xEF,0x2F,0xEF,0x24,0xD6,0x96,0xE6,0x76, - 0x87,0x56,0x15,0x17,0x58,0xBE,0xE0,0xD9,0x5C,0x15}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_191V2 = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000201", - "401028774D7777C7B7666D1366EA432071274F89FF01E718", - "0620048D28BCBD03B6249C99182B7C8CD19700C362C46A01", - "3809B2B7CC1B28CC5A87926AAD83FD28789E81E2C9E3BF10", - "17434386626D14F3DBF01760D9213A3E1CF37AEC437D668A", - "20000000000000000000000050508CB89F652824E06B8173", 4, - _EC_X9_62_CHAR2_191V2_SEED, 20, - "X9.62 curve over a 191 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } + _EC_X9_62_CHAR2_191V2 = { + { NID_X9_62_characteristic_two_field,20,24,4 }, + { 0x08,0x71,0xEF,0x2F,0xEF,0x24,0xD6,0x96,0xE6,0x76, /* seed */ + 0x87,0x56,0x15,0x17,0x58,0xBE,0xE0,0xD9,0x5C,0x15, + + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x02,0x01, + 0x40,0x10,0x28,0x77,0x4D,0x77,0x77,0xC7,0xB7,0x66, /* a */ + 0x6D,0x13,0x66,0xEA,0x43,0x20,0x71,0x27,0x4F,0x89, + 0xFF,0x01,0xE7,0x18, + 0x06,0x20,0x04,0x8D,0x28,0xBC,0xBD,0x03,0xB6,0x24, /* b */ + 0x9C,0x99,0x18,0x2B,0x7C,0x8C,0xD1,0x97,0x00,0xC3, + 0x62,0xC4,0x6A,0x01, + 0x38,0x09,0xB2,0xB7,0xCC,0x1B,0x28,0xCC,0x5A,0x87, /* x */ + 0x92,0x6A,0xAD,0x83,0xFD,0x28,0x78,0x9E,0x81,0xE2, + 0xC9,0xE3,0xBF,0x10, + 0x17,0x43,0x43,0x86,0x62,0x6D,0x14,0xF3,0xDB,0xF0, /* y */ + 0x17,0x60,0xD9,0x21,0x3A,0x3E,0x1C,0xF3,0x7A,0xEC, + 0x43,0x7D,0x66,0x8A, + 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x50,0x50,0x8C,0xB8,0x9F,0x65,0x28,0x24, + 0xE0,0x6B,0x81,0x73 } }; -static const unsigned char _EC_X9_62_CHAR2_191V3_SEED[] = { - 0xE0,0x53,0x51,0x2D,0xC6,0x84,0xD6,0x96,0xE6,0x76, - 0x87,0x56,0x15,0x17,0x50,0x67,0xAE,0x78,0x6D,0x1F}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_191V3 = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000201", - "6C01074756099122221056911C77D77E77A777E7E7E77FCB", - "71FE1AF926CF847989EFEF8DB459F66394D90F32AD3F15E8", - "375D4CE24FDE434489DE8746E71786015009E66E38A926DD", - "545A39176196575D985999366E6AD34CE0A77CD7127B06BE", - "155555555555555555555555610C0B196812BFB6288A3EA3", 6, - _EC_X9_62_CHAR2_191V3_SEED, 20, - "X9.62 curve over a 191 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+24*6]; } + _EC_X9_62_CHAR2_191V3 = { + { NID_X9_62_characteristic_two_field,20,24,6 }, + { 0xE0,0x53,0x51,0x2D,0xC6,0x84,0xD6,0x96,0xE6,0x76, /* seed */ + 0x87,0x56,0x15,0x17,0x50,0x67,0xAE,0x78,0x6D,0x1F, + + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x02,0x01, + 0x6C,0x01,0x07,0x47,0x56,0x09,0x91,0x22,0x22,0x10, /* a */ + 0x56,0x91,0x1C,0x77,0xD7,0x7E,0x77,0xA7,0x77,0xE7, + 0xE7,0xE7,0x7F,0xCB, + 0x71,0xFE,0x1A,0xF9,0x26,0xCF,0x84,0x79,0x89,0xEF, /* b */ + 0xEF,0x8D,0xB4,0x59,0xF6,0x63,0x94,0xD9,0x0F,0x32, + 0xAD,0x3F,0x15,0xE8, + 0x37,0x5D,0x4C,0xE2,0x4F,0xDE,0x43,0x44,0x89,0xDE, /* x */ + 0x87,0x46,0xE7,0x17,0x86,0x01,0x50,0x09,0xE6,0x6E, + 0x38,0xA9,0x26,0xDD, + 0x54,0x5A,0x39,0x17,0x61,0x96,0x57,0x5D,0x98,0x59, /* y */ + 0x99,0x36,0x6E,0x6A,0xD3,0x4C,0xE0,0xA7,0x7C,0xD7, + 0x12,0x7B,0x06,0xBE, + 0x15,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55, /* order */ + 0x55,0x55,0x61,0x0C,0x0B,0x19,0x68,0x12,0xBF,0xB6, + 0x28,0x8A,0x3E,0xA3 } }; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_208W1 = { - NID_X9_62_characteristic_two_field, - "010000000000000000000000000000000800000000000000000007", - "0000000000000000000000000000000000000000000000000000", - "C8619ED45A62E6212E1160349E2BFA844439FAFC2A3FD1638F9E", - "89FDFBE4ABE193DF9559ECF07AC0CE78554E2784EB8C1ED1A57A", - "0F55B51A06E78E9AC38A035FF520D8B01781BEB1A6BB08617DE3", - "000101BAF95C9723C57B6C21DA2EFF2D5ED588BDD5717E212F9D", 0xFE48, - NULL, 0, - "X9.62 curve over a 208 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+27*6]; } + _EC_X9_62_CHAR2_208W1 = { + { NID_X9_62_characteristic_two_field,0,27,0xFE48 }, + { /* no seed */ + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x07, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0xC8,0x61,0x9E,0xD4,0x5A,0x62,0xE6,0x21,0x2E, /* b */ + 0x11,0x60,0x34,0x9E,0x2B,0xFA,0x84,0x44,0x39,0xFA, + 0xFC,0x2A,0x3F,0xD1,0x63,0x8F,0x9E, + 0x00,0x89,0xFD,0xFB,0xE4,0xAB,0xE1,0x93,0xDF,0x95, /* x */ + 0x59,0xEC,0xF0,0x7A,0xC0,0xCE,0x78,0x55,0x4E,0x27, + 0x84,0xEB,0x8C,0x1E,0xD1,0xA5,0x7A, + 0x00,0x0F,0x55,0xB5,0x1A,0x06,0xE7,0x8E,0x9A,0xC3, /* y */ + 0x8A,0x03,0x5F,0xF5,0x20,0xD8,0xB0,0x17,0x81,0xBE, + 0xB1,0xA6,0xBB,0x08,0x61,0x7D,0xE3, + 0x00,0x00,0x01,0x01,0xBA,0xF9,0x5C,0x97,0x23,0xC5, /* order */ + 0x7B,0x6C,0x21,0xDA,0x2E,0xFF,0x2D,0x5E,0xD5,0x88, + 0xBD,0xD5,0x71,0x7E,0x21,0x2F,0x9D } }; -static const unsigned char _EC_X9_62_CHAR2_239V1_SEED[] = { - 0xD3,0x4B,0x9A,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, - 0x51,0x75,0xCA,0x71,0xB9,0x20,0xBF,0xEF,0xB0,0x5D}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_239V1 = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000000001000000001", - "32010857077C5431123A46B808906756F543423E8D27877578125778AC76", - "790408F2EEDAF392B012EDEFB3392F30F4327C0CA3F31FC383C422AA8C16", - "57927098FA932E7C0A96D3FD5B706EF7E5F5C156E16B7E7C86038552E91D", - "61D8EE5077C33FECF6F1A16B268DE469C3C7744EA9A971649FC7A9616305", - "2000000000000000000000000000000F4D42FFE1492A4993F1CAD666E447", 4, - _EC_X9_62_CHAR2_239V1_SEED, 20, - "X9.62 curve over a 239 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } + _EC_X9_62_CHAR2_239V1 = { + { NID_X9_62_characteristic_two_field,20,30,4 }, + { 0xD3,0x4B,0x9A,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ + 0x51,0x75,0xCA,0x71,0xB9,0x20,0xBF,0xEF,0xB0,0x5D, + + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, + + 0x32,0x01,0x08,0x57,0x07,0x7C,0x54,0x31,0x12,0x3A, /* a */ + 0x46,0xB8,0x08,0x90,0x67,0x56,0xF5,0x43,0x42,0x3E, + 0x8D,0x27,0x87,0x75,0x78,0x12,0x57,0x78,0xAC,0x76, + + 0x79,0x04,0x08,0xF2,0xEE,0xDA,0xF3,0x92,0xB0,0x12, /* b */ + 0xED,0xEF,0xB3,0x39,0x2F,0x30,0xF4,0x32,0x7C,0x0C, + 0xA3,0xF3,0x1F,0xC3,0x83,0xC4,0x22,0xAA,0x8C,0x16, + + 0x57,0x92,0x70,0x98,0xFA,0x93,0x2E,0x7C,0x0A,0x96, /* x */ + 0xD3,0xFD,0x5B,0x70,0x6E,0xF7,0xE5,0xF5,0xC1,0x56, + 0xE1,0x6B,0x7E,0x7C,0x86,0x03,0x85,0x52,0xE9,0x1D, + + 0x61,0xD8,0xEE,0x50,0x77,0xC3,0x3F,0xEC,0xF6,0xF1, /* y */ + 0xA1,0x6B,0x26,0x8D,0xE4,0x69,0xC3,0xC7,0x74,0x4E, + 0xA9,0xA9,0x71,0x64,0x9F,0xC7,0xA9,0x61,0x63,0x05, + + 0x20,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* order */ + 0x00,0x00,0x00,0x00,0x00,0x0F,0x4D,0x42,0xFF,0xE1, + 0x49,0x2A,0x49,0x93,0xF1,0xCA,0xD6,0x66,0xE4,0x47 } }; -static const unsigned char _EC_X9_62_CHAR2_239V2_SEED[] = { - 0x2A,0xA6,0x98,0x2F,0xDF,0xA4,0xD6,0x96,0xE6,0x76, - 0x87,0x56,0x15,0x17,0x5D,0x26,0x67,0x27,0x27,0x7D}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_239V2 = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000000001000000001", - "4230017757A767FAE42398569B746325D45313AF0766266479B75654E65F", - "5037EA654196CFF0CD82B2C14A2FCF2E3FF8775285B545722F03EACDB74B", - "28F9D04E900069C8DC47A08534FE76D2B900B7D7EF31F5709F200C4CA205", - "5667334C45AFF3B5A03BAD9DD75E2C71A99362567D5453F7FA6E227EC833", - "1555555555555555555555555555553C6F2885259C31E3FCDF154624522D", 6, - _EC_X9_62_CHAR2_239V2_SEED, 20, - "X9.62 curve over a 239 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } + _EC_X9_62_CHAR2_239V2 = { + { NID_X9_62_characteristic_two_field,20,30,6 }, + { 0x2A,0xA6,0x98,0x2F,0xDF,0xA4,0xD6,0x96,0xE6,0x76, /* seed */ + 0x87,0x56,0x15,0x17,0x5D,0x26,0x67,0x27,0x27,0x7D, + + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, + + 0x42,0x30,0x01,0x77,0x57,0xA7,0x67,0xFA,0xE4,0x23, /* a */ + 0x98,0x56,0x9B,0x74,0x63,0x25,0xD4,0x53,0x13,0xAF, + 0x07,0x66,0x26,0x64,0x79,0xB7,0x56,0x54,0xE6,0x5F, + + 0x50,0x37,0xEA,0x65,0x41,0x96,0xCF,0xF0,0xCD,0x82, /* b */ + 0xB2,0xC1,0x4A,0x2F,0xCF,0x2E,0x3F,0xF8,0x77,0x52, + 0x85,0xB5,0x45,0x72,0x2F,0x03,0xEA,0xCD,0xB7,0x4B, + + 0x28,0xF9,0xD0,0x4E,0x90,0x00,0x69,0xC8,0xDC,0x47, /* x */ + 0xA0,0x85,0x34,0xFE,0x76,0xD2,0xB9,0x00,0xB7,0xD7, + 0xEF,0x31,0xF5,0x70,0x9F,0x20,0x0C,0x4C,0xA2,0x05, + + 0x56,0x67,0x33,0x4C,0x45,0xAF,0xF3,0xB5,0xA0,0x3B, /* y */ + 0xAD,0x9D,0xD7,0x5E,0x2C,0x71,0xA9,0x93,0x62,0x56, + 0x7D,0x54,0x53,0xF7,0xFA,0x6E,0x22,0x7E,0xC8,0x33, + + 0x15,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55,0x55, /* order */ + 0x55,0x55,0x55,0x55,0x55,0x3C,0x6F,0x28,0x85,0x25, + 0x9C,0x31,0xE3,0xFC,0xDF,0x15,0x46,0x24,0x52,0x2D } }; -static const unsigned char _EC_X9_62_CHAR2_239V3_SEED[] = { - 0x9E,0x07,0x6F,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, - 0x51,0x75,0xE1,0x1E,0x9F,0xDD,0x77,0xF9,0x20,0x41}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_239V3 = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000000001000000001", - "01238774666A67766D6676F778E676B66999176666E687666D8766C66A9F", - "6A941977BA9F6A435199ACFC51067ED587F519C5ECB541B8E44111DE1D40", - "70F6E9D04D289C4E89913CE3530BFDE903977D42B146D539BF1BDE4E9C92", - "2E5A0EAF6E5E1305B9004DCE5C0ED7FE59A35608F33837C816D80B79F461", - "0CCCCCCCCCCCCCCCCCCCCCCCCCCCCCAC4912D2D9DF903EF9888B8A0E4CFF", 0xA, - _EC_X9_62_CHAR2_239V3_SEED, 20, - "X9.62 curve over a 239 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+30*6]; } + _EC_X9_62_CHAR2_239V3 = { + { NID_X9_62_characteristic_two_field,20,30,0xA }, + { 0x9E,0x07,0x6F,0x4D,0x69,0x6E,0x67,0x68,0x75,0x61, /* seed */ + 0x51,0x75,0xE1,0x1E,0x9F,0xDD,0x77,0xF9,0x20,0x41, + + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00,0x01, + + 0x01,0x23,0x87,0x74,0x66,0x6A,0x67,0x76,0x6D,0x66, /* a */ + 0x76,0xF7,0x78,0xE6,0x76,0xB6,0x69,0x99,0x17,0x66, + 0x66,0xE6,0x87,0x66,0x6D,0x87,0x66,0xC6,0x6A,0x9F, + + 0x6A,0x94,0x19,0x77,0xBA,0x9F,0x6A,0x43,0x51,0x99, /* b */ + 0xAC,0xFC,0x51,0x06,0x7E,0xD5,0x87,0xF5,0x19,0xC5, + 0xEC,0xB5,0x41,0xB8,0xE4,0x41,0x11,0xDE,0x1D,0x40, + + 0x70,0xF6,0xE9,0xD0,0x4D,0x28,0x9C,0x4E,0x89,0x91, /* x */ + 0x3C,0xE3,0x53,0x0B,0xFD,0xE9,0x03,0x97,0x7D,0x42, + 0xB1,0x46,0xD5,0x39,0xBF,0x1B,0xDE,0x4E,0x9C,0x92, + + 0x2E,0x5A,0x0E,0xAF,0x6E,0x5E,0x13,0x05,0xB9,0x00, /* y */ + 0x4D,0xCE,0x5C,0x0E,0xD7,0xFE,0x59,0xA3,0x56,0x08, + 0xF3,0x38,0x37,0xC8,0x16,0xD8,0x0B,0x79,0xF4,0x61, + + 0x0C,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC,0xCC, /* order */ + 0xCC,0xCC,0xCC,0xCC,0xCC,0xAC,0x49,0x12,0xD2,0xD9, + 0xDF,0x90,0x3E,0xF9,0x88,0x8B,0x8A,0x0E,0x4C,0xFF } }; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_272W1 = { - NID_X9_62_characteristic_two_field, - "010000000000000000000000000000000000000000000000000000010000000000000" - "B", - "91A091F03B5FBA4AB2CCF49C4EDD220FB028712D42BE752B2C40094DBACDB586FB20", - "7167EFC92BB2E3CE7C8AAAFF34E12A9C557003D7C73A6FAF003F99F6CC8482E540F7", - "6108BABB2CEEBCF787058A056CBE0CFE622D7723A289E08A07AE13EF0D10D171DD8D", - "10C7695716851EEF6BA7F6872E6142FBD241B830FF5EFCACECCAB05E02005DDE9D23", - "000100FAF51354E0E39E4892DF6E319C72C8161603FA45AA7B998A167B8F1E629521", - 0xFF06, - NULL, 0, - "X9.62 curve over a 272 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+35*6]; } + _EC_X9_62_CHAR2_272W1 = { + { NID_X9_62_characteristic_two_field,0,35,0xFF06 }, + { /* no seed */ + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00,0x00, + 0x00,0x00,0x00,0x00,0x0B, + 0x00,0x91,0xA0,0x91,0xF0,0x3B,0x5F,0xBA,0x4A,0xB2, /* a */ + 0xCC,0xF4,0x9C,0x4E,0xDD,0x22,0x0F,0xB0,0x28,0x71, + 0x2D,0x42,0xBE,0x75,0x2B,0x2C,0x40,0x09,0x4D,0xBA, + 0xCD,0xB5,0x86,0xFB,0x20, + 0x00,0x71,0x67,0xEF,0xC9,0x2B,0xB2,0xE3,0xCE,0x7C, /* b */ + 0x8A,0xAA,0xFF,0x34,0xE1,0x2A,0x9C,0x55,0x70,0x03, + 0xD7,0xC7,0x3A,0x6F,0xAF,0x00,0x3F,0x99,0xF6,0xCC, + 0x84,0x82,0xE5,0x40,0xF7, + 0x00,0x61,0x08,0xBA,0xBB,0x2C,0xEE,0xBC,0xF7,0x87, /* x */ + 0x05,0x8A,0x05,0x6C,0xBE,0x0C,0xFE,0x62,0x2D,0x77, + 0x23,0xA2,0x89,0xE0,0x8A,0x07,0xAE,0x13,0xEF,0x0D, + 0x10,0xD1,0x71,0xDD,0x8D, + 0x00,0x10,0xC7,0x69,0x57,0x16,0x85,0x1E,0xEF,0x6B, /* y */ + 0xA7,0xF6,0x87,0x2E,0x61,0x42,0xFB,0xD2,0x41,0xB8, + 0x30,0xFF,0x5E,0xFC,0xAC,0xEC,0xCA,0xB0,0x5E,0x02, + 0x00,0x5D,0xDE,0x9D,0x23, + 0x00,0x00,0x01,0x00,0xFA,0xF5,0x13,0x54,0xE0,0xE3, /* order */ + 0x9E,0x48,0x92,0xDF,0x6E,0x31,0x9C,0x72,0xC8,0x16, + 0x16,0x03,0xFA,0x45,0xAA,0x7B,0x99,0x8A,0x16,0x7B, + 0x8F,0x1E,0x62,0x95,0x21 } }; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_304W1 = { - NID_X9_62_characteristic_two_field, - "010000000000000000000000000000000000000000000000000000000000000000000" - "000000807", - "FD0D693149A118F651E6DCE6802085377E5F882D1B510B44160074C1288078365A039" - "6C8E681", - "BDDB97E555A50A908E43B01C798EA5DAA6788F1EA2794EFCF57166B8C14039601E558" - "27340BE", - "197B07845E9BE2D96ADB0F5F3C7F2CFFBD7A3EB8B6FEC35C7FD67F26DDF6285A644F7" - "40A2614", - "E19FBEB76E0DA171517ECF401B50289BF014103288527A9B416A105E80260B549FDC1" - "B92C03B", - "000101D556572AABAC800101D556572AABAC8001022D5C91DD173F8FB561DA6899164" - "443051D", 0xFE2E, - NULL, 0, - "X9.62 curve over a 304 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+39*6]; } + _EC_X9_62_CHAR2_304W1 = { + { NID_X9_62_characteristic_two_field,0,39,0xFE2E }, + { /* no seed */ + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x08,0x07, + 0x00,0xFD,0x0D,0x69,0x31,0x49,0xA1,0x18,0xF6,0x51, /* a */ + 0xE6,0xDC,0xE6,0x80,0x20,0x85,0x37,0x7E,0x5F,0x88, + 0x2D,0x1B,0x51,0x0B,0x44,0x16,0x00,0x74,0xC1,0x28, + 0x80,0x78,0x36,0x5A,0x03,0x96,0xC8,0xE6,0x81, + 0x00,0xBD,0xDB,0x97,0xE5,0x55,0xA5,0x0A,0x90,0x8E, /* b */ + 0x43,0xB0,0x1C,0x79,0x8E,0xA5,0xDA,0xA6,0x78,0x8F, + 0x1E,0xA2,0x79,0x4E,0xFC,0xF5,0x71,0x66,0xB8,0xC1, + 0x40,0x39,0x60,0x1E,0x55,0x82,0x73,0x40,0xBE, + 0x00,0x19,0x7B,0x07,0x84,0x5E,0x9B,0xE2,0xD9,0x6A, /* x */ + 0xDB,0x0F,0x5F,0x3C,0x7F,0x2C,0xFF,0xBD,0x7A,0x3E, + 0xB8,0xB6,0xFE,0xC3,0x5C,0x7F,0xD6,0x7F,0x26,0xDD, + 0xF6,0x28,0x5A,0x64,0x4F,0x74,0x0A,0x26,0x14, + 0x00,0xE1,0x9F,0xBE,0xB7,0x6E,0x0D,0xA1,0x71,0x51, /* y */ + 0x7E,0xCF,0x40,0x1B,0x50,0x28,0x9B,0xF0,0x14,0x10, + 0x32,0x88,0x52,0x7A,0x9B,0x41,0x6A,0x10,0x5E,0x80, + 0x26,0x0B,0x54,0x9F,0xDC,0x1B,0x92,0xC0,0x3B, + 0x00,0x00,0x01,0x01,0xD5,0x56,0x57,0x2A,0xAB,0xAC, /* order */ + 0x80,0x01,0x01,0xD5,0x56,0x57,0x2A,0xAB,0xAC,0x80, + 0x01,0x02,0x2D,0x5C,0x91,0xDD,0x17,0x3F,0x8F,0xB5, + 0x61,0xDA,0x68,0x99,0x16,0x44,0x43,0x05,0x1D } }; -static const unsigned char _EC_X9_62_CHAR2_359V1_SEED[] = { - 0x2B,0x35,0x49,0x20,0xB7,0x24,0xD6,0x96,0xE6,0x76, - 0x87,0x56,0x15,0x17,0x58,0x5B,0xA1,0x33,0x2D,0xC6}; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_359V1 = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000000000000000000000000000" - "000100000000000000001", - "5667676A654B20754F356EA92017D946567C46675556F19556A04616B567D223A5E05" - "656FB549016A96656A557", - "2472E2D0197C49363F1FE7F5B6DB075D52B6947D135D8CA445805D39BC34562608968" - "7742B6329E70680231988", - "3C258EF3047767E7EDE0F1FDAA79DAEE3841366A132E163ACED4ED2401DF9C6BDCDE9" - "8E8E707C07A2239B1B097", - "53D7E08529547048121E9C95F3791DD804963948F34FAE7BF44EA82365DC7868FE57E" - "4AE2DE211305A407104BD", - "01AF286BCA1AF286BCA1AF286BCA1AF286BCA1AF286BC9FB8F6B85C556892C20A7EB9" - "64FE7719E74F490758D3B", 0x4C, - _EC_X9_62_CHAR2_359V1_SEED, 20, - "X9.62 curve over a 359 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[20+45*6]; } + _EC_X9_62_CHAR2_359V1 = { + { NID_X9_62_characteristic_two_field,20,45,0x4C }, + { 0x2B,0x35,0x49,0x20,0xB7,0x24,0xD6,0x96,0xE6,0x76, /* seed */ + 0x87,0x56,0x15,0x17,0x58,0x5B,0xA1,0x33,0x2D,0xC6, + + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x10,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x01, + 0x56,0x67,0x67,0x6A,0x65,0x4B,0x20,0x75,0x4F,0x35, /* a */ + 0x6E,0xA9,0x20,0x17,0xD9,0x46,0x56,0x7C,0x46,0x67, + 0x55,0x56,0xF1,0x95,0x56,0xA0,0x46,0x16,0xB5,0x67, + 0xD2,0x23,0xA5,0xE0,0x56,0x56,0xFB,0x54,0x90,0x16, + 0xA9,0x66,0x56,0xA5,0x57, + 0x24,0x72,0xE2,0xD0,0x19,0x7C,0x49,0x36,0x3F,0x1F, /* b */ + 0xE7,0xF5,0xB6,0xDB,0x07,0x5D,0x52,0xB6,0x94,0x7D, + 0x13,0x5D,0x8C,0xA4,0x45,0x80,0x5D,0x39,0xBC,0x34, + 0x56,0x26,0x08,0x96,0x87,0x74,0x2B,0x63,0x29,0xE7, + 0x06,0x80,0x23,0x19,0x88, + 0x3C,0x25,0x8E,0xF3,0x04,0x77,0x67,0xE7,0xED,0xE0, /* x */ + 0xF1,0xFD,0xAA,0x79,0xDA,0xEE,0x38,0x41,0x36,0x6A, + 0x13,0x2E,0x16,0x3A,0xCE,0xD4,0xED,0x24,0x01,0xDF, + 0x9C,0x6B,0xDC,0xDE,0x98,0xE8,0xE7,0x07,0xC0,0x7A, + 0x22,0x39,0xB1,0xB0,0x97, + 0x53,0xD7,0xE0,0x85,0x29,0x54,0x70,0x48,0x12,0x1E, /* y */ + 0x9C,0x95,0xF3,0x79,0x1D,0xD8,0x04,0x96,0x39,0x48, + 0xF3,0x4F,0xAE,0x7B,0xF4,0x4E,0xA8,0x23,0x65,0xDC, + 0x78,0x68,0xFE,0x57,0xE4,0xAE,0x2D,0xE2,0x11,0x30, + 0x5A,0x40,0x71,0x04,0xBD, + 0x01,0xAF,0x28,0x6B,0xCA,0x1A,0xF2,0x86,0xBC,0xA1, /* order */ + 0xAF,0x28,0x6B,0xCA,0x1A,0xF2,0x86,0xBC,0xA1,0xAF, + 0x28,0x6B,0xC9,0xFB,0x8F,0x6B,0x85,0xC5,0x56,0x89, + 0x2C,0x20,0xA7,0xEB,0x96,0x4F,0xE7,0x71,0x9E,0x74, + 0xF4,0x90,0x75,0x8D,0x3B } }; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_368W1 = { - NID_X9_62_characteristic_two_field, - "010000000000000000000000000000000000000000000000000000000000000000000" - "0002000000000000000000007", - "E0D2EE25095206F5E2A4F9ED229F1F256E79A0E2B455970D8D0D865BD94778C576D62" - "F0AB7519CCD2A1A906AE30D", - "FC1217D4320A90452C760A58EDCD30C8DD069B3C34453837A34ED50CB54917E1C2112" - "D84D164F444F8F74786046A", - "1085E2755381DCCCE3C1557AFA10C2F0C0C2825646C5B34A394CBCFA8BC16B22E7E78" - "9E927BE216F02E1FB136A5F", - "7B3EB1BDDCBA62D5D8B2059B525797FC73822C59059C623A45FF3843CEE8F87CD1855" - "ADAA81E2A0750B80FDA2310", - "00010090512DA9AF72B08349D98A5DD4C7B0532ECA51CE03E2D10F3B7AC579BD87E90" - "9AE40A6F131E9CFCE5BD967", 0xFF70, - NULL, 0, - "X9.62 curve over a 368 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+47*6]; } + _EC_X9_62_CHAR2_368W1 = { + { NID_X9_62_characteristic_two_field,0,47,0xFF70 }, + { /* no seed */ + 0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x20,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x07, + 0x00,0xE0,0xD2,0xEE,0x25,0x09,0x52,0x06,0xF5,0xE2, /* a */ + 0xA4,0xF9,0xED,0x22,0x9F,0x1F,0x25,0x6E,0x79,0xA0, + 0xE2,0xB4,0x55,0x97,0x0D,0x8D,0x0D,0x86,0x5B,0xD9, + 0x47,0x78,0xC5,0x76,0xD6,0x2F,0x0A,0xB7,0x51,0x9C, + 0xCD,0x2A,0x1A,0x90,0x6A,0xE3,0x0D, + 0x00,0xFC,0x12,0x17,0xD4,0x32,0x0A,0x90,0x45,0x2C, /* b */ + 0x76,0x0A,0x58,0xED,0xCD,0x30,0xC8,0xDD,0x06,0x9B, + 0x3C,0x34,0x45,0x38,0x37,0xA3,0x4E,0xD5,0x0C,0xB5, + 0x49,0x17,0xE1,0xC2,0x11,0x2D,0x84,0xD1,0x64,0xF4, + 0x44,0xF8,0xF7,0x47,0x86,0x04,0x6A, + 0x00,0x10,0x85,0xE2,0x75,0x53,0x81,0xDC,0xCC,0xE3, /* x */ + 0xC1,0x55,0x7A,0xFA,0x10,0xC2,0xF0,0xC0,0xC2,0x82, + 0x56,0x46,0xC5,0xB3,0x4A,0x39,0x4C,0xBC,0xFA,0x8B, + 0xC1,0x6B,0x22,0xE7,0xE7,0x89,0xE9,0x27,0xBE,0x21, + 0x6F,0x02,0xE1,0xFB,0x13,0x6A,0x5F, + 0x00,0x7B,0x3E,0xB1,0xBD,0xDC,0xBA,0x62,0xD5,0xD8, /* y */ + 0xB2,0x05,0x9B,0x52,0x57,0x97,0xFC,0x73,0x82,0x2C, + 0x59,0x05,0x9C,0x62,0x3A,0x45,0xFF,0x38,0x43,0xCE, + 0xE8,0xF8,0x7C,0xD1,0x85,0x5A,0xDA,0xA8,0x1E,0x2A, + 0x07,0x50,0xB8,0x0F,0xDA,0x23,0x10, + 0x00,0x00,0x01,0x00,0x90,0x51,0x2D,0xA9,0xAF,0x72, /* order */ + 0xB0,0x83,0x49,0xD9,0x8A,0x5D,0xD4,0xC7,0xB0,0x53, + 0x2E,0xCA,0x51,0xCE,0x03,0xE2,0xD1,0x0F,0x3B,0x7A, + 0xC5,0x79,0xBD,0x87,0xE9,0x09,0xAE,0x40,0xA6,0xF1, + 0x31,0xE9,0xCF,0xCE,0x5B,0xD9,0x67 } }; -static const EC_CURVE_DATA _EC_X9_62_CHAR2_431R1 = { - NID_X9_62_characteristic_two_field, - "800000000000000000000000000000000000000000000000000000000000000000000" - "000000001000000000000000000000000000001", - "1A827EF00DD6FC0E234CAF046C6A5D8A85395B236CC4AD2CF32A0CADBDC9DDF620B0E" - "B9906D0957F6C6FEACD615468DF104DE296CD8F", - "10D9B4A3D9047D8B154359ABFB1B7F5485B04CEB868237DDC9DEDA982A679A5A919B6" - "26D4E50A8DD731B107A9962381FB5D807BF2618", - "120FC05D3C67A99DE161D2F4092622FECA701BE4F50F4758714E8A87BBF2A658EF8C2" - "1E7C5EFE965361F6C2999C0C247B0DBD70CE6B7", - "20D0AF8903A96F8D5FA2C255745D3C451B302C9346D9B7E485E7BCE41F6B591F3E8F6" - "ADDCBB0BC4C2F947A7DE1A89B625D6A598B3760", - "0340340340340340340340340340340340340340340340340340340323C313FAB5058" - "9703B5EC68D3587FEC60D161CC149C1AD4A91", 0x2760, - NULL, 0, - "X9.62 curve over a 431 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+54*6]; } + _EC_X9_62_CHAR2_431R1 = { + { NID_X9_62_characteristic_two_field,0,54,0x2760 }, + { /* no seed */ + 0x80,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x01, + 0x1A,0x82,0x7E,0xF0,0x0D,0xD6,0xFC,0x0E,0x23,0x4C, /* a */ + 0xAF,0x04,0x6C,0x6A,0x5D,0x8A,0x85,0x39,0x5B,0x23, + 0x6C,0xC4,0xAD,0x2C,0xF3,0x2A,0x0C,0xAD,0xBD,0xC9, + 0xDD,0xF6,0x20,0xB0,0xEB,0x99,0x06,0xD0,0x95,0x7F, + 0x6C,0x6F,0xEA,0xCD,0x61,0x54,0x68,0xDF,0x10,0x4D, + 0xE2,0x96,0xCD,0x8F, + 0x10,0xD9,0xB4,0xA3,0xD9,0x04,0x7D,0x8B,0x15,0x43, /* b */ + 0x59,0xAB,0xFB,0x1B,0x7F,0x54,0x85,0xB0,0x4C,0xEB, + 0x86,0x82,0x37,0xDD,0xC9,0xDE,0xDA,0x98,0x2A,0x67, + 0x9A,0x5A,0x91,0x9B,0x62,0x6D,0x4E,0x50,0xA8,0xDD, + 0x73,0x1B,0x10,0x7A,0x99,0x62,0x38,0x1F,0xB5,0xD8, + 0x07,0xBF,0x26,0x18, + 0x12,0x0F,0xC0,0x5D,0x3C,0x67,0xA9,0x9D,0xE1,0x61, /* x */ + 0xD2,0xF4,0x09,0x26,0x22,0xFE,0xCA,0x70,0x1B,0xE4, + 0xF5,0x0F,0x47,0x58,0x71,0x4E,0x8A,0x87,0xBB,0xF2, + 0xA6,0x58,0xEF,0x8C,0x21,0xE7,0xC5,0xEF,0xE9,0x65, + 0x36,0x1F,0x6C,0x29,0x99,0xC0,0xC2,0x47,0xB0,0xDB, + 0xD7,0x0C,0xE6,0xB7, + 0x20,0xD0,0xAF,0x89,0x03,0xA9,0x6F,0x8D,0x5F,0xA2, /* y */ + 0xC2,0x55,0x74,0x5D,0x3C,0x45,0x1B,0x30,0x2C,0x93, + 0x46,0xD9,0xB7,0xE4,0x85,0xE7,0xBC,0xE4,0x1F,0x6B, + 0x59,0x1F,0x3E,0x8F,0x6A,0xDD,0xCB,0xB0,0xBC,0x4C, + 0x2F,0x94,0x7A,0x7D,0xE1,0xA8,0x9B,0x62,0x5D,0x6A, + 0x59,0x8B,0x37,0x60, + 0x00,0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34, /* order */ + 0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34,0x03, + 0x40,0x34,0x03,0x40,0x34,0x03,0x40,0x34,0x03,0x23, + 0xC3,0x13,0xFA,0xB5,0x05,0x89,0x70,0x3B,0x5E,0xC6, + 0x8D,0x35,0x87,0xFE,0xC6,0x0D,0x16,0x1C,0xC1,0x49, + 0xC1,0xAD,0x4A,0x91 } }; -static const EC_CURVE_DATA _EC_WTLS_1 = { - NID_X9_62_characteristic_two_field, - "020000000000000000000000000201", - "1", - "1", - "01667979A40BA497E5D5C270780617", - "00F44B4AF1ECC2630E08785CEBCC15", - "00FFFFFFFFFFFFFFFDBF91AF6DEA73", 2, - NULL, 0, - "WTLS curve over a 113 bit binary field" +static const struct { EC_CURVE_DATA h; unsigned char data[0+15*6]; } + _EC_WTLS_1 = { + { NID_X9_62_characteristic_two_field,0,15,2 }, + { /* no seed */ + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x02,0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x01, + 0x01,0x66,0x79,0x79,0xA4,0x0B,0xA4,0x97,0xE5,0xD5, /* x */ + 0xC2,0x70,0x78,0x06,0x17, + 0x00,0xF4,0x4B,0x4A,0xF1,0xEC,0xC2,0x63,0x0E,0x08, /* y */ + 0x78,0x5C,0xEB,0xCC,0x15, + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFD,0xBF, /* order */ + 0x91,0xAF,0x6D,0xEA,0x73 } }; /* IPSec curves */ @@ -1001,17 +1768,27 @@ static const EC_CURVE_DATA _EC_WTLS_1 = { * As the group order is not a prime this curve is not suitable * for ECDSA. */ -static const EC_CURVE_DATA _EC_IPSEC_155_ID3 = { - NID_X9_62_characteristic_two_field, - "0800000000000000000000004000000000000001", - "0", - "07338f", - "7b", - "1c8", - "2AAAAAAAAAAAAAAAAAAC7F3C7881BD0868FA86C",3, - NULL, 0, - "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" - "\tNot suitable for ECDSA.\n\tQuestionable extension field!" +static const struct { EC_CURVE_DATA h; unsigned char data[0+20*6]; } + _EC_IPSEC_155_ID3 = { + { NID_X9_62_characteristic_two_field,0,20,3 }, + { /* no seed */ + 0x08,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x40,0x00,0x00,0x00,0x00,0x00,0x00,0x01, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x07,0x33,0x8f, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x7b, + + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01,0xc8, + + 0x02,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA,0xAA, /* order */ + 0xC7,0xF3,0xC7,0x88,0x1B,0xD0,0x86,0x8F,0xA8,0x6C } }; /* NOTE: The of curves over a extension field of non prime degree @@ -1019,136 +1796,185 @@ static const EC_CURVE_DATA _EC_IPSEC_155_ID3 = { * As the group order is not a prime this curve is not suitable * for ECDSA. */ -static const EC_CURVE_DATA _EC_IPSEC_185_ID4 = { - NID_X9_62_characteristic_two_field, - "020000000000000000000000000000200000000000000001", - "0", - "1ee9", - "18", - "0d", - "FFFFFFFFFFFFFFFFFFFFFFEDF97C44DB9F2420BAFCA75E",2, - NULL, 0, - "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" - "\tNot suitable for ECDSA.\n\tQuestionable extension field!" +static const struct { EC_CURVE_DATA h; unsigned char data[0+24*6]; } + _EC_IPSEC_185_ID4 = { + { NID_X9_62_characteristic_two_field,0,24,2 }, + { /* no seed */ + 0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* p */ + 0x00,0x00,0x00,0x00,0x00,0x20,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x01, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* a */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* b */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x1e,0xe9, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* x */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x18, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, /* y */ + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x0d, + 0x00,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* order */ + 0xFF,0xFF,0xED,0xF9,0x7C,0x44,0xDB,0x9F,0x24,0x20, + 0xBA,0xFC,0xA7,0x5E } }; +#endif + typedef struct _ec_list_element_st { int nid; const EC_CURVE_DATA *data; + const EC_METHOD *(*meth)(void); + const char *comment; } ec_list_element; static const ec_list_element curve_list[] = { - /* prime field curves */ + /* prime field curves */ /* secg curves */ - { NID_secp112r1, &_EC_SECG_PRIME_112R1}, - { NID_secp112r2, &_EC_SECG_PRIME_112R2}, - { NID_secp128r1, &_EC_SECG_PRIME_128R1}, - { NID_secp128r2, &_EC_SECG_PRIME_128R2}, - { NID_secp160k1, &_EC_SECG_PRIME_160K1}, - { NID_secp160r1, &_EC_SECG_PRIME_160R1}, - { NID_secp160r2, &_EC_SECG_PRIME_160R2}, + { NID_secp112r1, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, + { NID_secp112r2, &_EC_SECG_PRIME_112R2.h, 0, "SECG curve over a 112 bit prime field" }, + { NID_secp128r1, &_EC_SECG_PRIME_128R1.h, 0, "SECG curve over a 128 bit prime field" }, + { NID_secp128r2, &_EC_SECG_PRIME_128R2.h, 0, "SECG curve over a 128 bit prime field" }, + { NID_secp160k1, &_EC_SECG_PRIME_160K1.h, 0, "SECG curve over a 160 bit prime field" }, + { NID_secp160r1, &_EC_SECG_PRIME_160R1.h, 0, "SECG curve over a 160 bit prime field" }, + { NID_secp160r2, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, /* SECG secp192r1 is the same as X9.62 prime192v1 and hence omitted */ - { NID_secp192k1, &_EC_SECG_PRIME_192K1}, - { NID_secp224k1, &_EC_SECG_PRIME_224K1}, - { NID_secp224r1, &_EC_NIST_PRIME_224}, - { NID_secp256k1, &_EC_SECG_PRIME_256K1}, + { NID_secp192k1, &_EC_SECG_PRIME_192K1.h, 0, "SECG curve over a 192 bit prime field" }, + { NID_secp224k1, &_EC_SECG_PRIME_224K1.h, 0, "SECG curve over a 224 bit prime field" }, +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + { NID_secp224r1, &_EC_NIST_PRIME_224.h, EC_GFp_nistp224_method, "NIST/SECG curve over a 224 bit prime field" }, +#else + { NID_secp224r1, &_EC_NIST_PRIME_224.h, 0, "NIST/SECG curve over a 224 bit prime field" }, +#endif + { NID_secp256k1, &_EC_SECG_PRIME_256K1.h, 0, "SECG curve over a 256 bit prime field" }, /* SECG secp256r1 is the same as X9.62 prime256v1 and hence omitted */ - { NID_secp384r1, &_EC_NIST_PRIME_384}, - { NID_secp521r1, &_EC_NIST_PRIME_521}, + { NID_secp384r1, &_EC_NIST_PRIME_384.h, 0, "NIST/SECG curve over a 384 bit prime field" }, +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + { NID_secp521r1, &_EC_NIST_PRIME_521.h, EC_GFp_nistp521_method, "NIST/SECG curve over a 521 bit prime field" }, +#else + { NID_secp521r1, &_EC_NIST_PRIME_521.h, 0, "NIST/SECG curve over a 521 bit prime field" }, +#endif /* X9.62 curves */ - { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192}, - { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2}, - { NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3}, - { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1}, - { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2}, - { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3}, - { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1}, + { NID_X9_62_prime192v1, &_EC_NIST_PRIME_192.h, 0, "NIST/X9.62/SECG curve over a 192 bit prime field" }, + { NID_X9_62_prime192v2, &_EC_X9_62_PRIME_192V2.h, 0, "X9.62 curve over a 192 bit prime field" }, + { NID_X9_62_prime192v3, &_EC_X9_62_PRIME_192V3.h, 0, "X9.62 curve over a 192 bit prime field" }, + { NID_X9_62_prime239v1, &_EC_X9_62_PRIME_239V1.h, 0, "X9.62 curve over a 239 bit prime field" }, + { NID_X9_62_prime239v2, &_EC_X9_62_PRIME_239V2.h, 0, "X9.62 curve over a 239 bit prime field" }, + { NID_X9_62_prime239v3, &_EC_X9_62_PRIME_239V3.h, 0, "X9.62 curve over a 239 bit prime field" }, +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, EC_GFp_nistp256_method, "X9.62/SECG curve over a 256 bit prime field" }, +#else + { NID_X9_62_prime256v1, &_EC_X9_62_PRIME_256V1.h, 0, "X9.62/SECG curve over a 256 bit prime field" }, +#endif +#ifndef OPENSSL_NO_EC2M /* characteristic two field curves */ /* NIST/SECG curves */ - { NID_sect113r1, &_EC_SECG_CHAR2_113R1}, - { NID_sect113r2, &_EC_SECG_CHAR2_113R2}, - { NID_sect131r1, &_EC_SECG_CHAR2_131R1}, - { NID_sect131r2, &_EC_SECG_CHAR2_131R2}, - { NID_sect163k1, &_EC_NIST_CHAR2_163K }, - { NID_sect163r1, &_EC_SECG_CHAR2_163R1}, - { NID_sect163r2, &_EC_NIST_CHAR2_163B }, - { NID_sect193r1, &_EC_SECG_CHAR2_193R1}, - { NID_sect193r2, &_EC_SECG_CHAR2_193R2}, - { NID_sect233k1, &_EC_NIST_CHAR2_233K }, - { NID_sect233r1, &_EC_NIST_CHAR2_233B }, - { NID_sect239k1, &_EC_SECG_CHAR2_239K1}, - { NID_sect283k1, &_EC_NIST_CHAR2_283K }, - { NID_sect283r1, &_EC_NIST_CHAR2_283B }, - { NID_sect409k1, &_EC_NIST_CHAR2_409K }, - { NID_sect409r1, &_EC_NIST_CHAR2_409B }, - { NID_sect571k1, &_EC_NIST_CHAR2_571K }, - { NID_sect571r1, &_EC_NIST_CHAR2_571B }, + { NID_sect113r1, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_sect113r2, &_EC_SECG_CHAR2_113R2.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_sect131r1, &_EC_SECG_CHAR2_131R1.h, 0, "SECG/WTLS curve over a 131 bit binary field" }, + { NID_sect131r2, &_EC_SECG_CHAR2_131R2.h, 0, "SECG curve over a 131 bit binary field" }, + { NID_sect163k1, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, + { NID_sect163r1, &_EC_SECG_CHAR2_163R1.h, 0, "SECG curve over a 163 bit binary field" }, + { NID_sect163r2, &_EC_NIST_CHAR2_163B.h, 0, "NIST/SECG curve over a 163 bit binary field" }, + { NID_sect193r1, &_EC_SECG_CHAR2_193R1.h, 0, "SECG curve over a 193 bit binary field" }, + { NID_sect193r2, &_EC_SECG_CHAR2_193R2.h, 0, "SECG curve over a 193 bit binary field" }, + { NID_sect233k1, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_sect233r1, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_sect239k1, &_EC_SECG_CHAR2_239K1.h, 0, "SECG curve over a 239 bit binary field" }, + { NID_sect283k1, &_EC_NIST_CHAR2_283K.h, 0, "NIST/SECG curve over a 283 bit binary field" }, + { NID_sect283r1, &_EC_NIST_CHAR2_283B.h, 0, "NIST/SECG curve over a 283 bit binary field" }, + { NID_sect409k1, &_EC_NIST_CHAR2_409K.h, 0, "NIST/SECG curve over a 409 bit binary field" }, + { NID_sect409r1, &_EC_NIST_CHAR2_409B.h, 0, "NIST/SECG curve over a 409 bit binary field" }, + { NID_sect571k1, &_EC_NIST_CHAR2_571K.h, 0, "NIST/SECG curve over a 571 bit binary field" }, + { NID_sect571r1, &_EC_NIST_CHAR2_571B.h, 0, "NIST/SECG curve over a 571 bit binary field" }, /* X9.62 curves */ - { NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1}, - { NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2}, - { NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3}, - { NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1}, - { NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1}, - { NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2}, - { NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3}, - { NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1}, - { NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1}, - { NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2}, - { NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3}, - { NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1}, - { NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1}, - { NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1}, - { NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1}, - { NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1}, + { NID_X9_62_c2pnb163v1, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb163v2, &_EC_X9_62_CHAR2_163V2.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb163v3, &_EC_X9_62_CHAR2_163V3.h, 0, "X9.62 curve over a 163 bit binary field" }, + { NID_X9_62_c2pnb176v1, &_EC_X9_62_CHAR2_176V1.h, 0, "X9.62 curve over a 176 bit binary field" }, + { NID_X9_62_c2tnb191v1, &_EC_X9_62_CHAR2_191V1.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2tnb191v2, &_EC_X9_62_CHAR2_191V2.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2tnb191v3, &_EC_X9_62_CHAR2_191V3.h, 0, "X9.62 curve over a 191 bit binary field" }, + { NID_X9_62_c2pnb208w1, &_EC_X9_62_CHAR2_208W1.h, 0, "X9.62 curve over a 208 bit binary field" }, + { NID_X9_62_c2tnb239v1, &_EC_X9_62_CHAR2_239V1.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2tnb239v2, &_EC_X9_62_CHAR2_239V2.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2tnb239v3, &_EC_X9_62_CHAR2_239V3.h, 0, "X9.62 curve over a 239 bit binary field" }, + { NID_X9_62_c2pnb272w1, &_EC_X9_62_CHAR2_272W1.h, 0, "X9.62 curve over a 272 bit binary field" }, + { NID_X9_62_c2pnb304w1, &_EC_X9_62_CHAR2_304W1.h, 0, "X9.62 curve over a 304 bit binary field" }, + { NID_X9_62_c2tnb359v1, &_EC_X9_62_CHAR2_359V1.h, 0, "X9.62 curve over a 359 bit binary field" }, + { NID_X9_62_c2pnb368w1, &_EC_X9_62_CHAR2_368W1.h, 0, "X9.62 curve over a 368 bit binary field" }, + { NID_X9_62_c2tnb431r1, &_EC_X9_62_CHAR2_431R1.h, 0, "X9.62 curve over a 431 bit binary field" }, /* the WAP/WTLS curves * [unlike SECG, spec has its own OIDs for curves from X9.62] */ - { NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1}, - { NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K}, - { NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1}, - { NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1}, - { NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1}, - { NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2}, - { NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8}, - { NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9 }, - { NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K}, - { NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B}, - { NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12}, + { NID_wap_wsg_idm_ecid_wtls1, &_EC_WTLS_1.h, 0, "WTLS curve over a 113 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls3, &_EC_NIST_CHAR2_163K.h, 0, "NIST/SECG/WTLS curve over a 163 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls4, &_EC_SECG_CHAR2_113R1.h, 0, "SECG curve over a 113 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls5, &_EC_X9_62_CHAR2_163V1.h, 0, "X9.62 curve over a 163 bit binary field" }, +#endif + { NID_wap_wsg_idm_ecid_wtls6, &_EC_SECG_PRIME_112R1.h, 0, "SECG/WTLS curve over a 112 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls7, &_EC_SECG_PRIME_160R2.h, 0, "SECG/WTLS curve over a 160 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls8, &_EC_WTLS_8.h, 0, "WTLS curve over a 112 bit prime field" }, + { NID_wap_wsg_idm_ecid_wtls9, &_EC_WTLS_9.h, 0, "WTLS curve over a 160 bit prime field" }, +#ifndef OPENSSL_NO_EC2M + { NID_wap_wsg_idm_ecid_wtls10, &_EC_NIST_CHAR2_233K.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, + { NID_wap_wsg_idm_ecid_wtls11, &_EC_NIST_CHAR2_233B.h, 0, "NIST/SECG/WTLS curve over a 233 bit binary field" }, +#endif + { NID_wap_wsg_idm_ecid_wtls12, &_EC_WTLS_12.h, 0, "WTLS curvs over a 224 bit prime field" }, +#ifndef OPENSSL_NO_EC2M /* IPSec curves */ - { NID_ipsec3, &_EC_IPSEC_155_ID3}, - { NID_ipsec4, &_EC_IPSEC_185_ID4}, + { NID_ipsec3, &_EC_IPSEC_155_ID3.h, 0, "\n\tIPSec/IKE/Oakley curve #3 over a 155 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, + { NID_ipsec4, &_EC_IPSEC_185_ID4.h, 0, "\n\tIPSec/IKE/Oakley curve #4 over a 185 bit binary field.\n" + "\tNot suitable for ECDSA.\n\tQuestionable extension field!" }, +#endif }; -static size_t curve_list_length = sizeof(curve_list)/sizeof(ec_list_element); +#define curve_list_length (sizeof(curve_list)/sizeof(ec_list_element)) -static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) +static EC_GROUP *ec_group_new_from_data(const ec_list_element curve) { EC_GROUP *group=NULL; EC_POINT *P=NULL; BN_CTX *ctx=NULL; - BIGNUM *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL; + BIGNUM *p=NULL, *a=NULL, *b=NULL, *x=NULL, *y=NULL, *order=NULL; int ok=0; + int seed_len,param_len; + const EC_METHOD *meth; + const EC_CURVE_DATA *data; + const unsigned char *params; if ((ctx = BN_CTX_new()) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE); goto err; } - if ((p = BN_new()) == NULL || (a = BN_new()) == NULL || - (b = BN_new()) == NULL || (x = BN_new()) == NULL || - (y = BN_new()) == NULL || (order = BN_new()) == NULL) - { - ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_MALLOC_FAILURE); - goto err; - } - - if (!BN_hex2bn(&p, data->p) || !BN_hex2bn(&a, data->a) - || !BN_hex2bn(&b, data->b)) + + data = curve.data; + seed_len = data->seed_len; + param_len = data->param_len; + params = (const unsigned char *)(data+1); /* skip header */ + params += seed_len; /* skip seed */ + + if (!(p = BN_bin2bn(params+0*param_len, param_len, NULL)) + || !(a = BN_bin2bn(params+1*param_len, param_len, NULL)) + || !(b = BN_bin2bn(params+2*param_len, param_len, NULL))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; } - if (data->field_type == NID_X9_62_prime_field) + if (curve.meth != 0) + { + meth = curve.meth(); + if (((group = EC_GROUP_new(meth)) == NULL) || + (!(group->meth->group_set_curve(group, p, a, b, ctx)))) + { + ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); + goto err; + } + } + else if (data->field_type == NID_X9_62_prime_field) { if ((group = EC_GROUP_new_curve_GFp(p, a, b, ctx)) == NULL) { @@ -1156,32 +1982,36 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) goto err; } } - else - { /* field_type == NID_X9_62_characteristic_two_field */ +#ifndef OPENSSL_NO_EC2M + else /* field_type == NID_X9_62_characteristic_two_field */ + { if ((group = EC_GROUP_new_curve_GF2m(p, a, b, ctx)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; } } +#endif if ((P = EC_POINT_new(group)) == NULL) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; } - - if (!BN_hex2bn(&x, data->x) || !BN_hex2bn(&y, data->y)) + + if (!(x = BN_bin2bn(params+3*param_len, param_len, NULL)) + || !(y = BN_bin2bn(params+4*param_len, param_len, NULL))) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; } - if (!EC_POINT_set_affine_coordinates_GF2m(group, P, x, y, ctx)) + if (!EC_POINT_set_affine_coordinates_GFp(group, P, x, y, ctx)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; } - if (!BN_hex2bn(&order, data->order) || !BN_set_word(x, data->cofactor)) + if (!(order = BN_bin2bn(params+5*param_len, param_len, NULL)) + || !BN_set_word(x, (BN_ULONG)data->cofactor)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_BN_LIB); goto err; @@ -1191,9 +2021,9 @@ static EC_GROUP *ec_group_new_from_data(const EC_CURVE_DATA *data) ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; } - if (data->seed) + if (seed_len) { - if (!EC_GROUP_set_seed(group, data->seed, data->seed_len)) + if (!EC_GROUP_set_seed(group, params-seed_len, seed_len)) { ECerr(EC_F_EC_GROUP_NEW_FROM_DATA, ERR_R_EC_LIB); goto err; @@ -1236,7 +2066,7 @@ EC_GROUP *EC_GROUP_new_by_curve_name(int nid) for (i=0; i<curve_list_length; i++) if (curve_list[i].nid == nid) { - ret = ec_group_new_from_data(curve_list[i].data); + ret = ec_group_new_from_data(curve_list[i]); break; } @@ -1263,7 +2093,7 @@ size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems) for (i = 0; i < min; i++) { r[i].nid = curve_list[i].nid; - r[i].comment = curve_list[i].data->comment; + r[i].comment = curve_list[i].comment; } return curve_list_length; diff --git a/crypto/ec/ec_cvt.c b/crypto/ec/ec_cvt.c index d45640bab902f..bfcbab35fe695 100644 --- a/crypto/ec/ec_cvt.c +++ b/crypto/ec/ec_cvt.c @@ -78,7 +78,32 @@ EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM const EC_METHOD *meth; EC_GROUP *ret; +#if defined(OPENSSL_BN_ASM_MONT) + /* + * This might appear controversial, but the fact is that generic + * prime method was observed to deliver better performance even + * for NIST primes on a range of platforms, e.g.: 60%-15% + * improvement on IA-64, ~25% on ARM, 30%-90% on P4, 20%-25% + * in 32-bit build and 35%--12% in 64-bit build on Core2... + * Coefficients are relative to optimized bn_nist.c for most + * intensive ECDSA verify and ECDH operations for 192- and 521- + * bit keys respectively. Choice of these boundary values is + * arguable, because the dependency of improvement coefficient + * from key length is not a "monotone" curve. For example while + * 571-bit result is 23% on ARM, 384-bit one is -1%. But it's + * generally faster, sometimes "respectfully" faster, sometimes + * "tolerably" slower... What effectively happens is that loop + * with bn_mul_add_words is put against bn_mul_mont, and the + * latter "wins" on short vectors. Correct solution should be + * implementing dedicated NxN multiplication subroutines for + * small N. But till it materializes, let's stick to generic + * prime method... + * <appro> + */ + meth = EC_GFp_mont_method(); +#else meth = EC_GFp_nist_method(); +#endif ret = EC_GROUP_new(meth); if (ret == NULL) @@ -122,7 +147,7 @@ EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM return ret; } - +#ifndef OPENSSL_NO_EC2M EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { const EC_METHOD *meth; @@ -142,3 +167,4 @@ EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM return ret; } +#endif diff --git a/crypto/ec/ec_err.c b/crypto/ec/ec_err.c index d04c8955604e0..0d19398731acb 100644 --- a/crypto/ec/ec_err.c +++ b/crypto/ec/ec_err.c @@ -1,6 +1,6 @@ /* crypto/ec/ec_err.c */ /* ==================================================================== - * Copyright (c) 1999-2007 The OpenSSL Project. All rights reserved. + * Copyright (c) 1999-2011 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -70,10 +70,19 @@ static ERR_STRING_DATA EC_str_functs[]= { +{ERR_FUNC(EC_F_BN_TO_FELEM), "BN_TO_FELEM"}, {ERR_FUNC(EC_F_COMPUTE_WNAF), "COMPUTE_WNAF"}, {ERR_FUNC(EC_F_D2I_ECPARAMETERS), "d2i_ECParameters"}, {ERR_FUNC(EC_F_D2I_ECPKPARAMETERS), "d2i_ECPKParameters"}, {ERR_FUNC(EC_F_D2I_ECPRIVATEKEY), "d2i_ECPrivateKey"}, +{ERR_FUNC(EC_F_DO_EC_KEY_PRINT), "DO_EC_KEY_PRINT"}, +{ERR_FUNC(EC_F_ECKEY_PARAM2TYPE), "ECKEY_PARAM2TYPE"}, +{ERR_FUNC(EC_F_ECKEY_PARAM_DECODE), "ECKEY_PARAM_DECODE"}, +{ERR_FUNC(EC_F_ECKEY_PRIV_DECODE), "ECKEY_PRIV_DECODE"}, +{ERR_FUNC(EC_F_ECKEY_PRIV_ENCODE), "ECKEY_PRIV_ENCODE"}, +{ERR_FUNC(EC_F_ECKEY_PUB_DECODE), "ECKEY_PUB_DECODE"}, +{ERR_FUNC(EC_F_ECKEY_PUB_ENCODE), "ECKEY_PUB_ENCODE"}, +{ERR_FUNC(EC_F_ECKEY_TYPE2PARAM), "ECKEY_TYPE2PARAM"}, {ERR_FUNC(EC_F_ECPARAMETERS_PRINT), "ECParameters_print"}, {ERR_FUNC(EC_F_ECPARAMETERS_PRINT_FP), "ECParameters_print_fp"}, {ERR_FUNC(EC_F_ECPKPARAMETERS_PRINT), "ECPKParameters_print"}, @@ -104,6 +113,15 @@ static ERR_STRING_DATA EC_str_functs[]= {ERR_FUNC(EC_F_EC_GFP_MONT_FIELD_SQR), "ec_GFp_mont_field_sqr"}, {ERR_FUNC(EC_F_EC_GFP_MONT_GROUP_SET_CURVE), "ec_GFp_mont_group_set_curve"}, {ERR_FUNC(EC_F_EC_GFP_MONT_GROUP_SET_CURVE_GFP), "EC_GFP_MONT_GROUP_SET_CURVE_GFP"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE), "ec_GFp_nistp224_group_set_curve"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP224_POINTS_MUL), "ec_GFp_nistp224_points_mul"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp224_point_get_affine_coordinates"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE), "ec_GFp_nistp256_group_set_curve"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_POINTS_MUL), "ec_GFp_nistp256_points_mul"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp256_point_get_affine_coordinates"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE), "ec_GFp_nistp521_group_set_curve"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_POINTS_MUL), "ec_GFp_nistp521_points_mul"}, +{ERR_FUNC(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES), "ec_GFp_nistp521_point_get_affine_coordinates"}, {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_MUL), "ec_GFp_nist_field_mul"}, {ERR_FUNC(EC_F_EC_GFP_NIST_FIELD_SQR), "ec_GFp_nist_field_sqr"}, {ERR_FUNC(EC_F_EC_GFP_NIST_GROUP_SET_CURVE), "ec_GFp_nist_group_set_curve"}, @@ -146,8 +164,8 @@ static ERR_STRING_DATA EC_str_functs[]= {ERR_FUNC(EC_F_EC_KEY_NEW), "EC_KEY_new"}, {ERR_FUNC(EC_F_EC_KEY_PRINT), "EC_KEY_print"}, {ERR_FUNC(EC_F_EC_KEY_PRINT_FP), "EC_KEY_print_fp"}, +{ERR_FUNC(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES), "EC_KEY_set_public_key_affine_coordinates"}, {ERR_FUNC(EC_F_EC_POINTS_MAKE_AFFINE), "EC_POINTs_make_affine"}, -{ERR_FUNC(EC_F_EC_POINTS_MUL), "EC_POINTs_mul"}, {ERR_FUNC(EC_F_EC_POINT_ADD), "EC_POINT_add"}, {ERR_FUNC(EC_F_EC_POINT_CMP), "EC_POINT_cmp"}, {ERR_FUNC(EC_F_EC_POINT_COPY), "EC_POINT_copy"}, @@ -177,7 +195,17 @@ static ERR_STRING_DATA EC_str_functs[]= {ERR_FUNC(EC_F_I2D_ECPKPARAMETERS), "i2d_ECPKParameters"}, {ERR_FUNC(EC_F_I2D_ECPRIVATEKEY), "i2d_ECPrivateKey"}, {ERR_FUNC(EC_F_I2O_ECPUBLICKEY), "i2o_ECPublicKey"}, +{ERR_FUNC(EC_F_NISTP224_PRE_COMP_NEW), "NISTP224_PRE_COMP_NEW"}, +{ERR_FUNC(EC_F_NISTP256_PRE_COMP_NEW), "NISTP256_PRE_COMP_NEW"}, +{ERR_FUNC(EC_F_NISTP521_PRE_COMP_NEW), "NISTP521_PRE_COMP_NEW"}, {ERR_FUNC(EC_F_O2I_ECPUBLICKEY), "o2i_ECPublicKey"}, +{ERR_FUNC(EC_F_OLD_EC_PRIV_DECODE), "OLD_EC_PRIV_DECODE"}, +{ERR_FUNC(EC_F_PKEY_EC_CTRL), "PKEY_EC_CTRL"}, +{ERR_FUNC(EC_F_PKEY_EC_CTRL_STR), "PKEY_EC_CTRL_STR"}, +{ERR_FUNC(EC_F_PKEY_EC_DERIVE), "PKEY_EC_DERIVE"}, +{ERR_FUNC(EC_F_PKEY_EC_KEYGEN), "PKEY_EC_KEYGEN"}, +{ERR_FUNC(EC_F_PKEY_EC_PARAMGEN), "PKEY_EC_PARAMGEN"}, +{ERR_FUNC(EC_F_PKEY_EC_SIGN), "PKEY_EC_SIGN"}, {0,NULL} }; @@ -185,17 +213,23 @@ static ERR_STRING_DATA EC_str_reasons[]= { {ERR_REASON(EC_R_ASN1_ERROR) ,"asn1 error"}, {ERR_REASON(EC_R_ASN1_UNKNOWN_FIELD) ,"asn1 unknown field"}, +{ERR_REASON(EC_R_BIGNUM_OUT_OF_RANGE) ,"bignum out of range"}, {ERR_REASON(EC_R_BUFFER_TOO_SMALL) ,"buffer too small"}, +{ERR_REASON(EC_R_COORDINATES_OUT_OF_RANGE),"coordinates out of range"}, {ERR_REASON(EC_R_D2I_ECPKPARAMETERS_FAILURE),"d2i ecpkparameters failure"}, +{ERR_REASON(EC_R_DECODE_ERROR) ,"decode error"}, {ERR_REASON(EC_R_DISCRIMINANT_IS_ZERO) ,"discriminant is zero"}, {ERR_REASON(EC_R_EC_GROUP_NEW_BY_NAME_FAILURE),"ec group new by name failure"}, {ERR_REASON(EC_R_FIELD_TOO_LARGE) ,"field too large"}, +{ERR_REASON(EC_R_GF2M_NOT_SUPPORTED) ,"gf2m not supported"}, {ERR_REASON(EC_R_GROUP2PKPARAMETERS_FAILURE),"group2pkparameters failure"}, {ERR_REASON(EC_R_I2D_ECPKPARAMETERS_FAILURE),"i2d ecpkparameters failure"}, {ERR_REASON(EC_R_INCOMPATIBLE_OBJECTS) ,"incompatible objects"}, {ERR_REASON(EC_R_INVALID_ARGUMENT) ,"invalid argument"}, {ERR_REASON(EC_R_INVALID_COMPRESSED_POINT),"invalid compressed point"}, {ERR_REASON(EC_R_INVALID_COMPRESSION_BIT),"invalid compression bit"}, +{ERR_REASON(EC_R_INVALID_CURVE) ,"invalid curve"}, +{ERR_REASON(EC_R_INVALID_DIGEST_TYPE) ,"invalid digest type"}, {ERR_REASON(EC_R_INVALID_ENCODING) ,"invalid encoding"}, {ERR_REASON(EC_R_INVALID_FIELD) ,"invalid field"}, {ERR_REASON(EC_R_INVALID_FORM) ,"invalid form"}, @@ -203,6 +237,7 @@ static ERR_STRING_DATA EC_str_reasons[]= {ERR_REASON(EC_R_INVALID_PENTANOMIAL_BASIS),"invalid pentanomial basis"}, {ERR_REASON(EC_R_INVALID_PRIVATE_KEY) ,"invalid private key"}, {ERR_REASON(EC_R_INVALID_TRINOMIAL_BASIS),"invalid trinomial basis"}, +{ERR_REASON(EC_R_KEYS_NOT_SET) ,"keys not set"}, {ERR_REASON(EC_R_MISSING_PARAMETERS) ,"missing parameters"}, {ERR_REASON(EC_R_MISSING_PRIVATE_KEY) ,"missing private key"}, {ERR_REASON(EC_R_NOT_A_NIST_PRIME) ,"not a NIST prime"}, @@ -210,6 +245,7 @@ static ERR_STRING_DATA EC_str_reasons[]= {ERR_REASON(EC_R_NOT_IMPLEMENTED) ,"not implemented"}, {ERR_REASON(EC_R_NOT_INITIALIZED) ,"not initialized"}, {ERR_REASON(EC_R_NO_FIELD_MOD) ,"no field mod"}, +{ERR_REASON(EC_R_NO_PARAMETERS_SET) ,"no parameters set"}, {ERR_REASON(EC_R_PASSED_NULL_PARAMETER) ,"passed null parameter"}, {ERR_REASON(EC_R_PKPARAMETERS2GROUP_FAILURE),"pkparameters2group failure"}, {ERR_REASON(EC_R_POINT_AT_INFINITY) ,"point at infinity"}, @@ -220,6 +256,7 @@ static ERR_STRING_DATA EC_str_reasons[]= {ERR_REASON(EC_R_UNKNOWN_GROUP) ,"unknown group"}, {ERR_REASON(EC_R_UNKNOWN_ORDER) ,"unknown order"}, {ERR_REASON(EC_R_UNSUPPORTED_FIELD) ,"unsupported field"}, +{ERR_REASON(EC_R_WRONG_CURVE_PARAMETERS) ,"wrong curve parameters"}, {ERR_REASON(EC_R_WRONG_ORDER) ,"wrong order"}, {0,NULL} }; diff --git a/crypto/ec/ec_key.c b/crypto/ec/ec_key.c index 522802c07ae13..bf9fd2dc2c43c 100644 --- a/crypto/ec/ec_key.c +++ b/crypto/ec/ec_key.c @@ -64,7 +64,9 @@ #include <string.h> #include "ec_lcl.h" #include <openssl/err.h> -#include <string.h> +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif EC_KEY *EC_KEY_new(void) { @@ -78,6 +80,7 @@ EC_KEY *EC_KEY_new(void) } ret->version = 1; + ret->flags = 0; ret->group = NULL; ret->pub_key = NULL; ret->priv_key= NULL; @@ -197,6 +200,7 @@ EC_KEY *EC_KEY_copy(EC_KEY *dest, const EC_KEY *src) dest->enc_flag = src->enc_flag; dest->conv_form = src->conv_form; dest->version = src->version; + dest->flags = src->flags; return dest; } @@ -237,6 +241,11 @@ int EC_KEY_generate_key(EC_KEY *eckey) BIGNUM *priv_key = NULL, *order = NULL; EC_POINT *pub_key = NULL; +#ifdef OPENSSL_FIPS + if (FIPS_mode()) + return FIPS_ec_key_generate_key(eckey); +#endif + if (!eckey || !eckey->group) { ECerr(EC_F_EC_KEY_GENERATE_KEY, ERR_R_PASSED_NULL_PARAMETER); @@ -371,6 +380,82 @@ err: return(ok); } +int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y) + { + BN_CTX *ctx = NULL; + BIGNUM *tx, *ty; + EC_POINT *point = NULL; + int ok = 0, tmp_nid, is_char_two = 0; + + if (!key || !key->group || !x || !y) + { + ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, + ERR_R_PASSED_NULL_PARAMETER); + return 0; + } + ctx = BN_CTX_new(); + if (!ctx) + goto err; + + point = EC_POINT_new(key->group); + + if (!point) + goto err; + + tmp_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(key->group)); + + if (tmp_nid == NID_X9_62_characteristic_two_field) + is_char_two = 1; + + tx = BN_CTX_get(ctx); + ty = BN_CTX_get(ctx); +#ifndef OPENSSL_NO_EC2M + if (is_char_two) + { + if (!EC_POINT_set_affine_coordinates_GF2m(key->group, point, + x, y, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GF2m(key->group, point, + tx, ty, ctx)) + goto err; + } + else +#endif + { + if (!EC_POINT_set_affine_coordinates_GFp(key->group, point, + x, y, ctx)) + goto err; + if (!EC_POINT_get_affine_coordinates_GFp(key->group, point, + tx, ty, ctx)) + goto err; + } + /* Check if retrieved coordinates match originals: if not values + * are out of range. + */ + if (BN_cmp(x, tx) || BN_cmp(y, ty)) + { + ECerr(EC_F_EC_KEY_SET_PUBLIC_KEY_AFFINE_COORDINATES, + EC_R_COORDINATES_OUT_OF_RANGE); + goto err; + } + + if (!EC_KEY_set_public_key(key, point)) + goto err; + + if (EC_KEY_check_key(key) == 0) + goto err; + + ok = 1; + + err: + if (ctx) + BN_CTX_free(ctx); + if (point) + EC_POINT_free(point); + return ok; + + } + const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key) { return key->group; @@ -461,3 +546,18 @@ int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx) return 0; return EC_GROUP_precompute_mult(key->group, ctx); } + +int EC_KEY_get_flags(const EC_KEY *key) + { + return key->flags; + } + +void EC_KEY_set_flags(EC_KEY *key, int flags) + { + key->flags |= flags; + } + +void EC_KEY_clear_flags(EC_KEY *key, int flags) + { + key->flags &= ~flags; + } diff --git a/crypto/ec/ec_lcl.h b/crypto/ec/ec_lcl.h index fdd7aa275563a..da7967df38a36 100644 --- a/crypto/ec/ec_lcl.h +++ b/crypto/ec/ec_lcl.h @@ -3,7 +3,7 @@ * Originally written by Bodo Moeller for the OpenSSL project. */ /* ==================================================================== - * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. + * Copyright (c) 1998-2010 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -82,10 +82,15 @@ # endif #endif +/* Use default functions for poin2oct, oct2point and compressed coordinates */ +#define EC_FLAGS_DEFAULT_OCT 0x1 + /* Structure details are not part of the exported interface, * so all this may change in future versions. */ struct ec_method_st { + /* Various method flags */ + int flags; /* used by EC_METHOD_get_field_type: */ int field_type; /* a NID */ @@ -205,11 +210,14 @@ struct ec_group_st { * irreducible polynomial defining the field. */ - unsigned int poly[5]; /* Field specification for curves over GF(2^m). - * The irreducible f(t) is then of the form: - * t^poly[0] + t^poly[1] + ... + t^poly[k] - * where m = poly[0] > poly[1] > ... > poly[k] = 0. - */ + int poly[6]; /* Field specification for curves over GF(2^m). + * The irreducible f(t) is then of the form: + * t^poly[0] + t^poly[1] + ... + t^poly[k] + * where m = poly[0] > poly[1] > ... > poly[k] = 0. + * The array is terminated with poly[k+1]=-1. + * All elliptic curve irreducibles have at most 5 + * non-zero terms. + */ BIGNUM a, b; /* Curve coefficients. * (Here the assumption is that BIGNUMs can be used @@ -241,6 +249,7 @@ struct ec_key_st { point_conversion_form_t conv_form; int references; + int flags; EC_EXTRA_DATA *method_data; } /* EC_KEY */; @@ -388,3 +397,50 @@ int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); int ec_GF2m_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ec2_mult.c */ +int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, + size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GF2m_have_precompute_mult(const EC_GROUP *group); + +#ifndef OPENSSL_EC_NISTP_64_GCC_128 +/* method functions in ecp_nistp224.c */ +int ec_GFp_nistp224_group_init(EC_GROUP *group); +int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp224_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_nistp256.c */ +int ec_GFp_nistp256_group_init(EC_GROUP *group); +int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp256_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group); + +/* method functions in ecp_nistp521.c */ +int ec_GFp_nistp521_group_init(EC_GROUP *group); +int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *n, BN_CTX *); +int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx); +int ec_GFp_nistp521_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *); +int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx); +int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx); +int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group); + +/* utility functions in ecp_nistputil.c */ +void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, void *tmp_felems, + void (*felem_one)(void *out), + int (*felem_is_zero)(const void *in), + void (*felem_assign)(void *out, const void *in), + void (*felem_square)(void *out, const void *in), + void (*felem_mul)(void *out, const void *in1, const void *in2), + void (*felem_inv)(void *out, const void *in), + void (*felem_contract)(void *out, const void *in)); +void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in); +#endif diff --git a/crypto/ec/ec_lib.c b/crypto/ec/ec_lib.c index 5af84376c6025..25247b580332f 100644 --- a/crypto/ec/ec_lib.c +++ b/crypto/ec/ec_lib.c @@ -79,7 +79,7 @@ EC_GROUP *EC_GROUP_new(const EC_METHOD *meth) if (meth == NULL) { - ECerr(EC_F_EC_GROUP_NEW, ERR_R_PASSED_NULL_PARAMETER); + ECerr(EC_F_EC_GROUP_NEW, EC_R_SLOT_FULL); return NULL; } if (meth->group_init == 0) @@ -425,7 +425,7 @@ int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM * return group->meth->group_get_curve(group, p, a, b, ctx); } - +#ifndef OPENSSL_NO_EC2M int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) { if (group->meth->group_set_curve == 0) @@ -446,7 +446,7 @@ int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM } return group->meth->group_get_curve(group, p, a, b, ctx); } - +#endif int EC_GROUP_get_degree(const EC_GROUP *group) { @@ -740,7 +740,7 @@ void EC_POINT_clear_free(EC_POINT *point) if (point->meth->point_clear_finish != 0) point->meth->point_clear_finish(point); - else if (point->meth != NULL && point->meth->point_finish != 0) + else if (point->meth->point_finish != 0) point->meth->point_finish(point); OPENSSL_cleanse(point, sizeof *point); OPENSSL_free(point); @@ -856,7 +856,7 @@ int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); } - +#ifndef OPENSSL_NO_EC2M int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) { @@ -872,7 +872,7 @@ int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, } return group->meth->point_set_affine_coordinates(group, point, x, y, ctx); } - +#endif int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) @@ -890,7 +890,7 @@ int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group, const EC_POINT *p return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); } - +#ifndef OPENSSL_NO_EC2M int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) { @@ -906,75 +906,7 @@ int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group, const EC_POINT * } return group->meth->point_get_affine_coordinates(group, point, x, y, ctx); } - - -int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *ctx) - { - if (group->meth->point_set_compressed_coordinates == 0) - { - ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); - return 0; - } - if (group->meth != point->meth) - { - ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); - return 0; - } - return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); - } - - -int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x, int y_bit, BN_CTX *ctx) - { - if (group->meth->point_set_compressed_coordinates == 0) - { - ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); - return 0; - } - if (group->meth != point->meth) - { - ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); - return 0; - } - return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); - } - - -size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { - if (group->meth->point2oct == 0) - { - ECerr(EC_F_EC_POINT_POINT2OCT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); - return 0; - } - if (group->meth != point->meth) - { - ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_INCOMPATIBLE_OBJECTS); - return 0; - } - return group->meth->point2oct(group, point, form, buf, len, ctx); - } - - -int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - if (group->meth->oct2point == 0) - { - ECerr(EC_F_EC_POINT_OCT2POINT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); - return 0; - } - if (group->meth != point->meth) - { - ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_INCOMPATIBLE_OBJECTS); - return 0; - } - return group->meth->oct2point(group, point, buf, len, ctx); - } - +#endif int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { diff --git a/crypto/ec/ec_mult.c b/crypto/ec/ec_mult.c index ee422697267e6..19f21675fbd80 100644 --- a/crypto/ec/ec_mult.c +++ b/crypto/ec/ec_mult.c @@ -226,6 +226,12 @@ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) sign = -1; } + if (scalar->d == NULL || scalar->top == 0) + { + ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); + goto err; + } + len = BN_num_bits(scalar); r = OPENSSL_malloc(len + 1); /* modified wNAF may be one digit longer than binary representation * (*ret_len will be set to the actual length, i.e. at most @@ -235,12 +241,6 @@ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len) ECerr(EC_F_COMPUTE_WNAF, ERR_R_MALLOC_FAILURE); goto err; } - - if (scalar->d == NULL || scalar->top == 0) - { - ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); - goto err; - } window_val = scalar->d[0] & mask; j = 0; while ((window_val != 0) || (j + w + 1 < len)) /* if j+w+1 >= len, window_val will not increase */ @@ -421,7 +421,7 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, if (numblocks > pre_comp->numblocks) numblocks = pre_comp->numblocks; - pre_points_per_block = 1u << (pre_comp->w - 1); + pre_points_per_block = (size_t)1 << (pre_comp->w - 1); /* check that pre_comp looks sane */ if (pre_comp->num != (pre_comp->numblocks * pre_points_per_block)) @@ -463,7 +463,7 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); wsize[i] = EC_window_bits_for_scalar_size(bits); - num_val += 1u << (wsize[i] - 1); + num_val += (size_t)1 << (wsize[i] - 1); wNAF[i + 1] = NULL; /* make sure we always have a pivot */ wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i]); if (wNAF[i] == NULL) @@ -602,7 +602,7 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, for (i = 0; i < num + num_scalar; i++) { val_sub[i] = v; - for (j = 0; j < (1u << (wsize[i] - 1)); j++) + for (j = 0; j < ((size_t)1 << (wsize[i] - 1)); j++) { *v = EC_POINT_new(group); if (*v == NULL) goto err; @@ -638,7 +638,7 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, if (wsize[i] > 1) { if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; - for (j = 1; j < (1u << (wsize[i] - 1)); j++) + for (j = 1; j < ((size_t)1 << (wsize[i] - 1)); j++) { if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; } @@ -822,7 +822,7 @@ int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *ctx) numblocks = (bits + blocksize - 1) / blocksize; /* max. number of blocks to use for wNAF splitting */ - pre_points_per_block = 1u << (w - 1); + pre_points_per_block = (size_t)1 << (w - 1); num = pre_points_per_block * numblocks; /* number of points to compute and store */ points = OPENSSL_malloc(sizeof (EC_POINT*)*(num + 1)); diff --git a/crypto/ec/ec_oct.c b/crypto/ec/ec_oct.c new file mode 100644 index 0000000000000..fd9db0798d3d3 --- /dev/null +++ b/crypto/ec/ec_oct.c @@ -0,0 +1,199 @@ +/* crypto/ec/ec_lib.c */ +/* + * Originally written by Bodo Moeller for the OpenSSL project. + */ +/* ==================================================================== + * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Binary polynomial ECC support in OpenSSL originally developed by + * SUN MICROSYSTEMS, INC., and contributed to the OpenSSL project. + */ + +#include <string.h> + +#include <openssl/err.h> +#include <openssl/opensslv.h> + +#include "ec_lcl.h" + +int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, int y_bit, BN_CTX *ctx) + { + if (group->meth->point_set_compressed_coordinates == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) + { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_set_compressed_coordinates( + group, point, x, y_bit, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GFP, EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_set_compressed_coordinates( + group, point, x, y_bit, ctx); +#endif + } + return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); + } + +#ifndef OPENSSL_NO_EC2M +int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x, int y_bit, BN_CTX *ctx) + { + if (group->meth->point_set_compressed_coordinates == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) + { + ECerr(EC_F_EC_POINT_SET_COMPRESSED_COORDINATES_GF2M, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) + { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_set_compressed_coordinates( + group, point, x, y_bit, ctx); + else + return ec_GF2m_simple_set_compressed_coordinates( + group, point, x, y_bit, ctx); + } + return group->meth->point_set_compressed_coordinates(group, point, x, y_bit, ctx); + } +#endif + +size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) + { + if (group->meth->point2oct == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) + { + ECerr(EC_F_EC_POINT_POINT2OCT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) + { + ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) + { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_point2oct(group, point, + form, buf, len, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_POINT2OCT, EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_point2oct(group, point, + form, buf, len, ctx); +#endif + } + + return group->meth->point2oct(group, point, form, buf, len, ctx); + } + + +int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) + { + if (group->meth->oct2point == 0 + && !(group->meth->flags & EC_FLAGS_DEFAULT_OCT)) + { + ECerr(EC_F_EC_POINT_OCT2POINT, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED); + return 0; + } + if (group->meth != point->meth) + { + ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_INCOMPATIBLE_OBJECTS); + return 0; + } + if(group->meth->flags & EC_FLAGS_DEFAULT_OCT) + { + if (group->meth->field_type == NID_X9_62_prime_field) + return ec_GFp_simple_oct2point(group, point, + buf, len, ctx); + else +#ifdef OPENSSL_NO_EC2M + { + ECerr(EC_F_EC_POINT_OCT2POINT, EC_R_GF2M_NOT_SUPPORTED); + return 0; + } +#else + return ec_GF2m_simple_oct2point(group, point, + buf, len, ctx); +#endif + } + return group->meth->oct2point(group, point, buf, len, ctx); + } + diff --git a/crypto/ec/ec_pmeth.c b/crypto/ec/ec_pmeth.c new file mode 100644 index 0000000000000..d1ed66c37e76e --- /dev/null +++ b/crypto/ec/ec_pmeth.c @@ -0,0 +1,341 @@ +/* Written by Dr Stephen N Henson (steve@openssl.org) for the OpenSSL + * project 2006. + */ +/* ==================================================================== + * Copyright (c) 2006 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * licensing@OpenSSL.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ + +#include <stdio.h> +#include "cryptlib.h" +#include <openssl/asn1t.h> +#include <openssl/x509.h> +#include <openssl/ec.h> +#include <openssl/ecdsa.h> +#include <openssl/evp.h> +#include "evp_locl.h" + +/* EC pkey context structure */ + +typedef struct + { + /* Key and paramgen group */ + EC_GROUP *gen_group; + /* message digest */ + const EVP_MD *md; + } EC_PKEY_CTX; + +static int pkey_ec_init(EVP_PKEY_CTX *ctx) + { + EC_PKEY_CTX *dctx; + dctx = OPENSSL_malloc(sizeof(EC_PKEY_CTX)); + if (!dctx) + return 0; + dctx->gen_group = NULL; + dctx->md = NULL; + + ctx->data = dctx; + + return 1; + } + +static int pkey_ec_copy(EVP_PKEY_CTX *dst, EVP_PKEY_CTX *src) + { + EC_PKEY_CTX *dctx, *sctx; + if (!pkey_ec_init(dst)) + return 0; + sctx = src->data; + dctx = dst->data; + if (sctx->gen_group) + { + dctx->gen_group = EC_GROUP_dup(sctx->gen_group); + if (!dctx->gen_group) + return 0; + } + dctx->md = sctx->md; + return 1; + } + +static void pkey_ec_cleanup(EVP_PKEY_CTX *ctx) + { + EC_PKEY_CTX *dctx = ctx->data; + if (dctx) + { + if (dctx->gen_group) + EC_GROUP_free(dctx->gen_group); + OPENSSL_free(dctx); + } + } + +static int pkey_ec_sign(EVP_PKEY_CTX *ctx, unsigned char *sig, size_t *siglen, + const unsigned char *tbs, size_t tbslen) + { + int ret, type; + unsigned int sltmp; + EC_PKEY_CTX *dctx = ctx->data; + EC_KEY *ec = ctx->pkey->pkey.ec; + + if (!sig) + { + *siglen = ECDSA_size(ec); + return 1; + } + else if(*siglen < (size_t)ECDSA_size(ec)) + { + ECerr(EC_F_PKEY_EC_SIGN, EC_R_BUFFER_TOO_SMALL); + return 0; + } + + if (dctx->md) + type = EVP_MD_type(dctx->md); + else + type = NID_sha1; + + + ret = ECDSA_sign(type, tbs, tbslen, sig, &sltmp, ec); + + if (ret <= 0) + return ret; + *siglen = (size_t)sltmp; + return 1; + } + +static int pkey_ec_verify(EVP_PKEY_CTX *ctx, + const unsigned char *sig, size_t siglen, + const unsigned char *tbs, size_t tbslen) + { + int ret, type; + EC_PKEY_CTX *dctx = ctx->data; + EC_KEY *ec = ctx->pkey->pkey.ec; + + if (dctx->md) + type = EVP_MD_type(dctx->md); + else + type = NID_sha1; + + ret = ECDSA_verify(type, tbs, tbslen, sig, siglen, ec); + + return ret; + } + +static int pkey_ec_derive(EVP_PKEY_CTX *ctx, unsigned char *key, size_t *keylen) + { + int ret; + size_t outlen; + const EC_POINT *pubkey = NULL; + if (!ctx->pkey || !ctx->peerkey) + { + ECerr(EC_F_PKEY_EC_DERIVE, EC_R_KEYS_NOT_SET); + return 0; + } + + if (!key) + { + const EC_GROUP *group; + group = EC_KEY_get0_group(ctx->pkey->pkey.ec); + *keylen = (EC_GROUP_get_degree(group) + 7)/8; + return 1; + } + + pubkey = EC_KEY_get0_public_key(ctx->peerkey->pkey.ec); + + /* NB: unlike PKS#3 DH, if *outlen is less than maximum size this is + * not an error, the result is truncated. + */ + + outlen = *keylen; + + ret = ECDH_compute_key(key, outlen, pubkey, ctx->pkey->pkey.ec, 0); + if (ret < 0) + return ret; + *keylen = ret; + return 1; + } + +static int pkey_ec_ctrl(EVP_PKEY_CTX *ctx, int type, int p1, void *p2) + { + EC_PKEY_CTX *dctx = ctx->data; + EC_GROUP *group; + switch (type) + { + case EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID: + group = EC_GROUP_new_by_curve_name(p1); + if (group == NULL) + { + ECerr(EC_F_PKEY_EC_CTRL, EC_R_INVALID_CURVE); + return 0; + } + if (dctx->gen_group) + EC_GROUP_free(dctx->gen_group); + dctx->gen_group = group; + return 1; + + case EVP_PKEY_CTRL_MD: + if (EVP_MD_type((const EVP_MD *)p2) != NID_sha1 && + EVP_MD_type((const EVP_MD *)p2) != NID_ecdsa_with_SHA1 && + EVP_MD_type((const EVP_MD *)p2) != NID_sha224 && + EVP_MD_type((const EVP_MD *)p2) != NID_sha256 && + EVP_MD_type((const EVP_MD *)p2) != NID_sha384 && + EVP_MD_type((const EVP_MD *)p2) != NID_sha512) + { + ECerr(EC_F_PKEY_EC_CTRL, EC_R_INVALID_DIGEST_TYPE); + return 0; + } + dctx->md = p2; + return 1; + + case EVP_PKEY_CTRL_PEER_KEY: + /* Default behaviour is OK */ + case EVP_PKEY_CTRL_DIGESTINIT: + case EVP_PKEY_CTRL_PKCS7_SIGN: + case EVP_PKEY_CTRL_CMS_SIGN: + return 1; + + default: + return -2; + + } + } + +static int pkey_ec_ctrl_str(EVP_PKEY_CTX *ctx, + const char *type, const char *value) + { + if (!strcmp(type, "ec_paramgen_curve")) + { + int nid; + nid = OBJ_sn2nid(value); + if (nid == NID_undef) + nid = OBJ_ln2nid(value); + if (nid == NID_undef) + { + ECerr(EC_F_PKEY_EC_CTRL_STR, EC_R_INVALID_CURVE); + return 0; + } + return EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid); + } + return -2; + } + +static int pkey_ec_paramgen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) + { + EC_KEY *ec = NULL; + EC_PKEY_CTX *dctx = ctx->data; + int ret = 0; + if (dctx->gen_group == NULL) + { + ECerr(EC_F_PKEY_EC_PARAMGEN, EC_R_NO_PARAMETERS_SET); + return 0; + } + ec = EC_KEY_new(); + if (!ec) + return 0; + ret = EC_KEY_set_group(ec, dctx->gen_group); + if (ret) + EVP_PKEY_assign_EC_KEY(pkey, ec); + else + EC_KEY_free(ec); + return ret; + } + +static int pkey_ec_keygen(EVP_PKEY_CTX *ctx, EVP_PKEY *pkey) + { + EC_KEY *ec = NULL; + if (ctx->pkey == NULL) + { + ECerr(EC_F_PKEY_EC_KEYGEN, EC_R_NO_PARAMETERS_SET); + return 0; + } + ec = EC_KEY_new(); + if (!ec) + return 0; + EVP_PKEY_assign_EC_KEY(pkey, ec); + /* Note: if error return, pkey is freed by parent routine */ + if (!EVP_PKEY_copy_parameters(pkey, ctx->pkey)) + return 0; + return EC_KEY_generate_key(pkey->pkey.ec); + } + +const EVP_PKEY_METHOD ec_pkey_meth = + { + EVP_PKEY_EC, + 0, + pkey_ec_init, + pkey_ec_copy, + pkey_ec_cleanup, + + 0, + pkey_ec_paramgen, + + 0, + pkey_ec_keygen, + + 0, + pkey_ec_sign, + + 0, + pkey_ec_verify, + + 0,0, + + 0,0,0,0, + + 0,0, + + 0,0, + + 0, + pkey_ec_derive, + + pkey_ec_ctrl, + pkey_ec_ctrl_str + + }; diff --git a/crypto/ec/eck_prn.c b/crypto/ec/eck_prn.c new file mode 100644 index 0000000000000..06de8f3959d57 --- /dev/null +++ b/crypto/ec/eck_prn.c @@ -0,0 +1,392 @@ +/* crypto/ec/eck_prn.c */ +/* + * Written by Nils Larsch for the OpenSSL project. + */ +/* ==================================================================== + * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions originally developed by SUN MICROSYSTEMS, INC., and + * contributed to the OpenSSL project. + */ + +#include <stdio.h> +#include "cryptlib.h" +#include <openssl/evp.h> +#include <openssl/ec.h> +#include <openssl/bn.h> + +#ifndef OPENSSL_NO_FP_API +int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off) + { + BIO *b; + int ret; + + if ((b=BIO_new(BIO_s_file())) == NULL) + { + ECerr(EC_F_ECPKPARAMETERS_PRINT_FP,ERR_R_BUF_LIB); + return(0); + } + BIO_set_fp(b, fp, BIO_NOCLOSE); + ret = ECPKParameters_print(b, x, off); + BIO_free(b); + return(ret); + } + +int EC_KEY_print_fp(FILE *fp, const EC_KEY *x, int off) + { + BIO *b; + int ret; + + if ((b=BIO_new(BIO_s_file())) == NULL) + { + ECerr(EC_F_EC_KEY_PRINT_FP, ERR_R_BIO_LIB); + return(0); + } + BIO_set_fp(b, fp, BIO_NOCLOSE); + ret = EC_KEY_print(b, x, off); + BIO_free(b); + return(ret); + } + +int ECParameters_print_fp(FILE *fp, const EC_KEY *x) + { + BIO *b; + int ret; + + if ((b=BIO_new(BIO_s_file())) == NULL) + { + ECerr(EC_F_ECPARAMETERS_PRINT_FP, ERR_R_BIO_LIB); + return(0); + } + BIO_set_fp(b, fp, BIO_NOCLOSE); + ret = ECParameters_print(b, x); + BIO_free(b); + return(ret); + } +#endif + +int EC_KEY_print(BIO *bp, const EC_KEY *x, int off) + { + EVP_PKEY *pk; + int ret; + pk = EVP_PKEY_new(); + if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *)x)) + return 0; + ret = EVP_PKEY_print_private(bp, pk, off, NULL); + EVP_PKEY_free(pk); + return ret; + } + +int ECParameters_print(BIO *bp, const EC_KEY *x) + { + EVP_PKEY *pk; + int ret; + pk = EVP_PKEY_new(); + if (!pk || !EVP_PKEY_set1_EC_KEY(pk, (EC_KEY *)x)) + return 0; + ret = EVP_PKEY_print_params(bp, pk, 4, NULL); + EVP_PKEY_free(pk); + return ret; + } + +static int print_bin(BIO *fp, const char *str, const unsigned char *num, + size_t len, int off); + +int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off) + { + unsigned char *buffer=NULL; + size_t buf_len=0, i; + int ret=0, reason=ERR_R_BIO_LIB; + BN_CTX *ctx=NULL; + const EC_POINT *point=NULL; + BIGNUM *p=NULL, *a=NULL, *b=NULL, *gen=NULL, + *order=NULL, *cofactor=NULL; + const unsigned char *seed; + size_t seed_len=0; + + static const char *gen_compressed = "Generator (compressed):"; + static const char *gen_uncompressed = "Generator (uncompressed):"; + static const char *gen_hybrid = "Generator (hybrid):"; + + if (!x) + { + reason = ERR_R_PASSED_NULL_PARAMETER; + goto err; + } + + ctx = BN_CTX_new(); + if (ctx == NULL) + { + reason = ERR_R_MALLOC_FAILURE; + goto err; + } + + if (EC_GROUP_get_asn1_flag(x)) + { + /* the curve parameter are given by an asn1 OID */ + int nid; + + if (!BIO_indent(bp, off, 128)) + goto err; + + nid = EC_GROUP_get_curve_name(x); + if (nid == 0) + goto err; + + if (BIO_printf(bp, "ASN1 OID: %s", OBJ_nid2sn(nid)) <= 0) + goto err; + if (BIO_printf(bp, "\n") <= 0) + goto err; + } + else + { + /* explicit parameters */ + int is_char_two = 0; + point_conversion_form_t form; + int tmp_nid = EC_METHOD_get_field_type(EC_GROUP_method_of(x)); + + if (tmp_nid == NID_X9_62_characteristic_two_field) + is_char_two = 1; + + if ((p = BN_new()) == NULL || (a = BN_new()) == NULL || + (b = BN_new()) == NULL || (order = BN_new()) == NULL || + (cofactor = BN_new()) == NULL) + { + reason = ERR_R_MALLOC_FAILURE; + goto err; + } +#ifndef OPENSSL_NO_EC2M + if (is_char_two) + { + if (!EC_GROUP_get_curve_GF2m(x, p, a, b, ctx)) + { + reason = ERR_R_EC_LIB; + goto err; + } + } + else /* prime field */ +#endif + { + if (!EC_GROUP_get_curve_GFp(x, p, a, b, ctx)) + { + reason = ERR_R_EC_LIB; + goto err; + } + } + + if ((point = EC_GROUP_get0_generator(x)) == NULL) + { + reason = ERR_R_EC_LIB; + goto err; + } + if (!EC_GROUP_get_order(x, order, NULL) || + !EC_GROUP_get_cofactor(x, cofactor, NULL)) + { + reason = ERR_R_EC_LIB; + goto err; + } + + form = EC_GROUP_get_point_conversion_form(x); + + if ((gen = EC_POINT_point2bn(x, point, + form, NULL, ctx)) == NULL) + { + reason = ERR_R_EC_LIB; + goto err; + } + + buf_len = (size_t)BN_num_bytes(p); + if (buf_len < (i = (size_t)BN_num_bytes(a))) + buf_len = i; + if (buf_len < (i = (size_t)BN_num_bytes(b))) + buf_len = i; + if (buf_len < (i = (size_t)BN_num_bytes(gen))) + buf_len = i; + if (buf_len < (i = (size_t)BN_num_bytes(order))) + buf_len = i; + if (buf_len < (i = (size_t)BN_num_bytes(cofactor))) + buf_len = i; + + if ((seed = EC_GROUP_get0_seed(x)) != NULL) + seed_len = EC_GROUP_get_seed_len(x); + + buf_len += 10; + if ((buffer = OPENSSL_malloc(buf_len)) == NULL) + { + reason = ERR_R_MALLOC_FAILURE; + goto err; + } + + if (!BIO_indent(bp, off, 128)) + goto err; + + /* print the 'short name' of the field type */ + if (BIO_printf(bp, "Field Type: %s\n", OBJ_nid2sn(tmp_nid)) + <= 0) + goto err; + + if (is_char_two) + { + /* print the 'short name' of the base type OID */ + int basis_type = EC_GROUP_get_basis_type(x); + if (basis_type == 0) + goto err; + + if (!BIO_indent(bp, off, 128)) + goto err; + + if (BIO_printf(bp, "Basis Type: %s\n", + OBJ_nid2sn(basis_type)) <= 0) + goto err; + + /* print the polynomial */ + if ((p != NULL) && !ASN1_bn_print(bp, "Polynomial:", p, buffer, + off)) + goto err; + } + else + { + if ((p != NULL) && !ASN1_bn_print(bp, "Prime:", p, buffer,off)) + goto err; + } + if ((a != NULL) && !ASN1_bn_print(bp, "A: ", a, buffer, off)) + goto err; + if ((b != NULL) && !ASN1_bn_print(bp, "B: ", b, buffer, off)) + goto err; + if (form == POINT_CONVERSION_COMPRESSED) + { + if ((gen != NULL) && !ASN1_bn_print(bp, gen_compressed, gen, + buffer, off)) + goto err; + } + else if (form == POINT_CONVERSION_UNCOMPRESSED) + { + if ((gen != NULL) && !ASN1_bn_print(bp, gen_uncompressed, gen, + buffer, off)) + goto err; + } + else /* form == POINT_CONVERSION_HYBRID */ + { + if ((gen != NULL) && !ASN1_bn_print(bp, gen_hybrid, gen, + buffer, off)) + goto err; + } + if ((order != NULL) && !ASN1_bn_print(bp, "Order: ", order, + buffer, off)) goto err; + if ((cofactor != NULL) && !ASN1_bn_print(bp, "Cofactor: ", cofactor, + buffer, off)) goto err; + if (seed && !print_bin(bp, "Seed:", seed, seed_len, off)) + goto err; + } + ret=1; +err: + if (!ret) + ECerr(EC_F_ECPKPARAMETERS_PRINT, reason); + if (p) + BN_free(p); + if (a) + BN_free(a); + if (b) + BN_free(b); + if (gen) + BN_free(gen); + if (order) + BN_free(order); + if (cofactor) + BN_free(cofactor); + if (ctx) + BN_CTX_free(ctx); + if (buffer != NULL) + OPENSSL_free(buffer); + return(ret); + } + +static int print_bin(BIO *fp, const char *name, const unsigned char *buf, + size_t len, int off) + { + size_t i; + char str[128]; + + if (buf == NULL) + return 1; + if (off) + { + if (off > 128) + off=128; + memset(str,' ',off); + if (BIO_write(fp, str, off) <= 0) + return 0; + } + + if (BIO_printf(fp,"%s", name) <= 0) + return 0; + + for (i=0; i<len; i++) + { + if ((i%15) == 0) + { + str[0]='\n'; + memset(&(str[1]),' ',off+4); + if (BIO_write(fp, str, off+1+4) <= 0) + return 0; + } + if (BIO_printf(fp,"%02x%s",buf[i],((i+1) == len)?"":":") <= 0) + return 0; + } + if (BIO_write(fp,"\n",1) <= 0) + return 0; + + return 1; + } diff --git a/crypto/ec/ecp_mont.c b/crypto/ec/ecp_mont.c index 9fc4a466a59f2..079e47431b4f8 100644 --- a/crypto/ec/ecp_mont.c +++ b/crypto/ec/ecp_mont.c @@ -63,12 +63,20 @@ #include <openssl/err.h> +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif + #include "ec_lcl.h" const EC_METHOD *EC_GFp_mont_method(void) { +#ifdef OPENSSL_FIPS + return fips_ec_gfp_mont_method(); +#else static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_prime_field, ec_GFp_mont_group_init, ec_GFp_mont_group_finish, @@ -87,9 +95,7 @@ const EC_METHOD *EC_GFp_mont_method(void) ec_GFp_simple_get_Jprojective_coordinates_GFp, ec_GFp_simple_point_set_affine_coordinates, ec_GFp_simple_point_get_affine_coordinates, - ec_GFp_simple_set_compressed_coordinates, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, + 0,0,0, ec_GFp_simple_add, ec_GFp_simple_dbl, ec_GFp_simple_invert, @@ -108,7 +114,9 @@ const EC_METHOD *EC_GFp_mont_method(void) ec_GFp_mont_field_decode, ec_GFp_mont_field_set_to_one }; + return &ret; +#endif } diff --git a/crypto/ec/ecp_nist.c b/crypto/ec/ecp_nist.c index 71893d5eaba18..aad2d5f44389a 100644 --- a/crypto/ec/ecp_nist.c +++ b/crypto/ec/ecp_nist.c @@ -67,9 +67,17 @@ #include <openssl/obj_mac.h> #include "ec_lcl.h" +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif + const EC_METHOD *EC_GFp_nist_method(void) { +#ifdef OPENSSL_FIPS + return fips_ec_gfp_nist_method(); +#else static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_prime_field, ec_GFp_simple_group_init, ec_GFp_simple_group_finish, @@ -88,9 +96,7 @@ const EC_METHOD *EC_GFp_nist_method(void) ec_GFp_simple_get_Jprojective_coordinates_GFp, ec_GFp_simple_point_set_affine_coordinates, ec_GFp_simple_point_get_affine_coordinates, - ec_GFp_simple_set_compressed_coordinates, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, + 0,0,0, ec_GFp_simple_add, ec_GFp_simple_dbl, ec_GFp_simple_invert, @@ -110,11 +116,8 @@ const EC_METHOD *EC_GFp_nist_method(void) 0 /* field_set_to_one */ }; return &ret; - } - -#if BN_BITS2 == 64 -#define NO_32_BIT_TYPE #endif + } int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src) { @@ -139,34 +142,12 @@ int ec_GFp_nist_group_set_curve(EC_GROUP *group, const BIGNUM *p, if (BN_ucmp(BN_get0_nist_prime_192(), p) == 0) group->field_mod_func = BN_nist_mod_192; else if (BN_ucmp(BN_get0_nist_prime_224(), p) == 0) - { -#ifndef NO_32_BIT_TYPE group->field_mod_func = BN_nist_mod_224; -#else - ECerr(EC_F_EC_GFP_NIST_GROUP_SET_CURVE, EC_R_NOT_A_SUPPORTED_NIST_PRIME); - goto err; -#endif - } else if (BN_ucmp(BN_get0_nist_prime_256(), p) == 0) - { -#ifndef NO_32_BIT_TYPE group->field_mod_func = BN_nist_mod_256; -#else - ECerr(EC_F_EC_GFP_NIST_GROUP_SET_CURVE, EC_R_NOT_A_SUPPORTED_NIST_PRIME); - goto err; -#endif - } else if (BN_ucmp(BN_get0_nist_prime_384(), p) == 0) - { -#ifndef NO_32_BIT_TYPE group->field_mod_func = BN_nist_mod_384; -#else - ECerr(EC_F_EC_GFP_NIST_GROUP_SET_CURVE, EC_R_NOT_A_SUPPORTED_NIST_PRIME); - goto err; -#endif - } else if (BN_ucmp(BN_get0_nist_prime_521(), p) == 0) - /* this one works in the NO_32_BIT_TYPE case */ group->field_mod_func = BN_nist_mod_521; else { diff --git a/crypto/ec/ecp_nistp224.c b/crypto/ec/ecp_nistp224.c new file mode 100644 index 0000000000000..b5ff56c252776 --- /dev/null +++ b/crypto/ec/ecp_nistp224.c @@ -0,0 +1,1658 @@ +/* crypto/ec/ecp_nistp224.c */ +/* + * Written by Emilia Kasper (Google) for the OpenSSL project. + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-224 elliptic curve point multiplication + * + * Inspired by Daniel J. Bernstein's public domain nistp224 implementation + * and Adam Langley's public domain 64-bit C implementation of curve25519 + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +#ifndef OPENSSL_SYS_VMS +#include <stdint.h> +#else +#include <inttypes.h> +#endif + +#include <string.h> +#include <openssl/err.h> +#include "ec_lcl.h" + +#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ + typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ +#else + #error "Need GCC 3.1 or later to define type uint128_t" +#endif + +typedef uint8_t u8; +typedef uint64_t u64; +typedef int64_t s64; + + +/******************************************************************************/ +/* INTERNAL REPRESENTATION OF FIELD ELEMENTS + * + * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 + * using 64-bit coefficients called 'limbs', + * and sometimes (for multiplication results) as + * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6 + * using 128-bit coefficients called 'widelimbs'. + * A 4-limb representation is an 'felem'; + * a 7-widelimb representation is a 'widefelem'. + * Even within felems, bits of adjacent limbs overlap, and we don't always + * reduce the representations: we ensure that inputs to each felem + * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, + * and fit into a 128-bit word without overflow. The coefficients are then + * again partially reduced to obtain an felem satisfying a_i < 2^57. + * We only reduce to the unique minimal representation at the end of the + * computation. + */ + +typedef uint64_t limb; +typedef uint128_t widelimb; + +typedef limb felem[4]; +typedef widelimb widefelem[7]; + +/* Field element represented as a byte arrary. + * 28*8 = 224 bits is also the group order size for the elliptic curve, + * and we also use this type for scalars for point multiplication. + */ +typedef u8 felem_bytearray[28]; + +static const felem_bytearray nistp224_curve_params[5] = { + {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, + 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01}, + {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, + 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE}, + {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ + 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, + 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4}, + {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ + 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, + 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21}, + {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ + 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, + 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34} +}; + +/* Precomputed multiples of the standard generator + * Points are given in coordinates (X, Y, Z) where Z normally is 1 + * (0 for the point at infinity). + * For each field element, slice a_0 is word 0, etc. + * + * The table has 2 * 16 elements, starting with the following: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^56G + * 3 | 0 0 1 1 | (2^56 + 1)G + * 4 | 0 1 0 0 | 2^112G + * 5 | 0 1 0 1 | (2^112 + 1)G + * 6 | 0 1 1 0 | (2^112 + 2^56)G + * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G + * 8 | 1 0 0 0 | 2^168G + * 9 | 1 0 0 1 | (2^168 + 1)G + * 10 | 1 0 1 0 | (2^168 + 2^56)G + * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G + * 12 | 1 1 0 0 | (2^168 + 2^112)G + * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G + * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G + * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G + * followed by a copy of this with each element multiplied by 2^28. + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point, + * and then another four locations using the second 16 elements. + */ +static const felem gmul[2][16][3] = +{{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, + {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, + {1, 0, 0, 0}}, + {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, + {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, + {1, 0, 0, 0}}, + {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, + {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, + {1, 0, 0, 0}}, + {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, + {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, + {1, 0, 0, 0}}, + {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, + {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, + {1, 0, 0, 0}}, + {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, + {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, + {1, 0, 0, 0}}, + {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, + {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, + {1, 0, 0, 0}}, + {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, + {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, + {1, 0, 0, 0}}, + {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, + {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, + {1, 0, 0, 0}}, + {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, + {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, + {1, 0, 0, 0}}, + {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, + {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, + {1, 0, 0, 0}}, + {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, + {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, + {1, 0, 0, 0}}, + {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, + {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, + {1, 0, 0, 0}}, + {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, + {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, + {1, 0, 0, 0}}, + {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, + {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, + {1, 0, 0, 0}}}, + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, + {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, + {1, 0, 0, 0}}, + {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, + {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, + {1, 0, 0, 0}}, + {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, + {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, + {1, 0, 0, 0}}, + {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, + {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, + {1, 0, 0, 0}}, + {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, + {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, + {1, 0, 0, 0}}, + {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, + {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, + {1, 0, 0, 0}}, + {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, + {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, + {1, 0, 0, 0}}, + {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, + {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, + {1, 0, 0, 0}}, + {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, + {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, + {1, 0, 0, 0}}, + {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, + {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, + {1, 0, 0, 0}}, + {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, + {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, + {1, 0, 0, 0}}, + {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, + {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, + {1, 0, 0, 0}}, + {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, + {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, + {1, 0, 0, 0}}, + {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, + {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, + {1, 0, 0, 0}}, + {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, + {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, + {1, 0, 0, 0}}}}; + +/* Precomputation for the group generator. */ +typedef struct { + felem g_pre_comp[2][16][3]; + int references; +} NISTP224_PRE_COMP; + +const EC_METHOD *EC_GFp_nistp224_method(void) + { + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp224_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp224_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp224_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */, + 0 /* point2oct */, + 0 /* oct2point */, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp224_points_mul, + ec_GFp_nistp224_precompute_mult, + ec_GFp_nistp224_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */ }; + + return &ret; + } + +/* Helper functions to convert field elements to/from internal representation */ +static void bin28_to_felem(felem out, const u8 in[28]) + { + out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; + out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; + out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; + out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; + } + +static void felem_to_bin28(u8 out[28], const felem in) + { + unsigned i; + for (i = 0; i < 7; ++i) + { + out[i] = in[0]>>(8*i); + out[i+7] = in[1]>>(8*i); + out[i+14] = in[2]>>(8*i); + out[i+21] = in[3]>>(8*i); + } + } + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) + { + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len-1-i]; + } + +/* From OpenSSL BIGNUM to internal representation */ +static int BN_to_felem(felem out, const BIGNUM *bn) + { + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof b_out); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof b_out) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin28_to_felem(out, b_out); + return 1; + } + +/* From internal representation to OpenSSL BIGNUM */ +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) + { + felem_bytearray b_in, b_out; + felem_to_bin28(b_in, in); + flip_endian(b_out, b_in, sizeof b_out); + return BN_bin2bn(b_out, sizeof b_out, out); + } + +/******************************************************************************/ +/* FIELD OPERATIONS + * + * Field operations, using the internal representation of field elements. + * NB! These operations are specific to our point multiplication and cannot be + * expected to be correct in general - e.g., multiplication with a large scalar + * will cause an overflow. + * + */ + +static void felem_one(felem out) + { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + } + +static void felem_assign(felem out, const felem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + +/* Sum two field elements: out += in */ +static void felem_sum(felem out, const felem in) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + } + +/* Get negative value: out = -in */ +/* Assumes in[i] < 2^57 */ +static void felem_neg(felem out, const felem in) + { + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] = two58p2 - in[0]; + out[1] = two58m42m2 - in[1]; + out[2] = two58m2 - in[2]; + out[3] = two58m2 - in[3]; + } + +/* Subtract field elements: out -= in */ +/* Assumes in[i] < 2^57 */ +static void felem_diff(felem out, const felem in) + { + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two58p2; + out[1] += two58m42m2; + out[2] += two58m2; + out[3] += two58m2; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +/* Subtract in unreduced 128-bit mode: out -= in */ +/* Assumes in[i] < 2^119 */ +static void widefelem_diff(widefelem out, const widefelem in) + { + static const widelimb two120 = ((widelimb) 1) << 120; + static const widelimb two120m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 64); + static const widelimb two120m104m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 104) - (((widelimb) 1) << 64); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two120; + out[1] += two120m64; + out[2] += two120m64; + out[3] += two120; + out[4] += two120m104m64; + out[5] += two120m64; + out[6] += two120m64; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; + } + +/* Subtract in mixed mode: out128 -= in64 */ +/* in[i] < 2^63 */ +static void felem_diff_128_64(widefelem out, const felem in) + { + static const widelimb two64p8 = (((widelimb) 1) << 64) + + (((widelimb) 1) << 8); + static const widelimb two64m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 8); + static const widelimb two64m48m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 48) - (((widelimb) 1) << 8); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two64p8; + out[1] += two64m48m8; + out[2] += two64m8; + out[3] += two64m8; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +/* Multiply a field element by a scalar: out = out * scalar + * The scalars we actually use are small, so results fit without overflow */ +static void felem_scalar(felem out, const limb scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + } + +/* Multiply an unreduced field element by a scalar: out = out * scalar + * The scalars we actually use are small, so results fit without overflow */ +static void widefelem_scalar(widefelem out, const widelimb scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + } + +/* Square a field element: out = in^2 */ +static void felem_square(widefelem out, const felem in) + { + limb tmp0, tmp1, tmp2; + tmp0 = 2 * in[0]; tmp1 = 2 * in[1]; tmp2 = 2 * in[2]; + out[0] = ((widelimb) in[0]) * in[0]; + out[1] = ((widelimb) in[0]) * tmp1; + out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; + out[3] = ((widelimb) in[3]) * tmp0 + + ((widelimb) in[1]) * tmp2; + out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; + out[5] = ((widelimb) in[3]) * tmp2; + out[6] = ((widelimb) in[3]) * in[3]; + } + +/* Multiply two field elements: out = in1 * in2 */ +static void felem_mul(widefelem out, const felem in1, const felem in2) + { + out[0] = ((widelimb) in1[0]) * in2[0]; + out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; + out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + + ((widelimb) in1[2]) * in2[0]; + out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + + ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; + out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + + ((widelimb) in1[3]) * in2[1]; + out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; + out[6] = ((widelimb) in1[3]) * in2[3]; + } + +/* Reduce seven 128-bit coefficients to four 64-bit coefficients. + * Requires in[i] < 2^126, + * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ +static void felem_reduce(felem out, const widefelem in) + { + static const widelimb two127p15 = (((widelimb) 1) << 127) + + (((widelimb) 1) << 15); + static const widelimb two127m71 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71); + static const widelimb two127m71m55 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71) - (((widelimb) 1) << 55); + widelimb output[5]; + + /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ + output[0] = in[0] + two127p15; + output[1] = in[1] + two127m71m55; + output[2] = in[2] + two127m71; + output[3] = in[3]; + output[4] = in[4]; + + /* Eliminate in[4], in[5], in[6] */ + output[4] += in[6] >> 16; + output[3] += (in[6] & 0xffff) << 40; + output[2] -= in[6]; + + output[3] += in[5] >> 16; + output[2] += (in[5] & 0xffff) << 40; + output[1] -= in[5]; + + output[2] += output[4] >> 16; + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 2 -> 3 -> 4 */ + output[3] += output[2] >> 56; + output[2] &= 0x00ffffffffffffff; + + output[4] = output[3] >> 56; + output[3] &= 0x00ffffffffffffff; + + /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ + + /* Eliminate output[4] */ + output[2] += output[4] >> 16; + /* output[2] < 2^56 + 2^56 = 2^57 */ + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 0 -> 1 -> 2 -> 3 */ + output[1] += output[0] >> 56; + out[0] = output[0] & 0x00ffffffffffffff; + + output[2] += output[1] >> 56; + /* output[2] < 2^57 + 2^72 */ + out[1] = output[1] & 0x00ffffffffffffff; + output[3] += output[2] >> 56; + /* output[3] <= 2^56 + 2^16 */ + out[2] = output[2] & 0x00ffffffffffffff; + + /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, + * out[3] <= 2^56 + 2^16 (due to final carry), + * so out < 2*p */ + out[3] = output[3]; + } + +static void felem_square_reduce(felem out, const felem in) + { + widefelem tmp; + felem_square(tmp, in); + felem_reduce(out, tmp); + } + +static void felem_mul_reduce(felem out, const felem in1, const felem in2) + { + widefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); + } + +/* Reduce to unique minimal representation. + * Requires 0 <= in < 2*p (always call felem_reduce first) */ +static void felem_contract(felem out, const felem in) + { + static const int64_t two56 = ((limb) 1) << 56; + /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ + /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ + int64_t tmp[4], a; + tmp[0] = in[0]; + tmp[1] = in[1]; + tmp[2] = in[2]; + tmp[3] = in[3]; + /* Case 1: a = 1 iff in >= 2^224 */ + a = (in[3] >> 56); + tmp[0] -= a; + tmp[1] += a << 40; + tmp[3] &= 0x00ffffffffffffff; + /* Case 2: a = 0 iff p <= in < 2^224, i.e., + * the high 128 bits are all 1 and the lower part is non-zero */ + a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | + (((int64_t)(in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); + a &= 0x00ffffffffffffff; + /* turn a into an all-one mask (if a = 0) or an all-zero mask */ + a = (a - 1) >> 63; + /* subtract 2^224 - 2^96 + 1 if a is all-one*/ + tmp[3] &= a ^ 0xffffffffffffffff; + tmp[2] &= a ^ 0xffffffffffffffff; + tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; + tmp[0] -= 1 & a; + + /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must + * be non-zero, so we only need one step */ + a = tmp[0] >> 63; + tmp[0] += two56 & a; + tmp[1] -= 1 & a; + + /* carry 1 -> 2 -> 3 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + /* Now 0 <= out < p */ + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; + } + +/* Zero-check: returns 1 if input is 0, and 0 otherwise. + * We know that field elements are reduced to in < 2^225, + * so we only need to check three cases: 0, 2^224 - 2^96 + 1, + * and 2^225 - 2^97 + 2 */ +static limb felem_is_zero(const felem in) + { + limb zero, two224m96p1, two225m97p2; + + zero = in[0] | in[1] | in[2] | in[3]; + zero = (((int64_t)(zero) - 1) >> 63) & 1; + two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); + two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; + two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); + two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; + return (zero | two224m96p1 | two225m97p2); + } + +static limb felem_is_zero_int(const felem in) + { + return (int) (felem_is_zero(in) & ((limb)1)); + } + +/* Invert a field element */ +/* Computation chain copied from djb's code */ +static void felem_inv(felem out, const felem in) + { + felem ftmp, ftmp2, ftmp3, ftmp4; + widefelem tmp; + unsigned i; + + felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ + for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ + { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ + for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ + for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ + for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ + { + felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ + for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ + { + felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ + for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ + { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ + felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ + for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ + { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } + felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ + } + +/* Copy in constant time: + * if icopy == 1, copy in to out, + * if icopy == 0, copy out to itself. */ +static void +copy_conditional(felem out, const felem in, limb icopy) + { + unsigned i; + /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ + const limb copy = -icopy; + for (i = 0; i < 4; ++i) + { + const limb tmp = copy & (in[i] ^ out[i]); + out[i] ^= tmp; + } + } + +/******************************************************************************/ +/* ELLIPTIC CURVE POINT OPERATIONS + * + * Points are represented in Jacobian projective coordinates: + * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), + * or to the point at infinity if Z == 0. + * + */ + +/* Double an elliptic curve point: + * (X', Y', Z') = 2 * (X, Y, Z), where + * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 + * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 + * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, + * while x_out == y_in is not (maybe this works, but it's not tested). */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) + { + widefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^58 < 2^60 */ + felem_mul(tmp, ftmp, ftmp2); + /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^57 = 2^60 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^57 + 2^57 = 2^58 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^57 + 2^57 = 2^58 */ + felem_square(tmp, ftmp); + /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^57 = 2^59 */ + felem_diff(beta, x_out); + /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ + felem_mul(tmp, alpha, beta); + /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ + felem_square(tmp2, gamma); + /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ + widefelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 2^116 = 2^119 */ + widefelem_diff(tmp, tmp2); + /* tmp[i] < 2^119 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp); + } + +/* Add two elliptic curve points: + * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where + * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - + * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 + * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 - X_3) - + * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 + * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) + * + * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. + */ + +/* This function is not entirely constant-time: + * it includes a branch for checking whether the two input points are equal, + * (while not equal to the point at infinity). + * This case never happens during single point multiplication, + * so there is no timing leak for ECDH or ECDSA signing. */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) + { + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; + widefelem tmp, tmp2; + limb z1_is_zero, z2_is_zero, x_equal, y_equal; + + if (!mixed) + { + /* ftmp2 = z2^2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* ftmp4 = z2^3 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp4, tmp); + + /* ftmp4 = z2^3*y1 */ + felem_mul(tmp2, ftmp4, y1); + felem_reduce(ftmp4, tmp2); + + /* ftmp2 = z2^2*x1 */ + felem_mul(tmp2, ftmp2, x1); + felem_reduce(ftmp2, tmp2); + } + else + { + /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ + + /* ftmp4 = z2^3*y1 */ + felem_assign(ftmp4, y1); + + /* ftmp2 = z2^2*x1 */ + felem_assign(ftmp2, x1); + } + + /* ftmp = z1^2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + /* ftmp3 = z1^3 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp3, tmp); + + /* tmp = z1^3*y2 */ + felem_mul(tmp, ftmp3, y2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp3 = z1^3*y2 - z2^3*y1 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp3, tmp); + + /* tmp = z1^2*x2 */ + felem_mul(tmp, ftmp, x2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp = z1^2*x2 - z2^2*x1 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp, tmp); + + /* the formulae are incorrect if the points are equal + * so we check for this and do doubling if this happens */ + x_equal = felem_is_zero(ftmp); + y_equal = felem_is_zero(ftmp3); + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) + { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* ftmp5 = z1*z2 */ + if (!mixed) + { + felem_mul(tmp, z1, z2); + felem_reduce(ftmp5, tmp); + } + else + { + /* special case z2 = 0 is handled later */ + felem_assign(ftmp5, z1); + } + + /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(z_out, tmp); + + /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); + + /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp4, ftmp5); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ + felem_square(tmp2, ftmp3); + /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ + + /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp2); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2 * 2^57 = 2^58 */ + + /* x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - + 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ + felem_reduce(x_out, tmp2); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ + felem_diff(ftmp2, x_out); + /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) */ + felem_mul(tmp2, ftmp3, ftmp2); + /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ + + /* y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - + z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + widefelem_diff(tmp2, tmp); + /* tmp2[i] < 2^118 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp2); + + /* the result (x_out, y_out, z_out) is incorrect if one of the inputs is + * the point at infinity, so we need to check for this separately */ + + /* if point 1 is at infinity, copy point 2 to output, and vice versa */ + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); + } + +/* select_point selects the |idx|th point from a precomputation table and + * copies it to out. */ +static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3]) + { + unsigned i, j; + limb *outlimbs = &out[0][0]; + memset(outlimbs, 0, 3 * sizeof(felem)); + + for (i = 0; i < size; i++) + { + const limb *inlimbs = &pre_comp[i][0][0]; + u64 mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < 4 * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } + } + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, unsigned i) + { + if (i >= 224) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; + } + +/* Interleaved point multiplication using precomputed point multiples: + * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], + * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple + * of the generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3]) + { + int i, skip; + unsigned num; + unsigned gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + u64 bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, 3 * sizeof(felem)); + + /* Loop over all scalars msb-to-lsb, interleaving additions + * of multiples of the generator (two in each of the last 28 rounds) + * and additions of other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first round */ + for (i = (num_points ? 220 : 27); i >= 0; --i) + { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 27)) + { + /* first, look 28 bits upwards */ + bits = get_bit(g_scalar, i + 196) << 3; + bits |= get_bit(g_scalar, i + 140) << 2; + bits |= get_bit(g_scalar, i + 84) << 1; + bits |= get_bit(g_scalar, i + 28); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + else + { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 168) << 3; + bits |= get_bit(g_scalar, i + 112) << 2; + bits |= get_bit(g_scalar, i + 56) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) + { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) + { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + copy_conditional(tmp[1], tmp[3], sign); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } + else + { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); + } + +/******************************************************************************/ +/* FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP224_PRE_COMP *nistp224_pre_comp_new() + { + NISTP224_PRE_COMP *ret = NULL; + ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret); + if (!ret) + { + ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); + ret->references = 1; + return ret; + } + +static void *nistp224_pre_comp_dup(void *src_) + { + NISTP224_PRE_COMP *src = src_; + + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + + return src_; + } + +static void nistp224_pre_comp_free(void *pre_) + { + int i; + NISTP224_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_free(pre); + } + +static void nistp224_pre_comp_clear_free(void *pre_) + { + int i; + NISTP224_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_cleanse(pre, sizeof *pre); + OPENSSL_free(pre); + } + +/******************************************************************************/ +/* OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp224_group_init(EC_GROUP *group) + { + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; + } + +int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || + (BN_cmp(curve_b, b))) + { + ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_224; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + +/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns + * (X', Y') = (X/Z^2, Y/Z^3) */ +int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) + { + felem z1, z2, x_in, y_in, x_out, y_out; + widefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || + (!BN_to_felem(z1, &point->Z))) return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) + { + if (!felem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) + { + if (!felem_to_BN(y, y_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; + } + +static void make_points_affine(size_t num, felem points[/*num*/][3], felem tmp_felems[/*num+1*/]) + { + /* Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). */ + ec_GFp_nistp_points_make_affine_internal( + num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *)) felem_one, + (int (*)(const void *)) felem_is_zero_int, + (void (*)(void *, const void *)) felem_assign, + (void (*)(void *, const void *)) felem_square_reduce, + (void (*)(void *, const void *, const void *)) felem_mul_reduce, + (void (*)(void *, const void *)) felem_inv, + (void (*)(void *, const void *)) felem_contract); + } + +/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values + * Result is stored in r (r can equal one of the inputs). */ +int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) + { + int ret = 0; + int j; + unsigned i; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem (*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + felem_bytearray tmp; + unsigned num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP224_PRE_COMP *pre = NULL; + const felem (*g_pre_comp)[16][3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) + { + pre = EC_EX_DATA_get_data(group->extra_data, + nistp224_pre_comp_dup, nistp224_pre_comp_free, + nistp224_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = &gmul[0]; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[0][1][0]) || + !felem_to_BN(y, g_pre_comp[0][1][1]) || + !felem_to_BN(z, g_pre_comp[0][1][2])) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* we don't have valid precomputation: + * treat the generator as a random point */ + num_points = num_points + 1; + } + + if (num_points > 0) + { + if (num_points >= 3) + { + /* unless we precompute multiples for just one or two points, + * converting those into affine form is time well spent */ + mixed = 1; + } + secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); + pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem)); + if (mixed) + tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem)); + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination */ + memset(secrets, 0, num_points * sizeof(felem_bytearray)); + memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); + for (i = 0; i < num_points; ++i) + { + if (i == num) + /* the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } + else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) + { + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(p_scalar) > 224) || (BN_is_negative(p_scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, &p->X)) || + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) goto err; + felem_assign(pre_comp[i][1][0], x_out); + felem_assign(pre_comp[i][1][1], y_out); + felem_assign(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) + { + if (j & 1) + { + point_add( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); + } + else + { + point_double( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) + { + memset(g_secret, 0, sizeof g_secret); + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation*/ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + g_secret, + mixed, (const felem (*)[17][3]) pre_comp, + g_pre_comp); + } + else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) + { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + +err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (secrets != NULL) + OPENSSL_free(secrets); + if (pre_comp != NULL) + OPENSSL_free(pre_comp); + if (tmp_felems != NULL) + OPENSSL_free(tmp_felems); + return ret; + } + +int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) + { + int ret = 0; + NISTP224_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[32]; + + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x); + BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp224_pre_comp_new()) == NULL) + goto err; + /* if the generator is the standard one, use built-in precomputation */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + ret = 1; + goto err; + } + if ((!BN_to_felem(pre->g_pre_comp[0][1][0], &group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[0][1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[0][1][2], &group->generator->Z))) + goto err; + /* compute 2^56*G, 2^112*G, 2^168*G for the first table, + * 2^28*G, 2^84*G, 2^140*G, 2^196*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) + { + point_double( + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 27; ++j) + { + point_double( + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } + if (i == 8) + break; + point_double( + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 27; ++j) + { + point_double( + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); + } + } + for (i = 0; i < 2; i++) + { + /* g_pre_comp[i][0] is the point at infinity */ + memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); + /* the remaining multiples */ + /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ + point_add( + pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], + pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], + pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ + point_add( + pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], + pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ + point_add( + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], + pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G */ + point_add( + pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], + pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], + pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) + { + /* odd multiples: add G resp. 2^28*G */ + point_add( + pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], + pre->g_pre_comp[i][2*j+1][2], pre->g_pre_comp[i][2*j][0], + pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], + 0, pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], + pre->g_pre_comp[i][1][2]); + } + } + make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) + goto err; + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (pre) + nistp224_pre_comp_free(pre); + return ret; + } + +int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) + { + if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, + nistp224_pre_comp_free, nistp224_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; + } + +#else +static void *dummy=&dummy; +#endif diff --git a/crypto/ec/ecp_nistp256.c b/crypto/ec/ecp_nistp256.c new file mode 100644 index 0000000000000..4bc0f5dce0221 --- /dev/null +++ b/crypto/ec/ecp_nistp256.c @@ -0,0 +1,2171 @@ +/* crypto/ec/ecp_nistp256.c */ +/* + * Written by Adam Langley (Google) for the OpenSSL project + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-256 elliptic curve point multiplication + * + * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. + * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 + * work which got its smarts from Daniel J. Bernstein's work on the same. + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +#ifndef OPENSSL_SYS_VMS +#include <stdint.h> +#else +#include <inttypes.h> +#endif + +#include <string.h> +#include <openssl/err.h> +#include "ec_lcl.h" + +#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ + typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ + typedef __int128_t int128_t; +#else + #error "Need GCC 3.1 or later to define type uint128_t" +#endif + +typedef uint8_t u8; +typedef uint32_t u32; +typedef uint64_t u64; +typedef int64_t s64; + +/* The underlying field. + * + * P256 operates over GF(2^256-2^224+2^192+2^96-1). We can serialise an element + * of this field into 32 bytes. We call this an felem_bytearray. */ + +typedef u8 felem_bytearray[32]; + +/* These are the parameters of P256, taken from FIPS 186-3, page 86. These + * values are big-endian. */ +static const felem_bytearray nistp256_curve_params[5] = { + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* p */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff}, + {0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, /* a = -3 */ + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfc}, /* b */ + {0x5a, 0xc6, 0x35, 0xd8, 0xaa, 0x3a, 0x93, 0xe7, + 0xb3, 0xeb, 0xbd, 0x55, 0x76, 0x98, 0x86, 0xbc, + 0x65, 0x1d, 0x06, 0xb0, 0xcc, 0x53, 0xb0, 0xf6, + 0x3b, 0xce, 0x3c, 0x3e, 0x27, 0xd2, 0x60, 0x4b}, + {0x6b, 0x17, 0xd1, 0xf2, 0xe1, 0x2c, 0x42, 0x47, /* x */ + 0xf8, 0xbc, 0xe6, 0xe5, 0x63, 0xa4, 0x40, 0xf2, + 0x77, 0x03, 0x7d, 0x81, 0x2d, 0xeb, 0x33, 0xa0, + 0xf4, 0xa1, 0x39, 0x45, 0xd8, 0x98, 0xc2, 0x96}, + {0x4f, 0xe3, 0x42, 0xe2, 0xfe, 0x1a, 0x7f, 0x9b, /* y */ + 0x8e, 0xe7, 0xeb, 0x4a, 0x7c, 0x0f, 0x9e, 0x16, + 0x2b, 0xce, 0x33, 0x57, 0x6b, 0x31, 0x5e, 0xce, + 0xcb, 0xb6, 0x40, 0x68, 0x37, 0xbf, 0x51, 0xf5} +}; + +/* The representation of field elements. + * ------------------------------------ + * + * We represent field elements with either four 128-bit values, eight 128-bit + * values, or four 64-bit values. The field element represented is: + * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + v[3]*2^192 (mod p) + * or: + * v[0]*2^0 + v[1]*2^64 + v[2]*2^128 + ... + v[8]*2^512 (mod p) + * + * 128-bit values are called 'limbs'. Since the limbs are spaced only 64 bits + * apart, but are 128-bits wide, the most significant bits of each limb overlap + * with the least significant bits of the next. + * + * A field element with four limbs is an 'felem'. One with eight limbs is a + * 'longfelem' + * + * A field element with four, 64-bit values is called a 'smallfelem'. Small + * values are used as intermediate values before multiplication. + */ + +#define NLIMBS 4 + +typedef uint128_t limb; +typedef limb felem[NLIMBS]; +typedef limb longfelem[NLIMBS * 2]; +typedef u64 smallfelem[NLIMBS]; + +/* This is the value of the prime as four 64-bit words, little-endian. */ +static const u64 kPrime[4] = { 0xfffffffffffffffful, 0xffffffff, 0, 0xffffffff00000001ul }; +static const limb bottom32bits = 0xffffffff; +static const u64 bottom63bits = 0x7ffffffffffffffful; + +/* bin32_to_felem takes a little-endian byte array and converts it into felem + * form. This assumes that the CPU is little-endian. */ +static void bin32_to_felem(felem out, const u8 in[32]) + { + out[0] = *((u64*) &in[0]); + out[1] = *((u64*) &in[8]); + out[2] = *((u64*) &in[16]); + out[3] = *((u64*) &in[24]); + } + +/* smallfelem_to_bin32 takes a smallfelem and serialises into a little endian, + * 32 byte array. This assumes that the CPU is little-endian. */ +static void smallfelem_to_bin32(u8 out[32], const smallfelem in) + { + *((u64*) &out[0]) = in[0]; + *((u64*) &out[8]) = in[1]; + *((u64*) &out[16]) = in[2]; + *((u64*) &out[24]) = in[3]; + } + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) + { + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len-1-i]; + } + +/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ +static int BN_to_felem(felem out, const BIGNUM *bn) + { + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof b_out); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof b_out) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin32_to_felem(out, b_out); + return 1; + } + +/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ +static BIGNUM *smallfelem_to_BN(BIGNUM *out, const smallfelem in) + { + felem_bytearray b_in, b_out; + smallfelem_to_bin32(b_in, in); + flip_endian(b_out, b_in, sizeof b_out); + return BN_bin2bn(b_out, sizeof b_out, out); + } + + +/* Field operations + * ---------------- */ + +static void smallfelem_one(smallfelem out) + { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + } + +static void smallfelem_assign(smallfelem out, const smallfelem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + +static void felem_assign(felem out, const felem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + +/* felem_sum sets out = out + in. */ +static void felem_sum(felem out, const felem in) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + } + +/* felem_small_sum sets out = out + in. */ +static void felem_small_sum(felem out, const smallfelem in) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + } + +/* felem_scalar sets out = out * scalar */ +static void felem_scalar(felem out, const u64 scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + } + +/* longfelem_scalar sets out = out * scalar */ +static void longfelem_scalar(longfelem out, const u64 scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; + } + +#define two105m41m9 (((limb)1) << 105) - (((limb)1) << 41) - (((limb)1) << 9) +#define two105 (((limb)1) << 105) +#define two105m41p9 (((limb)1) << 105) - (((limb)1) << 41) + (((limb)1) << 9) + +/* zero105 is 0 mod p */ +static const felem zero105 = { two105m41m9, two105, two105m41p9, two105m41p9 }; + +/* smallfelem_neg sets |out| to |-small| + * On exit: + * out[i] < out[i] + 2^105 + */ +static void smallfelem_neg(felem out, const smallfelem small) + { + /* In order to prevent underflow, we subtract from 0 mod p. */ + out[0] = zero105[0] - small[0]; + out[1] = zero105[1] - small[1]; + out[2] = zero105[2] - small[2]; + out[3] = zero105[3] - small[3]; + } + +/* felem_diff subtracts |in| from |out| + * On entry: + * in[i] < 2^104 + * On exit: + * out[i] < out[i] + 2^105 + */ +static void felem_diff(felem out, const felem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + out[0] += zero105[0]; + out[1] += zero105[1]; + out[2] += zero105[2]; + out[3] += zero105[3]; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +#define two107m43m11 (((limb)1) << 107) - (((limb)1) << 43) - (((limb)1) << 11) +#define two107 (((limb)1) << 107) +#define two107m43p11 (((limb)1) << 107) - (((limb)1) << 43) + (((limb)1) << 11) + +/* zero107 is 0 mod p */ +static const felem zero107 = { two107m43m11, two107, two107m43p11, two107m43p11 }; + +/* An alternative felem_diff for larger inputs |in| + * felem_diff_zero107 subtracts |in| from |out| + * On entry: + * in[i] < 2^106 + * On exit: + * out[i] < out[i] + 2^107 + */ +static void felem_diff_zero107(felem out, const felem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + out[0] += zero107[0]; + out[1] += zero107[1]; + out[2] += zero107[2]; + out[3] += zero107[3]; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + } + +/* longfelem_diff subtracts |in| from |out| + * On entry: + * in[i] < 7*2^67 + * On exit: + * out[i] < out[i] + 2^70 + 2^40 + */ +static void longfelem_diff(longfelem out, const longfelem in) + { + static const limb two70m8p6 = (((limb)1) << 70) - (((limb)1) << 8) + (((limb)1) << 6); + static const limb two70p40 = (((limb)1) << 70) + (((limb)1) << 40); + static const limb two70 = (((limb)1) << 70); + static const limb two70m40m38p6 = (((limb)1) << 70) - (((limb)1) << 40) - (((limb)1) << 38) + (((limb)1) << 6); + static const limb two70m6 = (((limb)1) << 70) - (((limb)1) << 6); + + /* add 0 mod p to avoid underflow */ + out[0] += two70m8p6; + out[1] += two70p40; + out[2] += two70; + out[3] += two70m40m38p6; + out[4] += two70m6; + out[5] += two70m6; + out[6] += two70m6; + out[7] += two70m6; + + /* in[i] < 7*2^67 < 2^70 - 2^40 - 2^38 + 2^6 */ + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; + out[7] -= in[7]; + } + +#define two64m0 (((limb)1) << 64) - 1 +#define two110p32m0 (((limb)1) << 110) + (((limb)1) << 32) - 1 +#define two64m46 (((limb)1) << 64) - (((limb)1) << 46) +#define two64m32 (((limb)1) << 64) - (((limb)1) << 32) + +/* zero110 is 0 mod p */ +static const felem zero110 = { two64m0, two110p32m0, two64m46, two64m32 }; + +/* felem_shrink converts an felem into a smallfelem. The result isn't quite + * minimal as the value may be greater than p. + * + * On entry: + * in[i] < 2^109 + * On exit: + * out[i] < 2^64 + */ +static void felem_shrink(smallfelem out, const felem in) + { + felem tmp; + u64 a, b, mask; + s64 high, low; + static const u64 kPrime3Test = 0x7fffffff00000001ul; /* 2^63 - 2^32 + 1 */ + + /* Carry 2->3 */ + tmp[3] = zero110[3] + in[3] + ((u64) (in[2] >> 64)); + /* tmp[3] < 2^110 */ + + tmp[2] = zero110[2] + (u64) in[2]; + tmp[0] = zero110[0] + in[0]; + tmp[1] = zero110[1] + in[1]; + /* tmp[0] < 2**110, tmp[1] < 2^111, tmp[2] < 2**65 */ + + /* We perform two partial reductions where we eliminate the + * high-word of tmp[3]. We don't update the other words till the end. + */ + a = tmp[3] >> 64; /* a < 2^46 */ + tmp[3] = (u64) tmp[3]; + tmp[3] -= a; + tmp[3] += ((limb)a) << 32; + /* tmp[3] < 2^79 */ + + b = a; + a = tmp[3] >> 64; /* a < 2^15 */ + b += a; /* b < 2^46 + 2^15 < 2^47 */ + tmp[3] = (u64) tmp[3]; + tmp[3] -= a; + tmp[3] += ((limb)a) << 32; + /* tmp[3] < 2^64 + 2^47 */ + + /* This adjusts the other two words to complete the two partial + * reductions. */ + tmp[0] += b; + tmp[1] -= (((limb)b) << 32); + + /* In order to make space in tmp[3] for the carry from 2 -> 3, we + * conditionally subtract kPrime if tmp[3] is large enough. */ + high = tmp[3] >> 64; + /* As tmp[3] < 2^65, high is either 1 or 0 */ + high <<= 63; + high >>= 63; + /* high is: + * all ones if the high word of tmp[3] is 1 + * all zeros if the high word of tmp[3] if 0 */ + low = tmp[3]; + mask = low >> 63; + /* mask is: + * all ones if the MSB of low is 1 + * all zeros if the MSB of low if 0 */ + low &= bottom63bits; + low -= kPrime3Test; + /* if low was greater than kPrime3Test then the MSB is zero */ + low = ~low; + low >>= 63; + /* low is: + * all ones if low was > kPrime3Test + * all zeros if low was <= kPrime3Test */ + mask = (mask & low) | high; + tmp[0] -= mask & kPrime[0]; + tmp[1] -= mask & kPrime[1]; + /* kPrime[2] is zero, so omitted */ + tmp[3] -= mask & kPrime[3]; + /* tmp[3] < 2**64 - 2**32 + 1 */ + + tmp[1] += ((u64) (tmp[0] >> 64)); tmp[0] = (u64) tmp[0]; + tmp[2] += ((u64) (tmp[1] >> 64)); tmp[1] = (u64) tmp[1]; + tmp[3] += ((u64) (tmp[2] >> 64)); tmp[2] = (u64) tmp[2]; + /* tmp[i] < 2^64 */ + + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; + } + +/* smallfelem_expand converts a smallfelem to an felem */ +static void smallfelem_expand(felem out, const smallfelem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + } + +/* smallfelem_square sets |out| = |small|^2 + * On entry: + * small[i] < 2^64 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void smallfelem_square(longfelem out, const smallfelem small) + { + limb a; + u64 high, low; + + a = ((uint128_t) small[0]) * small[0]; + low = a; + high = a >> 64; + out[0] = low; + out[1] = high; + + a = ((uint128_t) small[0]) * small[1]; + low = a; + high = a >> 64; + out[1] += low; + out[1] += low; + out[2] = high; + + a = ((uint128_t) small[0]) * small[2]; + low = a; + high = a >> 64; + out[2] += low; + out[2] *= 2; + out[3] = high; + + a = ((uint128_t) small[0]) * small[3]; + low = a; + high = a >> 64; + out[3] += low; + out[4] = high; + + a = ((uint128_t) small[1]) * small[2]; + low = a; + high = a >> 64; + out[3] += low; + out[3] *= 2; + out[4] += high; + + a = ((uint128_t) small[1]) * small[1]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small[1]) * small[3]; + low = a; + high = a >> 64; + out[4] += low; + out[4] *= 2; + out[5] = high; + + a = ((uint128_t) small[2]) * small[3]; + low = a; + high = a >> 64; + out[5] += low; + out[5] *= 2; + out[6] = high; + out[6] += high; + + a = ((uint128_t) small[2]) * small[2]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small[3]) * small[3]; + low = a; + high = a >> 64; + out[6] += low; + out[7] = high; + } + +/* felem_square sets |out| = |in|^2 + * On entry: + * in[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_square(longfelem out, const felem in) + { + u64 small[4]; + felem_shrink(small, in); + smallfelem_square(out, small); + } + +/* smallfelem_mul sets |out| = |small1| * |small2| + * On entry: + * small1[i] < 2^64 + * small2[i] < 2^64 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void smallfelem_mul(longfelem out, const smallfelem small1, const smallfelem small2) + { + limb a; + u64 high, low; + + a = ((uint128_t) small1[0]) * small2[0]; + low = a; + high = a >> 64; + out[0] = low; + out[1] = high; + + + a = ((uint128_t) small1[0]) * small2[1]; + low = a; + high = a >> 64; + out[1] += low; + out[2] = high; + + a = ((uint128_t) small1[1]) * small2[0]; + low = a; + high = a >> 64; + out[1] += low; + out[2] += high; + + + a = ((uint128_t) small1[0]) * small2[2]; + low = a; + high = a >> 64; + out[2] += low; + out[3] = high; + + a = ((uint128_t) small1[1]) * small2[1]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + a = ((uint128_t) small1[2]) * small2[0]; + low = a; + high = a >> 64; + out[2] += low; + out[3] += high; + + + a = ((uint128_t) small1[0]) * small2[3]; + low = a; + high = a >> 64; + out[3] += low; + out[4] = high; + + a = ((uint128_t) small1[1]) * small2[2]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[2]) * small2[1]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + a = ((uint128_t) small1[3]) * small2[0]; + low = a; + high = a >> 64; + out[3] += low; + out[4] += high; + + + a = ((uint128_t) small1[1]) * small2[3]; + low = a; + high = a >> 64; + out[4] += low; + out[5] = high; + + a = ((uint128_t) small1[2]) * small2[2]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + a = ((uint128_t) small1[3]) * small2[1]; + low = a; + high = a >> 64; + out[4] += low; + out[5] += high; + + + a = ((uint128_t) small1[2]) * small2[3]; + low = a; + high = a >> 64; + out[5] += low; + out[6] = high; + + a = ((uint128_t) small1[3]) * small2[2]; + low = a; + high = a >> 64; + out[5] += low; + out[6] += high; + + + a = ((uint128_t) small1[3]) * small2[3]; + low = a; + high = a >> 64; + out[6] += low; + out[7] = high; + } + +/* felem_mul sets |out| = |in1| * |in2| + * On entry: + * in1[i] < 2^109 + * in2[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_mul(longfelem out, const felem in1, const felem in2) + { + smallfelem small1, small2; + felem_shrink(small1, in1); + felem_shrink(small2, in2); + smallfelem_mul(out, small1, small2); + } + +/* felem_small_mul sets |out| = |small1| * |in2| + * On entry: + * small1[i] < 2^64 + * in2[i] < 2^109 + * On exit: + * out[i] < 7 * 2^64 < 2^67 + */ +static void felem_small_mul(longfelem out, const smallfelem small1, const felem in2) + { + smallfelem small2; + felem_shrink(small2, in2); + smallfelem_mul(out, small1, small2); + } + +#define two100m36m4 (((limb)1) << 100) - (((limb)1) << 36) - (((limb)1) << 4) +#define two100 (((limb)1) << 100) +#define two100m36p4 (((limb)1) << 100) - (((limb)1) << 36) + (((limb)1) << 4) +/* zero100 is 0 mod p */ +static const felem zero100 = { two100m36m4, two100, two100m36p4, two100m36p4 }; + +/* Internal function for the different flavours of felem_reduce. + * felem_reduce_ reduces the higher coefficients in[4]-in[7]. + * On entry: + * out[0] >= in[6] + 2^32*in[6] + in[7] + 2^32*in[7] + * out[1] >= in[7] + 2^32*in[4] + * out[2] >= in[5] + 2^32*in[5] + * out[3] >= in[4] + 2^32*in[5] + 2^32*in[6] + * On exit: + * out[0] <= out[0] + in[4] + 2^32*in[5] + * out[1] <= out[1] + in[5] + 2^33*in[6] + * out[2] <= out[2] + in[7] + 2*in[6] + 2^33*in[7] + * out[3] <= out[3] + 2^32*in[4] + 3*in[7] + */ +static void felem_reduce_(felem out, const longfelem in) + { + int128_t c; + /* combine common terms from below */ + c = in[4] + (in[5] << 32); + out[0] += c; + out[3] -= c; + + c = in[5] - in[7]; + out[1] += c; + out[2] -= c; + + /* the remaining terms */ + /* 256: [(0,1),(96,-1),(192,-1),(224,1)] */ + out[1] -= (in[4] << 32); + out[3] += (in[4] << 32); + + /* 320: [(32,1),(64,1),(128,-1),(160,-1),(224,-1)] */ + out[2] -= (in[5] << 32); + + /* 384: [(0,-1),(32,-1),(96,2),(128,2),(224,-1)] */ + out[0] -= in[6]; + out[0] -= (in[6] << 32); + out[1] += (in[6] << 33); + out[2] += (in[6] * 2); + out[3] -= (in[6] << 32); + + /* 448: [(0,-1),(32,-1),(64,-1),(128,1),(160,2),(192,3)] */ + out[0] -= in[7]; + out[0] -= (in[7] << 32); + out[2] += (in[7] << 33); + out[3] += (in[7] * 3); + } + +/* felem_reduce converts a longfelem into an felem. + * To be called directly after felem_square or felem_mul. + * On entry: + * in[0] < 2^64, in[1] < 3*2^64, in[2] < 5*2^64, in[3] < 7*2^64 + * in[4] < 7*2^64, in[5] < 5*2^64, in[6] < 3*2^64, in[7] < 2*64 + * On exit: + * out[i] < 2^101 + */ +static void felem_reduce(felem out, const longfelem in) + { + out[0] = zero100[0] + in[0]; + out[1] = zero100[1] + in[1]; + out[2] = zero100[2] + in[2]; + out[3] = zero100[3] + in[3]; + + felem_reduce_(out, in); + + /* out[0] > 2^100 - 2^36 - 2^4 - 3*2^64 - 3*2^96 - 2^64 - 2^96 > 0 + * out[1] > 2^100 - 2^64 - 7*2^96 > 0 + * out[2] > 2^100 - 2^36 + 2^4 - 5*2^64 - 5*2^96 > 0 + * out[3] > 2^100 - 2^36 + 2^4 - 7*2^64 - 5*2^96 - 3*2^96 > 0 + * + * out[0] < 2^100 + 2^64 + 7*2^64 + 5*2^96 < 2^101 + * out[1] < 2^100 + 3*2^64 + 5*2^64 + 3*2^97 < 2^101 + * out[2] < 2^100 + 5*2^64 + 2^64 + 3*2^65 + 2^97 < 2^101 + * out[3] < 2^100 + 7*2^64 + 7*2^96 + 3*2^64 < 2^101 + */ + } + +/* felem_reduce_zero105 converts a larger longfelem into an felem. + * On entry: + * in[0] < 2^71 + * On exit: + * out[i] < 2^106 + */ +static void felem_reduce_zero105(felem out, const longfelem in) + { + out[0] = zero105[0] + in[0]; + out[1] = zero105[1] + in[1]; + out[2] = zero105[2] + in[2]; + out[3] = zero105[3] + in[3]; + + felem_reduce_(out, in); + + /* out[0] > 2^105 - 2^41 - 2^9 - 2^71 - 2^103 - 2^71 - 2^103 > 0 + * out[1] > 2^105 - 2^71 - 2^103 > 0 + * out[2] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 > 0 + * out[3] > 2^105 - 2^41 + 2^9 - 2^71 - 2^103 - 2^103 > 0 + * + * out[0] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 + * out[1] < 2^105 + 2^71 + 2^71 + 2^103 < 2^106 + * out[2] < 2^105 + 2^71 + 2^71 + 2^71 + 2^103 < 2^106 + * out[3] < 2^105 + 2^71 + 2^103 + 2^71 < 2^106 + */ + } + +/* subtract_u64 sets *result = *result - v and *carry to one if the subtraction + * underflowed. */ +static void subtract_u64(u64* result, u64* carry, u64 v) + { + uint128_t r = *result; + r -= v; + *carry = (r >> 64) & 1; + *result = (u64) r; + } + +/* felem_contract converts |in| to its unique, minimal representation. + * On entry: + * in[i] < 2^109 + */ +static void felem_contract(smallfelem out, const felem in) + { + unsigned i; + u64 all_equal_so_far = 0, result = 0, carry; + + felem_shrink(out, in); + /* small is minimal except that the value might be > p */ + + all_equal_so_far--; + /* We are doing a constant time test if out >= kPrime. We need to + * compare each u64, from most-significant to least significant. For + * each one, if all words so far have been equal (m is all ones) then a + * non-equal result is the answer. Otherwise we continue. */ + for (i = 3; i < 4; i--) + { + u64 equal; + uint128_t a = ((uint128_t) kPrime[i]) - out[i]; + /* if out[i] > kPrime[i] then a will underflow and the high + * 64-bits will all be set. */ + result |= all_equal_so_far & ((u64) (a >> 64)); + + /* if kPrime[i] == out[i] then |equal| will be all zeros and + * the decrement will make it all ones. */ + equal = kPrime[i] ^ out[i]; + equal--; + equal &= equal << 32; + equal &= equal << 16; + equal &= equal << 8; + equal &= equal << 4; + equal &= equal << 2; + equal &= equal << 1; + equal = ((s64) equal) >> 63; + + all_equal_so_far &= equal; + } + + /* if all_equal_so_far is still all ones then the two values are equal + * and so out >= kPrime is true. */ + result |= all_equal_so_far; + + /* if out >= kPrime then we subtract kPrime. */ + subtract_u64(&out[0], &carry, result & kPrime[0]); + subtract_u64(&out[1], &carry, carry); + subtract_u64(&out[2], &carry, carry); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[1], &carry, result & kPrime[1]); + subtract_u64(&out[2], &carry, carry); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[2], &carry, result & kPrime[2]); + subtract_u64(&out[3], &carry, carry); + + subtract_u64(&out[3], &carry, result & kPrime[3]); + } + +static void smallfelem_square_contract(smallfelem out, const smallfelem in) + { + longfelem longtmp; + felem tmp; + + smallfelem_square(longtmp, in); + felem_reduce(tmp, longtmp); + felem_contract(out, tmp); + } + +static void smallfelem_mul_contract(smallfelem out, const smallfelem in1, const smallfelem in2) + { + longfelem longtmp; + felem tmp; + + smallfelem_mul(longtmp, in1, in2); + felem_reduce(tmp, longtmp); + felem_contract(out, tmp); + } + +/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 + * otherwise. + * On entry: + * small[i] < 2^64 + */ +static limb smallfelem_is_zero(const smallfelem small) + { + limb result; + u64 is_p; + + u64 is_zero = small[0] | small[1] | small[2] | small[3]; + is_zero--; + is_zero &= is_zero << 32; + is_zero &= is_zero << 16; + is_zero &= is_zero << 8; + is_zero &= is_zero << 4; + is_zero &= is_zero << 2; + is_zero &= is_zero << 1; + is_zero = ((s64) is_zero) >> 63; + + is_p = (small[0] ^ kPrime[0]) | + (small[1] ^ kPrime[1]) | + (small[2] ^ kPrime[2]) | + (small[3] ^ kPrime[3]); + is_p--; + is_p &= is_p << 32; + is_p &= is_p << 16; + is_p &= is_p << 8; + is_p &= is_p << 4; + is_p &= is_p << 2; + is_p &= is_p << 1; + is_p = ((s64) is_p) >> 63; + + is_zero |= is_p; + + result = is_zero; + result |= ((limb) is_zero) << 64; + return result; + } + +static int smallfelem_is_zero_int(const smallfelem small) + { + return (int) (smallfelem_is_zero(small) & ((limb)1)); + } + +/* felem_inv calculates |out| = |in|^{-1} + * + * Based on Fermat's Little Theorem: + * a^p = a (mod p) + * a^{p-1} = 1 (mod p) + * a^{p-2} = a^{-1} (mod p) + */ +static void felem_inv(felem out, const felem in) + { + felem ftmp, ftmp2; + /* each e_I will hold |in|^{2^I - 1} */ + felem e2, e4, e8, e16, e32, e64; + longfelem tmp; + unsigned i; + + felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_assign(e2, ftmp); + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp, e2); felem_reduce(ftmp, tmp); /* 2^4 - 2^0 */ + felem_assign(e4, ftmp); + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^8 - 2^4 */ + felem_mul(tmp, ftmp, e4); felem_reduce(ftmp, tmp); /* 2^8 - 2^0 */ + felem_assign(e8, ftmp); + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } /* 2^16 - 2^8 */ + felem_mul(tmp, ftmp, e8); felem_reduce(ftmp, tmp); /* 2^16 - 2^0 */ + felem_assign(e16, ftmp); + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } /* 2^32 - 2^16 */ + felem_mul(tmp, ftmp, e16); felem_reduce(ftmp, tmp); /* 2^32 - 2^0 */ + felem_assign(e32, ftmp); + for (i = 0; i < 32; i++) { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } /* 2^64 - 2^32 */ + felem_assign(e64, ftmp); + felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^64 - 2^32 + 2^0 */ + for (i = 0; i < 192; i++) { + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); + } /* 2^256 - 2^224 + 2^192 */ + + felem_mul(tmp, e64, e32); felem_reduce(ftmp2, tmp); /* 2^64 - 2^0 */ + for (i = 0; i < 16; i++) { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } /* 2^80 - 2^16 */ + felem_mul(tmp, ftmp2, e16); felem_reduce(ftmp2, tmp); /* 2^80 - 2^0 */ + for (i = 0; i < 8; i++) { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } /* 2^88 - 2^8 */ + felem_mul(tmp, ftmp2, e8); felem_reduce(ftmp2, tmp); /* 2^88 - 2^0 */ + for (i = 0; i < 4; i++) { + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); + } /* 2^92 - 2^4 */ + felem_mul(tmp, ftmp2, e4); felem_reduce(ftmp2, tmp); /* 2^92 - 2^0 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^93 - 2^1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^2 */ + felem_mul(tmp, ftmp2, e2); felem_reduce(ftmp2, tmp); /* 2^94 - 2^0 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^95 - 2^1 */ + felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^96 - 2^2 */ + felem_mul(tmp, ftmp2, in); felem_reduce(ftmp2, tmp); /* 2^96 - 3 */ + + felem_mul(tmp, ftmp2, ftmp); felem_reduce(out, tmp); /* 2^256 - 2^224 + 2^192 + 2^96 - 3 */ + } + +static void smallfelem_inv_contract(smallfelem out, const smallfelem in) + { + felem tmp; + + smallfelem_expand(tmp, in); + felem_inv(tmp, tmp); + felem_contract(out, tmp); + } + +/* Group operations + * ---------------- + * + * Building on top of the field operations we have the operations on the + * elliptic curve group itself. Points on the curve are represented in Jacobian + * coordinates */ + +/* point_double calculates 2*(x_in, y_in, z_in) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b + * + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. + * while x_out == y_in is not (maybe this works, but it's not tested). */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) + { + longfelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + smallfelem small1, small2; + + felem_assign(ftmp, x_in); + /* ftmp[i] < 2^106 */ + felem_assign(ftmp2, x_in); + /* ftmp2[i] < 2^106 */ + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + /* delta[i] < 2^101 */ + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + /* gamma[i] < 2^101 */ + felem_shrink(small1, gamma); + + /* beta = x*gamma */ + felem_small_mul(tmp, small1, x_in); + felem_reduce(beta, tmp); + /* beta[i] < 2^101 */ + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^105 + 2^106 < 2^107 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^105 + 2^106 < 2^107 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^107 < 2^109 */ + felem_mul(tmp, ftmp, ftmp2); + felem_reduce(alpha, tmp); + /* alpha[i] < 2^101 */ + felem_shrink(small2, alpha); + + /* x' = alpha^2 - 8*beta */ + smallfelem_square(tmp, small2); + felem_reduce(x_out, tmp); + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^101 = 2^104 */ + felem_diff(x_out, ftmp); + /* x_out[i] < 2^105 + 2^101 < 2^106 */ + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^101 + 2^101 = 2^102 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^106 + 2^106 = 2^107 */ + felem_square(tmp, ftmp); + felem_reduce(z_out, tmp); + felem_diff(z_out, delta); + /* z_out[i] < 2^105 + 2^101 < 2^106 */ + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^101 = 2^103 */ + felem_diff_zero107(beta, x_out); + /* beta[i] < 2^107 + 2^103 < 2^108 */ + felem_small_mul(tmp, small2, beta); + /* tmp[i] < 7 * 2^64 < 2^67 */ + smallfelem_square(tmp2, small1); + /* tmp2[i] < 7 * 2^64 */ + longfelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 7 * 2^64 = 7 * 2^67 */ + longfelem_diff(tmp, tmp2); + /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ + felem_reduce_zero105(y_out, tmp); + /* y_out[i] < 2^106 */ + } + +/* point_double_small is the same as point_double, except that it operates on + * smallfelems */ +static void +point_double_small(smallfelem x_out, smallfelem y_out, smallfelem z_out, + const smallfelem x_in, const smallfelem y_in, const smallfelem z_in) + { + felem felem_x_out, felem_y_out, felem_z_out; + felem felem_x_in, felem_y_in, felem_z_in; + + smallfelem_expand(felem_x_in, x_in); + smallfelem_expand(felem_y_in, y_in); + smallfelem_expand(felem_z_in, z_in); + point_double(felem_x_out, felem_y_out, felem_z_out, + felem_x_in, felem_y_in, felem_z_in); + felem_shrink(x_out, felem_x_out); + felem_shrink(y_out, felem_y_out); + felem_shrink(z_out, felem_z_out); + } + +/* copy_conditional copies in to out iff mask is all ones. */ +static void +copy_conditional(felem out, const felem in, limb mask) + { + unsigned i; + for (i = 0; i < NLIMBS; ++i) + { + const limb tmp = mask & (in[i] ^ out[i]); + out[i] ^= tmp; + } + } + +/* copy_small_conditional copies in to out iff mask is all ones. */ +static void +copy_small_conditional(felem out, const smallfelem in, limb mask) + { + unsigned i; + const u64 mask64 = mask; + for (i = 0; i < NLIMBS; ++i) + { + out[i] = ((limb) (in[i] & mask64)) | (out[i] & ~mask); + } + } + +/* point_add calcuates (x1, y1, z1) + (x2, y2, z2) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, + * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). + * + * This function includes a branch for checking whether the two input points + * are equal, (while not equal to the point at infinity). This case never + * happens during single point multiplication, so there is no timing leak for + * ECDH or ECDSA signing. */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const smallfelem x2, const smallfelem y2, const smallfelem z2) + { + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; + longfelem tmp, tmp2; + smallfelem small1, small2, small3, small4, small5; + limb x_equal, y_equal, z1_is_zero, z2_is_zero; + + felem_shrink(small3, z1); + + z1_is_zero = smallfelem_is_zero(small3); + z2_is_zero = smallfelem_is_zero(z2); + + /* ftmp = z1z1 = z1**2 */ + smallfelem_square(tmp, small3); + felem_reduce(ftmp, tmp); + /* ftmp[i] < 2^101 */ + felem_shrink(small1, ftmp); + + if(!mixed) + { + /* ftmp2 = z2z2 = z2**2 */ + smallfelem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + /* ftmp2[i] < 2^101 */ + felem_shrink(small2, ftmp2); + + felem_shrink(small5, x1); + + /* u1 = ftmp3 = x1*z2z2 */ + smallfelem_mul(tmp, small5, small2); + felem_reduce(ftmp3, tmp); + /* ftmp3[i] < 2^101 */ + + /* ftmp5 = z1 + z2 */ + felem_assign(ftmp5, z1); + felem_small_sum(ftmp5, z2); + /* ftmp5[i] < 2^107 */ + + /* ftmp5 = (z1 + z2)**2 - (z1z1 + z2z2) = 2z1z2 */ + felem_square(tmp, ftmp5); + felem_reduce(ftmp5, tmp); + /* ftmp2 = z2z2 + z1z1 */ + felem_sum(ftmp2, ftmp); + /* ftmp2[i] < 2^101 + 2^101 = 2^102 */ + felem_diff(ftmp5, ftmp2); + /* ftmp5[i] < 2^105 + 2^101 < 2^106 */ + + /* ftmp2 = z2 * z2z2 */ + smallfelem_mul(tmp, small2, z2); + felem_reduce(ftmp2, tmp); + + /* s1 = ftmp2 = y1 * z2**3 */ + felem_mul(tmp, y1, ftmp2); + felem_reduce(ftmp6, tmp); + /* ftmp6[i] < 2^101 */ + } + else + { + /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_assign(ftmp3, x1); + /* ftmp3[i] < 2^106 */ + + /* ftmp5 = 2z1z2 */ + felem_assign(ftmp5, z1); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2*2^106 = 2^107 */ + + /* s1 = ftmp2 = y1 * z2**3 */ + felem_assign(ftmp6, y1); + /* ftmp6[i] < 2^106 */ + } + + /* u2 = x2*z1z1 */ + smallfelem_mul(tmp, x2, small1); + felem_reduce(ftmp4, tmp); + + /* h = ftmp4 = u2 - u1 */ + felem_diff_zero107(ftmp4, ftmp3); + /* ftmp4[i] < 2^107 + 2^101 < 2^108 */ + felem_shrink(small4, ftmp4); + + x_equal = smallfelem_is_zero(small4); + + /* z_out = ftmp5 * h */ + felem_small_mul(tmp, small4, ftmp5); + felem_reduce(z_out, tmp); + /* z_out[i] < 2^101 */ + + /* ftmp = z1 * z1z1 */ + smallfelem_mul(tmp, small1, small3); + felem_reduce(ftmp, tmp); + + /* s2 = tmp = y2 * z1**3 */ + felem_small_mul(tmp, y2, ftmp); + felem_reduce(ftmp5, tmp); + + /* r = ftmp5 = (s2 - s1)*2 */ + felem_diff_zero107(ftmp5, ftmp6); + /* ftmp5[i] < 2^107 + 2^107 = 2^108*/ + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2^109 */ + felem_shrink(small1, ftmp5); + y_equal = smallfelem_is_zero(small1); + + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) + { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* I = ftmp = (2h)**2 */ + felem_assign(ftmp, ftmp4); + felem_scalar(ftmp, 2); + /* ftmp[i] < 2*2^108 = 2^109 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* J = ftmp2 = h * I */ + felem_mul(tmp, ftmp4, ftmp); + felem_reduce(ftmp2, tmp); + + /* V = ftmp4 = U1 * I */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); + + /* x_out = r**2 - J - 2V */ + smallfelem_square(tmp, small1); + felem_reduce(x_out, tmp); + felem_assign(ftmp3, ftmp4); + felem_scalar(ftmp4, 2); + felem_sum(ftmp4, ftmp2); + /* ftmp4[i] < 2*2^101 + 2^101 < 2^103 */ + felem_diff(x_out, ftmp4); + /* x_out[i] < 2^105 + 2^101 */ + + /* y_out = r(V-x_out) - 2 * s1 * J */ + felem_diff_zero107(ftmp3, x_out); + /* ftmp3[i] < 2^107 + 2^101 < 2^108 */ + felem_small_mul(tmp, small1, ftmp3); + felem_mul(tmp2, ftmp6, ftmp2); + longfelem_scalar(tmp2, 2); + /* tmp2[i] < 2*2^67 = 2^68 */ + longfelem_diff(tmp, tmp2); + /* tmp[i] < 2^67 + 2^70 + 2^40 < 2^71 */ + felem_reduce_zero105(y_out, tmp); + /* y_out[i] < 2^106 */ + + copy_small_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_small_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_small_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); + } + +/* point_add_small is the same as point_add, except that it operates on + * smallfelems */ +static void point_add_small(smallfelem x3, smallfelem y3, smallfelem z3, + smallfelem x1, smallfelem y1, smallfelem z1, + smallfelem x2, smallfelem y2, smallfelem z2) + { + felem felem_x3, felem_y3, felem_z3; + felem felem_x1, felem_y1, felem_z1; + smallfelem_expand(felem_x1, x1); + smallfelem_expand(felem_y1, y1); + smallfelem_expand(felem_z1, z1); + point_add(felem_x3, felem_y3, felem_z3, felem_x1, felem_y1, felem_z1, 0, x2, y2, z2); + felem_shrink(x3, felem_x3); + felem_shrink(y3, felem_y3); + felem_shrink(z3, felem_z3); + } + +/* Base point pre computation + * -------------------------- + * + * Two different sorts of precomputed tables are used in the following code. + * Each contain various points on the curve, where each point is three field + * elements (x, y, z). + * + * For the base point table, z is usually 1 (0 for the point at infinity). + * This table has 2 * 16 elements, starting with the following: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^64G + * 3 | 0 0 1 1 | (2^64 + 1)G + * 4 | 0 1 0 0 | 2^128G + * 5 | 0 1 0 1 | (2^128 + 1)G + * 6 | 0 1 1 0 | (2^128 + 2^64)G + * 7 | 0 1 1 1 | (2^128 + 2^64 + 1)G + * 8 | 1 0 0 0 | 2^192G + * 9 | 1 0 0 1 | (2^192 + 1)G + * 10 | 1 0 1 0 | (2^192 + 2^64)G + * 11 | 1 0 1 1 | (2^192 + 2^64 + 1)G + * 12 | 1 1 0 0 | (2^192 + 2^128)G + * 13 | 1 1 0 1 | (2^192 + 2^128 + 1)G + * 14 | 1 1 1 0 | (2^192 + 2^128 + 2^64)G + * 15 | 1 1 1 1 | (2^192 + 2^128 + 2^64 + 1)G + * followed by a copy of this with each element multiplied by 2^32. + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point, + * and then another four locations using the second 16 elements. + * + * Tables for other points have table[i] = iG for i in 0 .. 16. */ + +/* gmul is the table of precomputed base points */ +static const smallfelem gmul[2][16][3] = +{{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0xf4a13945d898c296, 0x77037d812deb33a0, 0xf8bce6e563a440f2, 0x6b17d1f2e12c4247}, + {0xcbb6406837bf51f5, 0x2bce33576b315ece, 0x8ee7eb4a7c0f9e16, 0x4fe342e2fe1a7f9b}, + {1, 0, 0, 0}}, + {{0x90e75cb48e14db63, 0x29493baaad651f7e, 0x8492592e326e25de, 0x0fa822bc2811aaa5}, + {0xe41124545f462ee7, 0x34b1a65050fe82f5, 0x6f4ad4bcb3df188b, 0xbff44ae8f5dba80d}, + {1, 0, 0, 0}}, + {{0x93391ce2097992af, 0xe96c98fd0d35f1fa, 0xb257c0de95e02789, 0x300a4bbc89d6726f}, + {0xaa54a291c08127a0, 0x5bb1eeada9d806a5, 0x7f1ddb25ff1e3c6f, 0x72aac7e0d09b4644}, + {1, 0, 0, 0}}, + {{0x57c84fc9d789bd85, 0xfc35ff7dc297eac3, 0xfb982fd588c6766e, 0x447d739beedb5e67}, + {0x0c7e33c972e25b32, 0x3d349b95a7fae500, 0xe12e9d953a4aaff7, 0x2d4825ab834131ee}, + {1, 0, 0, 0}}, + {{0x13949c932a1d367f, 0xef7fbd2b1a0a11b7, 0xddc6068bb91dfc60, 0xef9519328a9c72ff}, + {0x196035a77376d8a8, 0x23183b0895ca1740, 0xc1ee9807022c219c, 0x611e9fc37dbb2c9b}, + {1, 0, 0, 0}}, + {{0xcae2b1920b57f4bc, 0x2936df5ec6c9bc36, 0x7dea6482e11238bf, 0x550663797b51f5d8}, + {0x44ffe216348a964c, 0x9fb3d576dbdefbe1, 0x0afa40018d9d50e5, 0x157164848aecb851}, + {1, 0, 0, 0}}, + {{0xe48ecafffc5cde01, 0x7ccd84e70d715f26, 0xa2e8f483f43e4391, 0xeb5d7745b21141ea}, + {0xcac917e2731a3479, 0x85f22cfe2844b645, 0x0990e6a158006cee, 0xeafd72ebdbecc17b}, + {1, 0, 0, 0}}, + {{0x6cf20ffb313728be, 0x96439591a3c6b94a, 0x2736ff8344315fc5, 0xa6d39677a7849276}, + {0xf2bab833c357f5f4, 0x824a920c2284059b, 0x66b8babd2d27ecdf, 0x674f84749b0b8816}, + {1, 0, 0, 0}}, + {{0x2df48c04677c8a3e, 0x74e02f080203a56b, 0x31855f7db8c7fedb, 0x4e769e7672c9ddad}, + {0xa4c36165b824bbb0, 0xfb9ae16f3b9122a5, 0x1ec0057206947281, 0x42b99082de830663}, + {1, 0, 0, 0}}, + {{0x6ef95150dda868b9, 0xd1f89e799c0ce131, 0x7fdc1ca008a1c478, 0x78878ef61c6ce04d}, + {0x9c62b9121fe0d976, 0x6ace570ebde08d4f, 0xde53142c12309def, 0xb6cb3f5d7b72c321}, + {1, 0, 0, 0}}, + {{0x7f991ed2c31a3573, 0x5b82dd5bd54fb496, 0x595c5220812ffcae, 0x0c88bc4d716b1287}, + {0x3a57bf635f48aca8, 0x7c8181f4df2564f3, 0x18d1b5b39c04e6aa, 0xdd5ddea3f3901dc6}, + {1, 0, 0, 0}}, + {{0xe96a79fb3e72ad0c, 0x43a0a28c42ba792f, 0xefe0a423083e49f3, 0x68f344af6b317466}, + {0xcdfe17db3fb24d4a, 0x668bfc2271f5c626, 0x604ed93c24d67ff3, 0x31b9c405f8540a20}, + {1, 0, 0, 0}}, + {{0xd36b4789a2582e7f, 0x0d1a10144ec39c28, 0x663c62c3edbad7a0, 0x4052bf4b6f461db9}, + {0x235a27c3188d25eb, 0xe724f33999bfcc5b, 0x862be6bd71d70cc8, 0xfecf4d5190b0fc61}, + {1, 0, 0, 0}}, + {{0x74346c10a1d4cfac, 0xafdf5cc08526a7a4, 0x123202a8f62bff7a, 0x1eddbae2c802e41a}, + {0x8fa0af2dd603f844, 0x36e06b7e4c701917, 0x0c45f45273db33a0, 0x43104d86560ebcfc}, + {1, 0, 0, 0}}, + {{0x9615b5110d1d78e5, 0x66b0de3225c4744b, 0x0a4a46fb6aaf363a, 0xb48e26b484f7a21c}, + {0x06ebb0f621a01b2d, 0xc004e4048b7b0f98, 0x64131bcdfed6f668, 0xfac015404d4d3dab}, + {1, 0, 0, 0}}}, + {{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3a5a9e22185a5943, 0x1ab919365c65dfb6, 0x21656b32262c71da, 0x7fe36b40af22af89}, + {0xd50d152c699ca101, 0x74b3d5867b8af212, 0x9f09f40407dca6f1, 0xe697d45825b63624}, + {1, 0, 0, 0}}, + {{0xa84aa9397512218e, 0xe9a521b074ca0141, 0x57880b3a18a2e902, 0x4a5b506612a677a6}, + {0x0beada7a4c4f3840, 0x626db15419e26d9d, 0xc42604fbe1627d40, 0xeb13461ceac089f1}, + {1, 0, 0, 0}}, + {{0xf9faed0927a43281, 0x5e52c4144103ecbc, 0xc342967aa815c857, 0x0781b8291c6a220a}, + {0x5a8343ceeac55f80, 0x88f80eeee54a05e3, 0x97b2a14f12916434, 0x690cde8df0151593}, + {1, 0, 0, 0}}, + {{0xaee9c75df7f82f2a, 0x9e4c35874afdf43a, 0xf5622df437371326, 0x8a535f566ec73617}, + {0xc5f9a0ac223094b7, 0xcde533864c8c7669, 0x37e02819085a92bf, 0x0455c08468b08bd7}, + {1, 0, 0, 0}}, + {{0x0c0a6e2c9477b5d9, 0xf9a4bf62876dc444, 0x5050a949b6cdc279, 0x06bada7ab77f8276}, + {0xc8b4aed1ea48dac9, 0xdebd8a4b7ea1070f, 0x427d49101366eb70, 0x5b476dfd0e6cb18a}, + {1, 0, 0, 0}}, + {{0x7c5c3e44278c340a, 0x4d54606812d66f3b, 0x29a751b1ae23c5d8, 0x3e29864e8a2ec908}, + {0x142d2a6626dbb850, 0xad1744c4765bd780, 0x1f150e68e322d1ed, 0x239b90ea3dc31e7e}, + {1, 0, 0, 0}}, + {{0x78c416527a53322a, 0x305dde6709776f8e, 0xdbcab759f8862ed4, 0x820f4dd949f72ff7}, + {0x6cc544a62b5debd4, 0x75be5d937b4e8cc4, 0x1b481b1b215c14d3, 0x140406ec783a05ec}, + {1, 0, 0, 0}}, + {{0x6a703f10e895df07, 0xfd75f3fa01876bd8, 0xeb5b06e70ce08ffe, 0x68f6b8542783dfee}, + {0x90c76f8a78712655, 0xcf5293d2f310bf7f, 0xfbc8044dfda45028, 0xcbe1feba92e40ce6}, + {1, 0, 0, 0}}, + {{0xe998ceea4396e4c1, 0xfc82ef0b6acea274, 0x230f729f2250e927, 0xd0b2f94d2f420109}, + {0x4305adddb38d4966, 0x10b838f8624c3b45, 0x7db2636658954e7a, 0x971459828b0719e5}, + {1, 0, 0, 0}}, + {{0x4bd6b72623369fc9, 0x57f2929e53d0b876, 0xc2d5cba4f2340687, 0x961610004a866aba}, + {0x49997bcd2e407a5e, 0x69ab197d92ddcb24, 0x2cf1f2438fe5131c, 0x7acb9fadcee75e44}, + {1, 0, 0, 0}}, + {{0x254e839423d2d4c0, 0xf57f0c917aea685b, 0xa60d880f6f75aaea, 0x24eb9acca333bf5b}, + {0xe3de4ccb1cda5dea, 0xfeef9341c51a6b4f, 0x743125f88bac4c4d, 0x69f891c5acd079cc}, + {1, 0, 0, 0}}, + {{0xeee44b35702476b5, 0x7ed031a0e45c2258, 0xb422d1e7bd6f8514, 0xe51f547c5972a107}, + {0xa25bcd6fc9cf343d, 0x8ca922ee097c184e, 0xa62f98b3a9fe9a06, 0x1c309a2b25bb1387}, + {1, 0, 0, 0}}, + {{0x9295dbeb1967c459, 0xb00148833472c98e, 0xc504977708011828, 0x20b87b8aa2c4e503}, + {0x3063175de057c277, 0x1bd539338fe582dd, 0x0d11adef5f69a044, 0xf5c6fa49919776be}, + {1, 0, 0, 0}}, + {{0x8c944e760fd59e11, 0x3876cba1102fad5f, 0xa454c3fad83faa56, 0x1ed7d1b9332010b9}, + {0xa1011a270024b889, 0x05e4d0dcac0cd344, 0x52b520f0eb6a2a24, 0x3a2b03f03217257a}, + {1, 0, 0, 0}}, + {{0xf20fc2afdf1d043d, 0xf330240db58d5a62, 0xfc7d229ca0058c3b, 0x15fee545c78dd9f6}, + {0x501e82885bc98cda, 0x41ef80e5d046ac04, 0x557d9f49461210fb, 0x4ab5b6b2b8753f81}, + {1, 0, 0, 0}}}}; + +/* select_point selects the |idx|th point from a precomputation table and + * copies it to out. */ +static void select_point(const u64 idx, unsigned int size, const smallfelem pre_comp[16][3], smallfelem out[3]) + { + unsigned i, j; + u64 *outlimbs = &out[0][0]; + memset(outlimbs, 0, 3 * sizeof(smallfelem)); + + for (i = 0; i < size; i++) + { + const u64 *inlimbs = (u64*) &pre_comp[i][0][0]; + u64 mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < NLIMBS * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } + } + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, int i) + { + if ((i < 0) || (i >= 256)) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; + } + +/* Interleaved point multiplication using precomputed point multiples: + * The small point multiples 0*P, 1*P, ..., 17*P are in pre_comp[], + * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple + * of the generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, + const int mixed, const smallfelem pre_comp[][17][3], const smallfelem g_pre_comp[2][16][3]) + { + int i, skip; + unsigned num, gen_mul = (g_scalar != NULL); + felem nq[3], ftmp; + smallfelem tmp[3]; + u64 bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, 3 * sizeof(felem)); + + /* Loop over all scalars msb-to-lsb, interleaving additions + * of multiples of the generator (two in each of the last 32 rounds) + * and additions of other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first round */ + for (i = (num_points ? 255 : 31); i >= 0; --i) + { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 31)) + { + /* first, look 32 bits upwards */ + bits = get_bit(g_scalar, i + 224) << 3; + bits |= get_bit(g_scalar, i + 160) << 2; + bits |= get_bit(g_scalar, i + 96) << 1; + bits |= get_bit(g_scalar, i + 32); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + else + { + smallfelem_expand(nq[0], tmp[0]); + smallfelem_expand(nq[1], tmp[1]); + smallfelem_expand(nq[2], tmp[2]); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 192) << 3; + bits |= get_bit(g_scalar, i + 128) << 2; + bits |= get_bit(g_scalar, i + 64) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) + { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) + { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract, in constant time */ + select_point(digit, 17, pre_comp[num], tmp); + smallfelem_neg(ftmp, tmp[1]); /* (X, -Y, Z) is the negative point */ + copy_small_conditional(ftmp, tmp[1], (((limb) sign) - 1)); + felem_contract(tmp[1], ftmp); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } + else + { + smallfelem_expand(nq[0], tmp[0]); + smallfelem_expand(nq[1], tmp[1]); + smallfelem_expand(nq[2], tmp[2]); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); + } + +/* Precomputation for the group generator. */ +typedef struct { + smallfelem g_pre_comp[2][16][3]; + int references; +} NISTP256_PRE_COMP; + +const EC_METHOD *EC_GFp_nistp256_method(void) + { + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp256_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp256_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp256_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */, + 0 /* point2oct */, + 0 /* oct2point */, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp256_points_mul, + ec_GFp_nistp256_precompute_mult, + ec_GFp_nistp256_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */ }; + + return &ret; + } + +/******************************************************************************/ +/* FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP256_PRE_COMP *nistp256_pre_comp_new() + { + NISTP256_PRE_COMP *ret = NULL; + ret = (NISTP256_PRE_COMP *) OPENSSL_malloc(sizeof *ret); + if (!ret) + { + ECerr(EC_F_NISTP256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); + ret->references = 1; + return ret; + } + +static void *nistp256_pre_comp_dup(void *src_) + { + NISTP256_PRE_COMP *src = src_; + + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + + return src_; + } + +static void nistp256_pre_comp_free(void *pre_) + { + int i; + NISTP256_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_free(pre); + } + +static void nistp256_pre_comp_clear_free(void *pre_) + { + int i; + NISTP256_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_cleanse(pre, sizeof *pre); + OPENSSL_free(pre); + } + +/******************************************************************************/ +/* OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp256_group_init(EC_GROUP *group) + { + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; + } + +int ec_GFp_nistp256_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + BN_bin2bn(nistp256_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp256_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp256_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || + (BN_cmp(curve_b, b))) + { + ECerr(EC_F_EC_GFP_NISTP256_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_256; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + +/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns + * (X', Y') = (X/Z^2, Y/Z^3) */ +int ec_GFp_nistp256_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) + { + felem z1, z2, x_in, y_in; + smallfelem x_out, y_out; + longfelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) + { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || + (!BN_to_felem(z1, &point->Z))) return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) + { + if (!smallfelem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) + { + if (!smallfelem_to_BN(y, y_out)) + { + ECerr(EC_F_EC_GFP_NISTP256_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; + } + +static void make_points_affine(size_t num, smallfelem points[/* num */][3], smallfelem tmp_smallfelems[/* num+1 */]) + { + /* Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). */ + ec_GFp_nistp_points_make_affine_internal( + num, + points, + sizeof(smallfelem), + tmp_smallfelems, + (void (*)(void *)) smallfelem_one, + (int (*)(const void *)) smallfelem_is_zero_int, + (void (*)(void *, const void *)) smallfelem_assign, + (void (*)(void *, const void *)) smallfelem_square_contract, + (void (*)(void *, const void *, const void *)) smallfelem_mul_contract, + (void (*)(void *, const void *)) smallfelem_inv_contract, + (void (*)(void *, const void *)) smallfelem_assign /* nothing to contract */); + } + +/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values + * Result is stored in r (r can equal one of the inputs). */ +int ec_GFp_nistp256_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) + { + int ret = 0; + int j; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + smallfelem (*pre_comp)[17][3] = NULL; + smallfelem *tmp_smallfelems = NULL; + felem_bytearray tmp; + unsigned i, num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + smallfelem x_in, y_in, z_in; + felem x_out, y_out, z_out; + NISTP256_PRE_COMP *pre = NULL; + const smallfelem (*g_pre_comp)[16][3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) + { + pre = EC_EX_DATA_get_data(group->extra_data, + nistp256_pre_comp_dup, nistp256_pre_comp_free, + nistp256_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const smallfelem (*)[16][3]) pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = &gmul[0]; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!smallfelem_to_BN(x, g_pre_comp[0][1][0]) || + !smallfelem_to_BN(y, g_pre_comp[0][1][1]) || + !smallfelem_to_BN(z, g_pre_comp[0][1][2])) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* we don't have valid precomputation: + * treat the generator as a random point */ + num_points++; + } + if (num_points > 0) + { + if (num_points >= 3) + { + /* unless we precompute multiples for just one or two points, + * converting those into affine form is time well spent */ + mixed = 1; + } + secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); + pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(smallfelem)); + if (mixed) + tmp_smallfelems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(smallfelem)); + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_smallfelems == NULL))) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination */ + memset(secrets, 0, num_points * sizeof(felem_bytearray)); + memset(pre_comp, 0, num_points * 17 * 3 * sizeof(smallfelem)); + for (i = 0; i < num_points; ++i) + { + if (i == num) + /* we didn't have a valid precomputation, so we pick + * the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } + else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) + { + /* reduce scalar to 0 <= scalar < 2^256 */ + if ((BN_num_bits(p_scalar) > 256) || (BN_is_negative(p_scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, &p->X)) || + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) goto err; + felem_shrink(pre_comp[i][1][0], x_out); + felem_shrink(pre_comp[i][1][1], y_out); + felem_shrink(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) + { + if (j & 1) + { + point_add_small( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); + } + else + { + point_double_small( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_smallfelems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) + { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^256 */ + if ((BN_num_bits(scalar) > 256) || (BN_is_negative(scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation*/ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + g_secret, + mixed, (const smallfelem (*)[17][3]) pre_comp, + g_pre_comp); + } + else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + NULL, mixed, (const smallfelem (*)[17][3]) pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!smallfelem_to_BN(x, x_in)) || (!smallfelem_to_BN(y, y_in)) || + (!smallfelem_to_BN(z, z_in))) + { + ECerr(EC_F_EC_GFP_NISTP256_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + +err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (secrets != NULL) + OPENSSL_free(secrets); + if (pre_comp != NULL) + OPENSSL_free(pre_comp); + if (tmp_smallfelems != NULL) + OPENSSL_free(tmp_smallfelems); + return ret; + } + +int ec_GFp_nistp256_precompute_mult(EC_GROUP *group, BN_CTX *ctx) + { + int ret = 0; + NISTP256_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + smallfelem tmp_smallfelems[32]; + felem x_tmp, y_tmp, z_tmp; + + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp256_pre_comp_dup, + nistp256_pre_comp_free, nistp256_pre_comp_clear_free); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp256_curve_params[3], sizeof (felem_bytearray), x); + BN_bin2bn(nistp256_curve_params[4], sizeof (felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp256_pre_comp_new()) == NULL) + goto err; + /* if the generator is the standard one, use built-in precomputation */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + ret = 1; + goto err; + } + if ((!BN_to_felem(x_tmp, &group->generator->X)) || + (!BN_to_felem(y_tmp, &group->generator->Y)) || + (!BN_to_felem(z_tmp, &group->generator->Z))) + goto err; + felem_shrink(pre->g_pre_comp[0][1][0], x_tmp); + felem_shrink(pre->g_pre_comp[0][1][1], y_tmp); + felem_shrink(pre->g_pre_comp[0][1][2], z_tmp); + /* compute 2^64*G, 2^128*G, 2^192*G for the first table, + * 2^32*G, 2^96*G, 2^160*G, 2^224*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) + { + point_double_small( + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[0][i][0], pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 31; ++j) + { + point_double_small( + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } + if (i == 8) + break; + point_double_small( + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], + pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 31; ++j) + { + point_double_small( + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2], + pre->g_pre_comp[0][2*i][0], pre->g_pre_comp[0][2*i][1], pre->g_pre_comp[0][2*i][2]); + } + } + for (i = 0; i < 2; i++) + { + /* g_pre_comp[i][0] is the point at infinity */ + memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); + /* the remaining multiples */ + /* 2^64*G + 2^128*G resp. 2^96*G + 2^160*G */ + point_add_small( + pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], pre->g_pre_comp[i][6][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + /* 2^64*G + 2^192*G resp. 2^96*G + 2^224*G */ + point_add_small( + pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], pre->g_pre_comp[i][10][2], + pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + /* 2^128*G + 2^192*G resp. 2^160*G + 2^224*G */ + point_add_small( + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][8][0], pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2]); + /* 2^64*G + 2^128*G + 2^192*G resp. 2^96*G + 2^160*G + 2^224*G */ + point_add_small( + pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], pre->g_pre_comp[i][14][2], + pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) + { + /* odd multiples: add G resp. 2^32*G */ + point_add_small( + pre->g_pre_comp[i][2*j+1][0], pre->g_pre_comp[i][2*j+1][1], pre->g_pre_comp[i][2*j+1][2], + pre->g_pre_comp[i][2*j][0], pre->g_pre_comp[i][2*j][1], pre->g_pre_comp[i][2*j][2], + pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], pre->g_pre_comp[i][1][2]); + } + } + make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_smallfelems); + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp256_pre_comp_dup, + nistp256_pre_comp_free, nistp256_pre_comp_clear_free)) + goto err; + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (pre) + nistp256_pre_comp_free(pre); + return ret; + } + +int ec_GFp_nistp256_have_precompute_mult(const EC_GROUP *group) + { + if (EC_EX_DATA_get_data(group->extra_data, nistp256_pre_comp_dup, + nistp256_pre_comp_free, nistp256_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; + } +#else +static void *dummy=&dummy; +#endif diff --git a/crypto/ec/ecp_nistp521.c b/crypto/ec/ecp_nistp521.c new file mode 100644 index 0000000000000..178b655f7f177 --- /dev/null +++ b/crypto/ec/ecp_nistp521.c @@ -0,0 +1,2025 @@ +/* crypto/ec/ecp_nistp521.c */ +/* + * Written by Adam Langley (Google) for the OpenSSL project + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +/* + * A 64-bit implementation of the NIST P-521 elliptic curve point multiplication + * + * OpenSSL integration was taken from Emilia Kasper's work in ecp_nistp224.c. + * Otherwise based on Emilia's P224 work, which was inspired by my curve25519 + * work which got its smarts from Daniel J. Bernstein's work on the same. + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +#ifndef OPENSSL_SYS_VMS +#include <stdint.h> +#else +#include <inttypes.h> +#endif + +#include <string.h> +#include <openssl/err.h> +#include "ec_lcl.h" + +#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) + /* even with gcc, the typedef won't work for 32-bit platforms */ + typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ +#else + #error "Need GCC 3.1 or later to define type uint128_t" +#endif + +typedef uint8_t u8; +typedef uint64_t u64; +typedef int64_t s64; + +/* The underlying field. + * + * P521 operates over GF(2^521-1). We can serialise an element of this field + * into 66 bytes where the most significant byte contains only a single bit. We + * call this an felem_bytearray. */ + +typedef u8 felem_bytearray[66]; + +/* These are the parameters of P521, taken from FIPS 186-3, section D.1.2.5. + * These values are big-endian. */ +static const felem_bytearray nistp521_curve_params[5] = + { + {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* p */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff}, + {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* a = -3 */ + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, + 0xff, 0xfc}, + {0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, /* b */ + 0x9a, 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85, + 0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3, + 0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1, + 0x09, 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e, + 0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1, + 0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c, + 0x34, 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50, + 0x3f, 0x00}, + {0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, /* x */ + 0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95, + 0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f, + 0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d, + 0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7, + 0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff, + 0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a, + 0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5, + 0xbd, 0x66}, + {0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, /* y */ + 0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d, + 0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b, + 0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e, + 0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4, + 0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad, + 0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72, + 0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1, + 0x66, 0x50} + }; + +/* The representation of field elements. + * ------------------------------------ + * + * We represent field elements with nine values. These values are either 64 or + * 128 bits and the field element represented is: + * v[0]*2^0 + v[1]*2^58 + v[2]*2^116 + ... + v[8]*2^464 (mod p) + * Each of the nine values is called a 'limb'. Since the limbs are spaced only + * 58 bits apart, but are greater than 58 bits in length, the most significant + * bits of each limb overlap with the least significant bits of the next. + * + * A field element with 64-bit limbs is an 'felem'. One with 128-bit limbs is a + * 'largefelem' */ + +#define NLIMBS 9 + +typedef uint64_t limb; +typedef limb felem[NLIMBS]; +typedef uint128_t largefelem[NLIMBS]; + +static const limb bottom57bits = 0x1ffffffffffffff; +static const limb bottom58bits = 0x3ffffffffffffff; + +/* bin66_to_felem takes a little-endian byte array and converts it into felem + * form. This assumes that the CPU is little-endian. */ +static void bin66_to_felem(felem out, const u8 in[66]) + { + out[0] = (*((limb*) &in[0])) & bottom58bits; + out[1] = (*((limb*) &in[7]) >> 2) & bottom58bits; + out[2] = (*((limb*) &in[14]) >> 4) & bottom58bits; + out[3] = (*((limb*) &in[21]) >> 6) & bottom58bits; + out[4] = (*((limb*) &in[29])) & bottom58bits; + out[5] = (*((limb*) &in[36]) >> 2) & bottom58bits; + out[6] = (*((limb*) &in[43]) >> 4) & bottom58bits; + out[7] = (*((limb*) &in[50]) >> 6) & bottom58bits; + out[8] = (*((limb*) &in[58])) & bottom57bits; + } + +/* felem_to_bin66 takes an felem and serialises into a little endian, 66 byte + * array. This assumes that the CPU is little-endian. */ +static void felem_to_bin66(u8 out[66], const felem in) + { + memset(out, 0, 66); + (*((limb*) &out[0])) = in[0]; + (*((limb*) &out[7])) |= in[1] << 2; + (*((limb*) &out[14])) |= in[2] << 4; + (*((limb*) &out[21])) |= in[3] << 6; + (*((limb*) &out[29])) = in[4]; + (*((limb*) &out[36])) |= in[5] << 2; + (*((limb*) &out[43])) |= in[6] << 4; + (*((limb*) &out[50])) |= in[7] << 6; + (*((limb*) &out[58])) = in[8]; + } + +/* To preserve endianness when using BN_bn2bin and BN_bin2bn */ +static void flip_endian(u8 *out, const u8 *in, unsigned len) + { + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len-1-i]; + } + +/* BN_to_felem converts an OpenSSL BIGNUM into an felem */ +static int BN_to_felem(felem out, const BIGNUM *bn) + { + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof b_out); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof b_out) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) + { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin66_to_felem(out, b_out); + return 1; + } + +/* felem_to_BN converts an felem into an OpenSSL BIGNUM */ +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) + { + felem_bytearray b_in, b_out; + felem_to_bin66(b_in, in); + flip_endian(b_out, b_in, sizeof b_out); + return BN_bin2bn(b_out, sizeof b_out, out); + } + + +/* Field operations + * ---------------- */ + +static void felem_one(felem out) + { + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; + out[4] = 0; + out[5] = 0; + out[6] = 0; + out[7] = 0; + out[8] = 0; + } + +static void felem_assign(felem out, const felem in) + { + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; + out[4] = in[4]; + out[5] = in[5]; + out[6] = in[6]; + out[7] = in[7]; + out[8] = in[8]; + } + +/* felem_sum64 sets out = out + in. */ +static void felem_sum64(felem out, const felem in) + { + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; + out[4] += in[4]; + out[5] += in[5]; + out[6] += in[6]; + out[7] += in[7]; + out[8] += in[8]; + } + +/* felem_scalar sets out = in * scalar */ +static void felem_scalar(felem out, const felem in, limb scalar) + { + out[0] = in[0] * scalar; + out[1] = in[1] * scalar; + out[2] = in[2] * scalar; + out[3] = in[3] * scalar; + out[4] = in[4] * scalar; + out[5] = in[5] * scalar; + out[6] = in[6] * scalar; + out[7] = in[7] * scalar; + out[8] = in[8] * scalar; + } + +/* felem_scalar64 sets out = out * scalar */ +static void felem_scalar64(felem out, limb scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; + out[8] *= scalar; + } + +/* felem_scalar128 sets out = out * scalar */ +static void felem_scalar128(largefelem out, limb scalar) + { + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; + out[7] *= scalar; + out[8] *= scalar; + } + +/* felem_neg sets |out| to |-in| + * On entry: + * in[i] < 2^59 + 2^14 + * On exit: + * out[i] < 2^62 + */ +static void felem_neg(felem out, const felem in) + { + /* In order to prevent underflow, we subtract from 0 mod p. */ + static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); + static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + + out[0] = two62m3 - in[0]; + out[1] = two62m2 - in[1]; + out[2] = two62m2 - in[2]; + out[3] = two62m2 - in[3]; + out[4] = two62m2 - in[4]; + out[5] = two62m2 - in[5]; + out[6] = two62m2 - in[6]; + out[7] = two62m2 - in[7]; + out[8] = two62m2 - in[8]; + } + +/* felem_diff64 subtracts |in| from |out| + * On entry: + * in[i] < 2^59 + 2^14 + * On exit: + * out[i] < out[i] + 2^62 + */ +static void felem_diff64(felem out, const felem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5); + static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4); + + out[0] += two62m3 - in[0]; + out[1] += two62m2 - in[1]; + out[2] += two62m2 - in[2]; + out[3] += two62m2 - in[3]; + out[4] += two62m2 - in[4]; + out[5] += two62m2 - in[5]; + out[6] += two62m2 - in[6]; + out[7] += two62m2 - in[7]; + out[8] += two62m2 - in[8]; + } + +/* felem_diff_128_64 subtracts |in| from |out| + * On entry: + * in[i] < 2^62 + 2^17 + * On exit: + * out[i] < out[i] + 2^63 + */ +static void felem_diff_128_64(largefelem out, const felem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + static const limb two63m6 = (((limb)1) << 62) - (((limb)1) << 5); + static const limb two63m5 = (((limb)1) << 62) - (((limb)1) << 4); + + out[0] += two63m6 - in[0]; + out[1] += two63m5 - in[1]; + out[2] += two63m5 - in[2]; + out[3] += two63m5 - in[3]; + out[4] += two63m5 - in[4]; + out[5] += two63m5 - in[5]; + out[6] += two63m5 - in[6]; + out[7] += two63m5 - in[7]; + out[8] += two63m5 - in[8]; + } + +/* felem_diff_128_64 subtracts |in| from |out| + * On entry: + * in[i] < 2^126 + * On exit: + * out[i] < out[i] + 2^127 - 2^69 + */ +static void felem_diff128(largefelem out, const largefelem in) + { + /* In order to prevent underflow, we add 0 mod p before subtracting. */ + static const uint128_t two127m70 = (((uint128_t)1) << 127) - (((uint128_t)1) << 70); + static const uint128_t two127m69 = (((uint128_t)1) << 127) - (((uint128_t)1) << 69); + + out[0] += (two127m70 - in[0]); + out[1] += (two127m69 - in[1]); + out[2] += (two127m69 - in[2]); + out[3] += (two127m69 - in[3]); + out[4] += (two127m69 - in[4]); + out[5] += (two127m69 - in[5]); + out[6] += (two127m69 - in[6]); + out[7] += (two127m69 - in[7]); + out[8] += (two127m69 - in[8]); + } + +/* felem_square sets |out| = |in|^2 + * On entry: + * in[i] < 2^62 + * On exit: + * out[i] < 17 * max(in[i]) * max(in[i]) + */ +static void felem_square(largefelem out, const felem in) + { + felem inx2, inx4; + felem_scalar(inx2, in, 2); + felem_scalar(inx4, in, 4); + + /* We have many cases were we want to do + * in[x] * in[y] + + * in[y] * in[x] + * This is obviously just + * 2 * in[x] * in[y] + * However, rather than do the doubling on the 128 bit result, we + * double one of the inputs to the multiplication by reading from + * |inx2| */ + + out[0] = ((uint128_t) in[0]) * in[0]; + out[1] = ((uint128_t) in[0]) * inx2[1]; + out[2] = ((uint128_t) in[0]) * inx2[2] + + ((uint128_t) in[1]) * in[1]; + out[3] = ((uint128_t) in[0]) * inx2[3] + + ((uint128_t) in[1]) * inx2[2]; + out[4] = ((uint128_t) in[0]) * inx2[4] + + ((uint128_t) in[1]) * inx2[3] + + ((uint128_t) in[2]) * in[2]; + out[5] = ((uint128_t) in[0]) * inx2[5] + + ((uint128_t) in[1]) * inx2[4] + + ((uint128_t) in[2]) * inx2[3]; + out[6] = ((uint128_t) in[0]) * inx2[6] + + ((uint128_t) in[1]) * inx2[5] + + ((uint128_t) in[2]) * inx2[4] + + ((uint128_t) in[3]) * in[3]; + out[7] = ((uint128_t) in[0]) * inx2[7] + + ((uint128_t) in[1]) * inx2[6] + + ((uint128_t) in[2]) * inx2[5] + + ((uint128_t) in[3]) * inx2[4]; + out[8] = ((uint128_t) in[0]) * inx2[8] + + ((uint128_t) in[1]) * inx2[7] + + ((uint128_t) in[2]) * inx2[6] + + ((uint128_t) in[3]) * inx2[5] + + ((uint128_t) in[4]) * in[4]; + + /* The remaining limbs fall above 2^521, with the first falling at + * 2^522. They correspond to locations one bit up from the limbs + * produced above so we would have to multiply by two to align them. + * Again, rather than operate on the 128-bit result, we double one of + * the inputs to the multiplication. If we want to double for both this + * reason, and the reason above, then we end up multiplying by four. */ + + /* 9 */ + out[0] += ((uint128_t) in[1]) * inx4[8] + + ((uint128_t) in[2]) * inx4[7] + + ((uint128_t) in[3]) * inx4[6] + + ((uint128_t) in[4]) * inx4[5]; + + /* 10 */ + out[1] += ((uint128_t) in[2]) * inx4[8] + + ((uint128_t) in[3]) * inx4[7] + + ((uint128_t) in[4]) * inx4[6] + + ((uint128_t) in[5]) * inx2[5]; + + /* 11 */ + out[2] += ((uint128_t) in[3]) * inx4[8] + + ((uint128_t) in[4]) * inx4[7] + + ((uint128_t) in[5]) * inx4[6]; + + /* 12 */ + out[3] += ((uint128_t) in[4]) * inx4[8] + + ((uint128_t) in[5]) * inx4[7] + + ((uint128_t) in[6]) * inx2[6]; + + /* 13 */ + out[4] += ((uint128_t) in[5]) * inx4[8] + + ((uint128_t) in[6]) * inx4[7]; + + /* 14 */ + out[5] += ((uint128_t) in[6]) * inx4[8] + + ((uint128_t) in[7]) * inx2[7]; + + /* 15 */ + out[6] += ((uint128_t) in[7]) * inx4[8]; + + /* 16 */ + out[7] += ((uint128_t) in[8]) * inx2[8]; + } + +/* felem_mul sets |out| = |in1| * |in2| + * On entry: + * in1[i] < 2^64 + * in2[i] < 2^63 + * On exit: + * out[i] < 17 * max(in1[i]) * max(in2[i]) + */ +static void felem_mul(largefelem out, const felem in1, const felem in2) + { + felem in2x2; + felem_scalar(in2x2, in2, 2); + + out[0] = ((uint128_t) in1[0]) * in2[0]; + + out[1] = ((uint128_t) in1[0]) * in2[1] + + ((uint128_t) in1[1]) * in2[0]; + + out[2] = ((uint128_t) in1[0]) * in2[2] + + ((uint128_t) in1[1]) * in2[1] + + ((uint128_t) in1[2]) * in2[0]; + + out[3] = ((uint128_t) in1[0]) * in2[3] + + ((uint128_t) in1[1]) * in2[2] + + ((uint128_t) in1[2]) * in2[1] + + ((uint128_t) in1[3]) * in2[0]; + + out[4] = ((uint128_t) in1[0]) * in2[4] + + ((uint128_t) in1[1]) * in2[3] + + ((uint128_t) in1[2]) * in2[2] + + ((uint128_t) in1[3]) * in2[1] + + ((uint128_t) in1[4]) * in2[0]; + + out[5] = ((uint128_t) in1[0]) * in2[5] + + ((uint128_t) in1[1]) * in2[4] + + ((uint128_t) in1[2]) * in2[3] + + ((uint128_t) in1[3]) * in2[2] + + ((uint128_t) in1[4]) * in2[1] + + ((uint128_t) in1[5]) * in2[0]; + + out[6] = ((uint128_t) in1[0]) * in2[6] + + ((uint128_t) in1[1]) * in2[5] + + ((uint128_t) in1[2]) * in2[4] + + ((uint128_t) in1[3]) * in2[3] + + ((uint128_t) in1[4]) * in2[2] + + ((uint128_t) in1[5]) * in2[1] + + ((uint128_t) in1[6]) * in2[0]; + + out[7] = ((uint128_t) in1[0]) * in2[7] + + ((uint128_t) in1[1]) * in2[6] + + ((uint128_t) in1[2]) * in2[5] + + ((uint128_t) in1[3]) * in2[4] + + ((uint128_t) in1[4]) * in2[3] + + ((uint128_t) in1[5]) * in2[2] + + ((uint128_t) in1[6]) * in2[1] + + ((uint128_t) in1[7]) * in2[0]; + + out[8] = ((uint128_t) in1[0]) * in2[8] + + ((uint128_t) in1[1]) * in2[7] + + ((uint128_t) in1[2]) * in2[6] + + ((uint128_t) in1[3]) * in2[5] + + ((uint128_t) in1[4]) * in2[4] + + ((uint128_t) in1[5]) * in2[3] + + ((uint128_t) in1[6]) * in2[2] + + ((uint128_t) in1[7]) * in2[1] + + ((uint128_t) in1[8]) * in2[0]; + + /* See comment in felem_square about the use of in2x2 here */ + + out[0] += ((uint128_t) in1[1]) * in2x2[8] + + ((uint128_t) in1[2]) * in2x2[7] + + ((uint128_t) in1[3]) * in2x2[6] + + ((uint128_t) in1[4]) * in2x2[5] + + ((uint128_t) in1[5]) * in2x2[4] + + ((uint128_t) in1[6]) * in2x2[3] + + ((uint128_t) in1[7]) * in2x2[2] + + ((uint128_t) in1[8]) * in2x2[1]; + + out[1] += ((uint128_t) in1[2]) * in2x2[8] + + ((uint128_t) in1[3]) * in2x2[7] + + ((uint128_t) in1[4]) * in2x2[6] + + ((uint128_t) in1[5]) * in2x2[5] + + ((uint128_t) in1[6]) * in2x2[4] + + ((uint128_t) in1[7]) * in2x2[3] + + ((uint128_t) in1[8]) * in2x2[2]; + + out[2] += ((uint128_t) in1[3]) * in2x2[8] + + ((uint128_t) in1[4]) * in2x2[7] + + ((uint128_t) in1[5]) * in2x2[6] + + ((uint128_t) in1[6]) * in2x2[5] + + ((uint128_t) in1[7]) * in2x2[4] + + ((uint128_t) in1[8]) * in2x2[3]; + + out[3] += ((uint128_t) in1[4]) * in2x2[8] + + ((uint128_t) in1[5]) * in2x2[7] + + ((uint128_t) in1[6]) * in2x2[6] + + ((uint128_t) in1[7]) * in2x2[5] + + ((uint128_t) in1[8]) * in2x2[4]; + + out[4] += ((uint128_t) in1[5]) * in2x2[8] + + ((uint128_t) in1[6]) * in2x2[7] + + ((uint128_t) in1[7]) * in2x2[6] + + ((uint128_t) in1[8]) * in2x2[5]; + + out[5] += ((uint128_t) in1[6]) * in2x2[8] + + ((uint128_t) in1[7]) * in2x2[7] + + ((uint128_t) in1[8]) * in2x2[6]; + + out[6] += ((uint128_t) in1[7]) * in2x2[8] + + ((uint128_t) in1[8]) * in2x2[7]; + + out[7] += ((uint128_t) in1[8]) * in2x2[8]; + } + +static const limb bottom52bits = 0xfffffffffffff; + +/* felem_reduce converts a largefelem to an felem. + * On entry: + * in[i] < 2^128 + * On exit: + * out[i] < 2^59 + 2^14 + */ +static void felem_reduce(felem out, const largefelem in) + { + u64 overflow1, overflow2; + + out[0] = ((limb) in[0]) & bottom58bits; + out[1] = ((limb) in[1]) & bottom58bits; + out[2] = ((limb) in[2]) & bottom58bits; + out[3] = ((limb) in[3]) & bottom58bits; + out[4] = ((limb) in[4]) & bottom58bits; + out[5] = ((limb) in[5]) & bottom58bits; + out[6] = ((limb) in[6]) & bottom58bits; + out[7] = ((limb) in[7]) & bottom58bits; + out[8] = ((limb) in[8]) & bottom58bits; + + /* out[i] < 2^58 */ + + out[1] += ((limb) in[0]) >> 58; + out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6; + /* out[1] < 2^58 + 2^6 + 2^58 + * = 2^59 + 2^6 */ + out[2] += ((limb) (in[0] >> 64)) >> 52; + + out[2] += ((limb) in[1]) >> 58; + out[2] += (((limb) (in[1] >> 64)) & bottom52bits) << 6; + out[3] += ((limb) (in[1] >> 64)) >> 52; + + out[3] += ((limb) in[2]) >> 58; + out[3] += (((limb) (in[2] >> 64)) & bottom52bits) << 6; + out[4] += ((limb) (in[2] >> 64)) >> 52; + + out[4] += ((limb) in[3]) >> 58; + out[4] += (((limb) (in[3] >> 64)) & bottom52bits) << 6; + out[5] += ((limb) (in[3] >> 64)) >> 52; + + out[5] += ((limb) in[4]) >> 58; + out[5] += (((limb) (in[4] >> 64)) & bottom52bits) << 6; + out[6] += ((limb) (in[4] >> 64)) >> 52; + + out[6] += ((limb) in[5]) >> 58; + out[6] += (((limb) (in[5] >> 64)) & bottom52bits) << 6; + out[7] += ((limb) (in[5] >> 64)) >> 52; + + out[7] += ((limb) in[6]) >> 58; + out[7] += (((limb) (in[6] >> 64)) & bottom52bits) << 6; + out[8] += ((limb) (in[6] >> 64)) >> 52; + + out[8] += ((limb) in[7]) >> 58; + out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6; + /* out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12 + * < 2^59 + 2^13 */ + overflow1 = ((limb) (in[7] >> 64)) >> 52; + + overflow1 += ((limb) in[8]) >> 58; + overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6; + overflow2 = ((limb) (in[8] >> 64)) >> 52; + + overflow1 <<= 1; /* overflow1 < 2^13 + 2^7 + 2^59 */ + overflow2 <<= 1; /* overflow2 < 2^13 */ + + out[0] += overflow1; /* out[0] < 2^60 */ + out[1] += overflow2; /* out[1] < 2^59 + 2^6 + 2^13 */ + + out[1] += out[0] >> 58; out[0] &= bottom58bits; + /* out[0] < 2^58 + * out[1] < 2^59 + 2^6 + 2^13 + 2^2 + * < 2^59 + 2^14 */ + } + +static void felem_square_reduce(felem out, const felem in) + { + largefelem tmp; + felem_square(tmp, in); + felem_reduce(out, tmp); + } + +static void felem_mul_reduce(felem out, const felem in1, const felem in2) + { + largefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); + } + +/* felem_inv calculates |out| = |in|^{-1} + * + * Based on Fermat's Little Theorem: + * a^p = a (mod p) + * a^{p-1} = 1 (mod p) + * a^{p-2} = a^{-1} (mod p) + */ +static void felem_inv(felem out, const felem in) + { + felem ftmp, ftmp2, ftmp3, ftmp4; + largefelem tmp; + unsigned i; + + felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2^1 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 2^0 */ + felem_assign(ftmp2, ftmp); + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^1 */ + felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2^0 */ + felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^4 - 2^1 */ + + felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^3 - 2^1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^4 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */ + + felem_assign(ftmp2, ftmp3); + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^5 - 2^1 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^6 - 2^2 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^7 - 2^3 */ + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^8 - 2^4 */ + felem_assign(ftmp4, ftmp3); + felem_mul(tmp, ftmp3, ftmp); felem_reduce(ftmp4, tmp); /* 2^8 - 2^1 */ + felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); /* 2^9 - 2^2 */ + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 8; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 16; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 32; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 64; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 128; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */ + felem_assign(ftmp2, ftmp3); + + for (i = 0; i < 256; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */ + } + felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */ + + for (i = 0; i < 9; i++) + { + felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */ + } + felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */ + felem_mul(tmp, ftmp3, in); felem_reduce(out, tmp); /* 2^512 - 3 */ +} + +/* This is 2^521-1, expressed as an felem */ +static const felem kPrime = + { + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff, + 0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff + }; + +/* felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0 + * otherwise. + * On entry: + * in[i] < 2^59 + 2^14 + */ +static limb felem_is_zero(const felem in) + { + felem ftmp; + limb is_zero, is_p; + felem_assign(ftmp, in); + + ftmp[0] += ftmp[8] >> 57; ftmp[8] &= bottom57bits; + /* ftmp[8] < 2^57 */ + ftmp[1] += ftmp[0] >> 58; ftmp[0] &= bottom58bits; + ftmp[2] += ftmp[1] >> 58; ftmp[1] &= bottom58bits; + ftmp[3] += ftmp[2] >> 58; ftmp[2] &= bottom58bits; + ftmp[4] += ftmp[3] >> 58; ftmp[3] &= bottom58bits; + ftmp[5] += ftmp[4] >> 58; ftmp[4] &= bottom58bits; + ftmp[6] += ftmp[5] >> 58; ftmp[5] &= bottom58bits; + ftmp[7] += ftmp[6] >> 58; ftmp[6] &= bottom58bits; + ftmp[8] += ftmp[7] >> 58; ftmp[7] &= bottom58bits; + /* ftmp[8] < 2^57 + 4 */ + + /* The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is + * greater than our bound for ftmp[8]. Therefore we only have to check + * if the zero is zero or 2^521-1. */ + + is_zero = 0; + is_zero |= ftmp[0]; + is_zero |= ftmp[1]; + is_zero |= ftmp[2]; + is_zero |= ftmp[3]; + is_zero |= ftmp[4]; + is_zero |= ftmp[5]; + is_zero |= ftmp[6]; + is_zero |= ftmp[7]; + is_zero |= ftmp[8]; + + is_zero--; + /* We know that ftmp[i] < 2^63, therefore the only way that the top bit + * can be set is if is_zero was 0 before the decrement. */ + is_zero = ((s64) is_zero) >> 63; + + is_p = ftmp[0] ^ kPrime[0]; + is_p |= ftmp[1] ^ kPrime[1]; + is_p |= ftmp[2] ^ kPrime[2]; + is_p |= ftmp[3] ^ kPrime[3]; + is_p |= ftmp[4] ^ kPrime[4]; + is_p |= ftmp[5] ^ kPrime[5]; + is_p |= ftmp[6] ^ kPrime[6]; + is_p |= ftmp[7] ^ kPrime[7]; + is_p |= ftmp[8] ^ kPrime[8]; + + is_p--; + is_p = ((s64) is_p) >> 63; + + is_zero |= is_p; + return is_zero; + } + +static int felem_is_zero_int(const felem in) + { + return (int) (felem_is_zero(in) & ((limb)1)); + } + +/* felem_contract converts |in| to its unique, minimal representation. + * On entry: + * in[i] < 2^59 + 2^14 + */ +static void felem_contract(felem out, const felem in) + { + limb is_p, is_greater, sign; + static const limb two58 = ((limb)1) << 58; + + felem_assign(out, in); + + out[0] += out[8] >> 57; out[8] &= bottom57bits; + /* out[8] < 2^57 */ + out[1] += out[0] >> 58; out[0] &= bottom58bits; + out[2] += out[1] >> 58; out[1] &= bottom58bits; + out[3] += out[2] >> 58; out[2] &= bottom58bits; + out[4] += out[3] >> 58; out[3] &= bottom58bits; + out[5] += out[4] >> 58; out[4] &= bottom58bits; + out[6] += out[5] >> 58; out[5] &= bottom58bits; + out[7] += out[6] >> 58; out[6] &= bottom58bits; + out[8] += out[7] >> 58; out[7] &= bottom58bits; + /* out[8] < 2^57 + 4 */ + + /* If the value is greater than 2^521-1 then we have to subtract + * 2^521-1 out. See the comments in felem_is_zero regarding why we + * don't test for other multiples of the prime. */ + + /* First, if |out| is equal to 2^521-1, we subtract it out to get zero. */ + + is_p = out[0] ^ kPrime[0]; + is_p |= out[1] ^ kPrime[1]; + is_p |= out[2] ^ kPrime[2]; + is_p |= out[3] ^ kPrime[3]; + is_p |= out[4] ^ kPrime[4]; + is_p |= out[5] ^ kPrime[5]; + is_p |= out[6] ^ kPrime[6]; + is_p |= out[7] ^ kPrime[7]; + is_p |= out[8] ^ kPrime[8]; + + is_p--; + is_p &= is_p << 32; + is_p &= is_p << 16; + is_p &= is_p << 8; + is_p &= is_p << 4; + is_p &= is_p << 2; + is_p &= is_p << 1; + is_p = ((s64) is_p) >> 63; + is_p = ~is_p; + + /* is_p is 0 iff |out| == 2^521-1 and all ones otherwise */ + + out[0] &= is_p; + out[1] &= is_p; + out[2] &= is_p; + out[3] &= is_p; + out[4] &= is_p; + out[5] &= is_p; + out[6] &= is_p; + out[7] &= is_p; + out[8] &= is_p; + + /* In order to test that |out| >= 2^521-1 we need only test if out[8] + * >> 57 is greater than zero as (2^521-1) + x >= 2^522 */ + is_greater = out[8] >> 57; + is_greater |= is_greater << 32; + is_greater |= is_greater << 16; + is_greater |= is_greater << 8; + is_greater |= is_greater << 4; + is_greater |= is_greater << 2; + is_greater |= is_greater << 1; + is_greater = ((s64) is_greater) >> 63; + + out[0] -= kPrime[0] & is_greater; + out[1] -= kPrime[1] & is_greater; + out[2] -= kPrime[2] & is_greater; + out[3] -= kPrime[3] & is_greater; + out[4] -= kPrime[4] & is_greater; + out[5] -= kPrime[5] & is_greater; + out[6] -= kPrime[6] & is_greater; + out[7] -= kPrime[7] & is_greater; + out[8] -= kPrime[8] & is_greater; + + /* Eliminate negative coefficients */ + sign = -(out[0] >> 63); out[0] += (two58 & sign); out[1] -= (1 & sign); + sign = -(out[1] >> 63); out[1] += (two58 & sign); out[2] -= (1 & sign); + sign = -(out[2] >> 63); out[2] += (two58 & sign); out[3] -= (1 & sign); + sign = -(out[3] >> 63); out[3] += (two58 & sign); out[4] -= (1 & sign); + sign = -(out[4] >> 63); out[4] += (two58 & sign); out[5] -= (1 & sign); + sign = -(out[0] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); + sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); + sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); + sign = -(out[5] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign); + sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign); + sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign); + } + +/* Group operations + * ---------------- + * + * Building on top of the field operations we have the operations on the + * elliptic curve group itself. Points on the curve are represented in Jacobian + * coordinates */ + +/* point_double calcuates 2*(x_in, y_in, z_in) + * + * The method is taken from: + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b + * + * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed. + * while x_out == y_in is not (maybe this works, but it's not tested). */ +static void +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) + { + largefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); /* delta[i] < 2^59 + 2^14 */ + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); /* gamma[i] < 2^59 + 2^14 */ + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); /* beta[i] < 2^59 + 2^14 */ + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff64(ftmp, delta); + /* ftmp[i] < 2^61 */ + felem_sum64(ftmp2, delta); + /* ftmp2[i] < 2^60 + 2^15 */ + felem_scalar64(ftmp2, 3); + /* ftmp2[i] < 3*2^60 + 3*2^15 */ + felem_mul(tmp, ftmp, ftmp2); + /* tmp[i] < 17(3*2^121 + 3*2^76) + * = 61*2^121 + 61*2^76 + * < 64*2^121 + 64*2^76 + * = 2^127 + 2^82 + * < 2^128 */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* tmp[i] < 17*2^120 + * < 2^125 */ + felem_assign(ftmp, beta); + felem_scalar64(ftmp, 8); + /* ftmp[i] < 2^62 + 2^17 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^125 + 2^63 + 2^62 + 2^17 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum64(delta, gamma); + /* delta[i] < 2^60 + 2^15 */ + felem_assign(ftmp, y_in); + felem_sum64(ftmp, z_in); + /* ftmp[i] < 2^60 + 2^15 */ + felem_square(tmp, ftmp); + /* tmp[i] < 17(2^122) + * < 2^127 */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^127 + 2^63 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar64(beta, 4); + /* beta[i] < 2^61 + 2^16 */ + felem_diff64(beta, x_out); + /* beta[i] < 2^61 + 2^60 + 2^16 */ + felem_mul(tmp, alpha, beta); + /* tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16)) + * = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) + * = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30) + * < 2^128 */ + felem_square(tmp2, gamma); + /* tmp2[i] < 17*(2^59 + 2^14)^2 + * = 17*(2^118 + 2^74 + 2^28) */ + felem_scalar128(tmp2, 8); + /* tmp2[i] < 8*17*(2^118 + 2^74 + 2^28) + * = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31 + * < 2^126 */ + felem_diff128(tmp, tmp2); + /* tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30) + * = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 + + * 2^74 + 2^69 + 2^34 + 2^30 + * < 2^128 */ + felem_reduce(y_out, tmp); + } + +/* copy_conditional copies in to out iff mask is all ones. */ +static void +copy_conditional(felem out, const felem in, limb mask) + { + unsigned i; + for (i = 0; i < NLIMBS; ++i) + { + const limb tmp = mask & (in[i] ^ out[i]); + out[i] ^= tmp; + } + } + +/* point_add calcuates (x1, y1, z1) + (x2, y2, z2) + * + * The method is taken from + * http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl, + * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity). + * + * This function includes a branch for checking whether the two input points + * are equal (while not equal to the point at infinity). This case never + * happens during single point multiplication, so there is no timing leak for + * ECDH or ECDSA signing. */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, const felem z2) + { + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out; + largefelem tmp, tmp2; + limb x_equal, y_equal, z1_is_zero, z2_is_zero; + + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + + /* ftmp = z1z1 = z1**2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + if (!mixed) + { + /* ftmp2 = z2z2 = z2**2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* u1 = ftmp3 = x1*z2z2 */ + felem_mul(tmp, x1, ftmp2); + felem_reduce(ftmp3, tmp); + + /* ftmp5 = z1 + z2 */ + felem_assign(ftmp5, z1); + felem_sum64(ftmp5, z2); + /* ftmp5[i] < 2^61 */ + + /* ftmp5 = (z1 + z2)**2 - z1z1 - z2z2 = 2*z1z2 */ + felem_square(tmp, ftmp5); + /* tmp[i] < 17*2^122 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 17*2^122 + 2^63 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 17*2^122 + 2^64 */ + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2 * z2z2 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp2, tmp); + + /* s1 = ftmp6 = y1 * z2**3 */ + felem_mul(tmp, y1, ftmp2); + felem_reduce(ftmp6, tmp); + } + else + { + /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */ + + /* u1 = ftmp3 = x1*z2z2 */ + felem_assign(ftmp3, x1); + + /* ftmp5 = 2*z1z2 */ + felem_scalar(ftmp5, z1, 2); + + /* s1 = ftmp6 = y1 * z2**3 */ + felem_assign(ftmp6, y1); + } + + /* u2 = x2*z1z1 */ + felem_mul(tmp, x2, ftmp); + /* tmp[i] < 17*2^120 */ + + /* h = ftmp4 = u2 - u1 */ + felem_diff_128_64(tmp, ftmp3); + /* tmp[i] < 17*2^120 + 2^63 */ + felem_reduce(ftmp4, tmp); + + x_equal = felem_is_zero(ftmp4); + + /* z_out = ftmp5 * h */ + felem_mul(tmp, ftmp5, ftmp4); + felem_reduce(z_out, tmp); + + /* ftmp = z1 * z1z1 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp, tmp); + + /* s2 = tmp = y2 * z1**3 */ + felem_mul(tmp, y2, ftmp); + /* tmp[i] < 17*2^120 */ + + /* r = ftmp5 = (s2 - s1)*2 */ + felem_diff_128_64(tmp, ftmp6); + /* tmp[i] < 17*2^120 + 2^63 */ + felem_reduce(ftmp5, tmp); + y_equal = felem_is_zero(ftmp5); + felem_scalar64(ftmp5, 2); + /* ftmp5[i] < 2^61 */ + + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) + { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* I = ftmp = (2h)**2 */ + felem_assign(ftmp, ftmp4); + felem_scalar64(ftmp, 2); + /* ftmp[i] < 2^61 */ + felem_square(tmp, ftmp); + /* tmp[i] < 17*2^122 */ + felem_reduce(ftmp, tmp); + + /* J = ftmp2 = h * I */ + felem_mul(tmp, ftmp4, ftmp); + felem_reduce(ftmp2, tmp); + + /* V = ftmp4 = U1 * I */ + felem_mul(tmp, ftmp3, ftmp); + felem_reduce(ftmp4, tmp); + + /* x_out = r**2 - J - 2V */ + felem_square(tmp, ftmp5); + /* tmp[i] < 17*2^122 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 17*2^122 + 2^63 */ + felem_assign(ftmp3, ftmp4); + felem_scalar64(ftmp4, 2); + /* ftmp4[i] < 2^61 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 17*2^122 + 2^64 */ + felem_reduce(x_out, tmp); + + /* y_out = r(V-x_out) - 2 * s1 * J */ + felem_diff64(ftmp3, x_out); + /* ftmp3[i] < 2^60 + 2^60 + * = 2^61 */ + felem_mul(tmp, ftmp5, ftmp3); + /* tmp[i] < 17*2^122 */ + felem_mul(tmp2, ftmp6, ftmp2); + /* tmp2[i] < 17*2^120 */ + felem_scalar128(tmp2, 2); + /* tmp2[i] < 17*2^121 */ + felem_diff128(tmp, tmp2); + /* tmp[i] < 2^127 - 2^69 + 17*2^122 + * = 2^126 - 2^122 - 2^6 - 2^2 - 1 + * < 2^127 */ + felem_reduce(y_out, tmp); + + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); + } + +/* Base point pre computation + * -------------------------- + * + * Two different sorts of precomputed tables are used in the following code. + * Each contain various points on the curve, where each point is three field + * elements (x, y, z). + * + * For the base point table, z is usually 1 (0 for the point at infinity). + * This table has 16 elements: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^130G + * 3 | 0 0 1 1 | (2^130 + 1)G + * 4 | 0 1 0 0 | 2^260G + * 5 | 0 1 0 1 | (2^260 + 1)G + * 6 | 0 1 1 0 | (2^260 + 2^130)G + * 7 | 0 1 1 1 | (2^260 + 2^130 + 1)G + * 8 | 1 0 0 0 | 2^390G + * 9 | 1 0 0 1 | (2^390 + 1)G + * 10 | 1 0 1 0 | (2^390 + 2^130)G + * 11 | 1 0 1 1 | (2^390 + 2^130 + 1)G + * 12 | 1 1 0 0 | (2^390 + 2^260)G + * 13 | 1 1 0 1 | (2^390 + 2^260 + 1)G + * 14 | 1 1 1 0 | (2^390 + 2^260 + 2^130)G + * 15 | 1 1 1 1 | (2^390 + 2^260 + 2^130 + 1)G + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point. + * + * Tables for other points have table[i] = iG for i in 0 .. 16. */ + +/* gmul is the table of precomputed base points */ +static const felem gmul[16][3] = + {{{0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0}, + {0, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334, + 0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8, + 0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404}, + {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353, + 0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45, + 0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad, + 0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e, + 0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5}, + {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58, + 0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c, + 0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873, + 0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c, + 0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9}, + {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52, + 0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e, + 0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2, + 0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561, + 0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065}, + {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a, + 0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e, + 0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6, + 0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51, + 0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe}, + {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d, + 0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c, + 0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27, + 0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f, + 0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256}, + {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa, + 0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2, + 0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890, + 0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74, + 0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23}, + {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516, + 0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1, + 0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce, + 0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7, + 0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5}, + {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318, + 0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83, + 0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae, + 0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef, + 0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203}, + {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447, + 0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283, + 0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5, + 0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c, + 0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a}, + {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df, + 0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645, + 0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292, + 0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422, + 0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b}, + {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30, + 0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb, + 0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767, + 0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3, + 0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf}, + {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2, + 0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692, + 0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3, + 0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade, + 0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684}, + {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8, + 0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a, + 0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608, + 0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610, + 0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d}, + {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006, + 0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86, + 0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}, + {{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c, + 0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9, + 0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f}, + {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7, + 0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c, + 0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055}, + {1, 0, 0, 0, 0, 0, 0, 0, 0}}}; + +/* select_point selects the |idx|th point from a precomputation table and + * copies it to out. */ +static void select_point(const limb idx, unsigned int size, const felem pre_comp[/* size */][3], + felem out[3]) + { + unsigned i, j; + limb *outlimbs = &out[0][0]; + memset(outlimbs, 0, 3 * sizeof(felem)); + + for (i = 0; i < size; i++) + { + const limb *inlimbs = &pre_comp[i][0][0]; + limb mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < NLIMBS * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } + } + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, int i) + { + if (i < 0) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; + } + +/* Interleaved point multiplication using precomputed point multiples: + * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], + * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple + * of the generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3]) + { + int i, skip; + unsigned num, gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + limb bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, 3 * sizeof(felem)); + + /* Loop over all scalars msb-to-lsb, interleaving additions + * of multiples of the generator (last quarter of rounds) + * and additions of other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first round */ + for (i = (num_points ? 520 : 130); i >= 0; --i) + { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 130)) + { + bits = get_bit(g_scalar, i + 390) << 3; + if (i < 130) + { + bits |= get_bit(g_scalar, i + 260) << 2; + bits |= get_bit(g_scalar, i + 130) << 1; + bits |= get_bit(g_scalar, i); + } + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp, tmp); + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */, tmp[0], tmp[1], tmp[2]); + } + else + { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) + { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) + { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract, in constant time */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */ + copy_conditional(tmp[1], tmp[3], (-(limb) sign)); + + if (!skip) + { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } + else + { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); + } + + +/* Precomputation for the group generator. */ +typedef struct { + felem g_pre_comp[16][3]; + int references; +} NISTP521_PRE_COMP; + +const EC_METHOD *EC_GFp_nistp521_method(void) + { + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp521_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp521_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp521_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */, + 0 /* point2oct */, + 0 /* oct2point */, + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp521_points_mul, + ec_GFp_nistp521_precompute_mult, + ec_GFp_nistp521_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */, + 0 /* field_encode */, + 0 /* field_decode */, + 0 /* field_set_to_one */ }; + + return &ret; + } + + +/******************************************************************************/ +/* FUNCTIONS TO MANAGE PRECOMPUTATION + */ + +static NISTP521_PRE_COMP *nistp521_pre_comp_new() + { + NISTP521_PRE_COMP *ret = NULL; + ret = (NISTP521_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP521_PRE_COMP)); + if (!ret) + { + ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); + ret->references = 1; + return ret; + } + +static void *nistp521_pre_comp_dup(void *src_) + { + NISTP521_PRE_COMP *src = src_; + + /* no need to actually copy, these objects never change! */ + CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + + return src_; + } + +static void nistp521_pre_comp_free(void *pre_) + { + int i; + NISTP521_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_free(pre); + } + +static void nistp521_pre_comp_clear_free(void *pre_) + { + int i; + NISTP521_PRE_COMP *pre = pre_; + + if (!pre) + return; + + i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); + if (i > 0) + return; + + OPENSSL_cleanse(pre, sizeof(*pre)); + OPENSSL_free(pre); + } + +/******************************************************************************/ +/* OPENSSL EC_METHOD FUNCTIONS + */ + +int ec_GFp_nistp521_group_init(EC_GROUP *group) + { + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; + } + +int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p, + const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) + { + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((curve_p = BN_CTX_get(ctx)) == NULL) || + ((curve_a = BN_CTX_get(ctx)) == NULL) || + ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; + BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || + (BN_cmp(curve_b, b))) + { + ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_521; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); +err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + +/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns + * (X', Y') = (X/Z^2, Y/Z^3) */ +int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group, + const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) + { + felem z1, z2, x_in, y_in, x_out, y_out; + largefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || + (!BN_to_felem(z1, &point->Z))) return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) + { + if (!felem_to_BN(x, x_out)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) + { + if (!felem_to_BN(y, y_out)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB); + return 0; + } + } + return 1; + } + +static void make_points_affine(size_t num, felem points[/* num */][3], felem tmp_felems[/* num+1 */]) + { + /* Runs in constant time, unless an input is the point at infinity + * (which normally shouldn't happen). */ + ec_GFp_nistp_points_make_affine_internal( + num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *)) felem_one, + (int (*)(const void *)) felem_is_zero_int, + (void (*)(void *, const void *)) felem_assign, + (void (*)(void *, const void *)) felem_square_reduce, + (void (*)(void *, const void *, const void *)) felem_mul_reduce, + (void (*)(void *, const void *)) felem_inv, + (void (*)(void *, const void *)) felem_contract); + } + +/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values + * Result is stored in r (r can equal one of the inputs). */ +int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r, + const BIGNUM *scalar, size_t num, const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) + { + int ret = 0; + int j; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem (*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + felem_bytearray tmp; + unsigned i, num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP521_PRE_COMP *pre = NULL; + felem (*g_pre_comp)[3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL) || + ((z = BN_CTX_get(ctx)) == NULL) || + ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) + goto err; + + if (scalar != NULL) + { + pre = EC_EX_DATA_get_data(group->extra_data, + nistp521_pre_comp_dup, nistp521_pre_comp_free, + nistp521_pre_comp_clear_free); + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = &pre->g_pre_comp[0]; + else + /* try to use the standard precomputation */ + g_pre_comp = (felem (*)[3]) gmul; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[1][0]) || + !felem_to_BN(y, g_pre_comp[1][1]) || + !felem_to_BN(z, g_pre_comp[1][2])) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* we don't have valid precomputation: + * treat the generator as a random point */ + num_points++; + } + + if (num_points > 0) + { + if (num_points >= 2) + { + /* unless we precompute multiples for just one point, + * converting those into affine form is time well spent */ + mixed = 1; + } + secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); + pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem)); + if (mixed) + tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem)); + if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL))) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination */ + memset(secrets, 0, num_points * sizeof(felem_bytearray)); + memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem)); + for (i = 0; i < num_points; ++i) + { + if (i == num) + /* we didn't have a valid precomputation, so we pick + * the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } + else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) + { + /* reduce scalar to 0 <= scalar < 2^521 */ + if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, &p->X)) || + (!BN_to_felem(y_out, &p->Y)) || + (!BN_to_felem(z_out, &p->Z))) goto err; + memcpy(pre_comp[i][1][0], x_out, sizeof(felem)); + memcpy(pre_comp[i][1][1], y_out, sizeof(felem)); + memcpy(pre_comp[i][1][2], z_out, sizeof(felem)); + for (j = 2; j <= 16; ++j) + { + if (j & 1) + { + point_add( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2], + 0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]); + } + else + { + point_double( + pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2], + pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) + { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^521 */ + if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) + { + /* this is an unusual input, and we don't guarantee + * constant-timeness */ + if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } + else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation*/ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + g_secret, + mixed, (const felem (*)[17][3]) pre_comp, + (const felem (*)[3]) g_pre_comp); + } + else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray (*)) secrets, num_points, + NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) + { + ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + +err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (secrets != NULL) + OPENSSL_free(secrets); + if (pre_comp != NULL) + OPENSSL_free(pre_comp); + if (tmp_felems != NULL) + OPENSSL_free(tmp_felems); + return ret; + } + +int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx) + { + int ret = 0; + NISTP521_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[16]; + + /* throw away old precomputation */ + EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup, + nistp521_pre_comp_free, nistp521_pre_comp_clear_free); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; + BN_CTX_start(ctx); + if (((x = BN_CTX_get(ctx)) == NULL) || + ((y = BN_CTX_get(ctx)) == NULL)) + goto err; + /* get the generator */ + if (group->generator == NULL) goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp521_curve_params[3], sizeof (felem_bytearray), x); + BN_bin2bn(nistp521_curve_params[4], sizeof (felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp521_pre_comp_new()) == NULL) + goto err; + /* if the generator is the standard one, use built-in precomputation */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + ret = 1; + goto err; + } + if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) + goto err; + /* compute 2^130*G, 2^260*G, 2^390*G */ + for (i = 1; i <= 4; i <<= 1) + { + point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1], + pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0], + pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); + for (j = 0; j < 129; ++j) + { + point_double(pre->g_pre_comp[2*i][0], + pre->g_pre_comp[2*i][1], + pre->g_pre_comp[2*i][2], + pre->g_pre_comp[2*i][0], + pre->g_pre_comp[2*i][1], + pre->g_pre_comp[2*i][2]); + } + } + /* g_pre_comp[0] is the point at infinity */ + memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); + /* the remaining multiples */ + /* 2^130*G + 2^260*G */ + point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], + pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], + pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + /* 2^130*G + 2^390*G */ + point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], + pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + /* 2^260*G + 2^390*G */ + point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], + pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], + pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], + 0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], + pre->g_pre_comp[4][2]); + /* 2^130*G + 2^260*G + 2^390*G */ + point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], + pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], + pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], + 0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], + pre->g_pre_comp[2][2]); + for (i = 1; i < 8; ++i) + { + /* odd multiples: add G */ + point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1], + pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0], + pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2], + 0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], + pre->g_pre_comp[1][2]); + } + make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems); + + if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup, + nistp521_pre_comp_free, nistp521_pre_comp_clear_free)) + goto err; + ret = 1; + pre = NULL; + err: + BN_CTX_end(ctx); + if (generator != NULL) + EC_POINT_free(generator); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + if (pre) + nistp521_pre_comp_free(pre); + return ret; + } + +int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group) + { + if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup, + nistp521_pre_comp_free, nistp521_pre_comp_clear_free) + != NULL) + return 1; + else + return 0; + } + +#else +static void *dummy=&dummy; +#endif diff --git a/crypto/ec/ecp_nistputil.c b/crypto/ec/ecp_nistputil.c new file mode 100644 index 0000000000000..c8140c807fb07 --- /dev/null +++ b/crypto/ec/ecp_nistputil.c @@ -0,0 +1,197 @@ +/* crypto/ec/ecp_nistputil.c */ +/* + * Written by Bodo Moeller for the OpenSSL project. + */ +/* Copyright 2011 Google Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#include <openssl/opensslconf.h> +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + +/* + * Common utility functions for ecp_nistp224.c, ecp_nistp256.c, ecp_nistp521.c. + */ + +#include <stddef.h> +#include "ec_lcl.h" + +/* Convert an array of points into affine coordinates. + * (If the point at infinity is found (Z = 0), it remains unchanged.) + * This function is essentially an equivalent to EC_POINTs_make_affine(), but + * works with the internal representation of points as used by ecp_nistp###.c + * rather than with (BIGNUM-based) EC_POINT data structures. + * + * point_array is the input/output buffer ('num' points in projective form, + * i.e. three coordinates each), based on an internal representation of + * field elements of size 'felem_size'. + * + * tmp_felems needs to point to a temporary array of 'num'+1 field elements + * for storage of intermediate values. + */ +void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array, + size_t felem_size, void *tmp_felems, + void (*felem_one)(void *out), + int (*felem_is_zero)(const void *in), + void (*felem_assign)(void *out, const void *in), + void (*felem_square)(void *out, const void *in), + void (*felem_mul)(void *out, const void *in1, const void *in2), + void (*felem_inv)(void *out, const void *in), + void (*felem_contract)(void *out, const void *in)) + { + int i = 0; + +#define tmp_felem(I) (&((char *)tmp_felems)[(I) * felem_size]) +#define X(I) (&((char *)point_array)[3*(I) * felem_size]) +#define Y(I) (&((char *)point_array)[(3*(I) + 1) * felem_size]) +#define Z(I) (&((char *)point_array)[(3*(I) + 2) * felem_size]) + + if (!felem_is_zero(Z(0))) + felem_assign(tmp_felem(0), Z(0)); + else + felem_one(tmp_felem(0)); + for (i = 1; i < (int)num; i++) + { + if (!felem_is_zero(Z(i))) + felem_mul(tmp_felem(i), tmp_felem(i-1), Z(i)); + else + felem_assign(tmp_felem(i), tmp_felem(i-1)); + } + /* Now each tmp_felem(i) is the product of Z(0) .. Z(i), skipping any zero-valued factors: + * if Z(i) = 0, we essentially pretend that Z(i) = 1 */ + + felem_inv(tmp_felem(num-1), tmp_felem(num-1)); + for (i = num - 1; i >= 0; i--) + { + if (i > 0) + /* tmp_felem(i-1) is the product of Z(0) .. Z(i-1), + * tmp_felem(i) is the inverse of the product of Z(0) .. Z(i) + */ + felem_mul(tmp_felem(num), tmp_felem(i-1), tmp_felem(i)); /* 1/Z(i) */ + else + felem_assign(tmp_felem(num), tmp_felem(0)); /* 1/Z(0) */ + + if (!felem_is_zero(Z(i))) + { + if (i > 0) + /* For next iteration, replace tmp_felem(i-1) by its inverse */ + felem_mul(tmp_felem(i-1), tmp_felem(i), Z(i)); + + /* Convert point (X, Y, Z) into affine form (X/(Z^2), Y/(Z^3), 1) */ + felem_square(Z(i), tmp_felem(num)); /* 1/(Z^2) */ + felem_mul(X(i), X(i), Z(i)); /* X/(Z^2) */ + felem_mul(Z(i), Z(i), tmp_felem(num)); /* 1/(Z^3) */ + felem_mul(Y(i), Y(i), Z(i)); /* Y/(Z^3) */ + felem_contract(X(i), X(i)); + felem_contract(Y(i), Y(i)); + felem_one(Z(i)); + } + else + { + if (i > 0) + /* For next iteration, replace tmp_felem(i-1) by its inverse */ + felem_assign(tmp_felem(i-1), tmp_felem(i)); + } + } + } + +/* + * This function looks at 5+1 scalar bits (5 current, 1 adjacent less + * significant bit), and recodes them into a signed digit for use in fast point + * multiplication: the use of signed rather than unsigned digits means that + * fewer points need to be precomputed, given that point inversion is easy + * (a precomputed point dP makes -dP available as well). + * + * BACKGROUND: + * + * Signed digits for multiplication were introduced by Booth ("A signed binary + * multiplication technique", Quart. Journ. Mech. and Applied Math., vol. IV, + * pt. 2 (1951), pp. 236-240), in that case for multiplication of integers. + * Booth's original encoding did not generally improve the density of nonzero + * digits over the binary representation, and was merely meant to simplify the + * handling of signed factors given in two's complement; but it has since been + * shown to be the basis of various signed-digit representations that do have + * further advantages, including the wNAF, using the following general approach: + * + * (1) Given a binary representation + * + * b_k ... b_2 b_1 b_0, + * + * of a nonnegative integer (b_k in {0, 1}), rewrite it in digits 0, 1, -1 + * by using bit-wise subtraction as follows: + * + * b_k b_(k-1) ... b_2 b_1 b_0 + * - b_k ... b_3 b_2 b_1 b_0 + * ------------------------------------- + * s_k b_(k-1) ... s_3 s_2 s_1 s_0 + * + * A left-shift followed by subtraction of the original value yields a new + * representation of the same value, using signed bits s_i = b_(i+1) - b_i. + * This representation from Booth's paper has since appeared in the + * literature under a variety of different names including "reversed binary + * form", "alternating greedy expansion", "mutual opposite form", and + * "sign-alternating {+-1}-representation". + * + * An interesting property is that among the nonzero bits, values 1 and -1 + * strictly alternate. + * + * (2) Various window schemes can be applied to the Booth representation of + * integers: for example, right-to-left sliding windows yield the wNAF + * (a signed-digit encoding independently discovered by various researchers + * in the 1990s), and left-to-right sliding windows yield a left-to-right + * equivalent of the wNAF (independently discovered by various researchers + * around 2004). + * + * To prevent leaking information through side channels in point multiplication, + * we need to recode the given integer into a regular pattern: sliding windows + * as in wNAFs won't do, we need their fixed-window equivalent -- which is a few + * decades older: we'll be using the so-called "modified Booth encoding" due to + * MacSorley ("High-speed arithmetic in binary computers", Proc. IRE, vol. 49 + * (1961), pp. 67-91), in a radix-2^5 setting. That is, we always combine five + * signed bits into a signed digit: + * + * s_(4j + 4) s_(4j + 3) s_(4j + 2) s_(4j + 1) s_(4j) + * + * The sign-alternating property implies that the resulting digit values are + * integers from -16 to 16. + * + * Of course, we don't actually need to compute the signed digits s_i as an + * intermediate step (that's just a nice way to see how this scheme relates + * to the wNAF): a direct computation obtains the recoded digit from the + * six bits b_(4j + 4) ... b_(4j - 1). + * + * This function takes those five bits as an integer (0 .. 63), writing the + * recoded digit to *sign (0 for positive, 1 for negative) and *digit (absolute + * value, in the range 0 .. 8). Note that this integer essentially provides the + * input bits "shifted to the left" by one position: for example, the input to + * compute the least significant recoded digit, given that there's no bit b_-1, + * has to be b_4 b_3 b_2 b_1 b_0 0. + * + */ +void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign, unsigned char *digit, unsigned char in) + { + unsigned char s, d; + + s = ~((in >> 5) - 1); /* sets all bits to MSB(in), 'in' seen as 6-bit value */ + d = (1 << 6) - in - 1; + d = (d & s) | (in & ~s); + d = (d >> 1) + (d & 1); + + *sign = s & 1; + *digit = d; + } +#else +static void *dummy=&dummy; +#endif diff --git a/crypto/ec/ecp_oct.c b/crypto/ec/ecp_oct.c new file mode 100644 index 0000000000000..374a0ee731ae0 --- /dev/null +++ b/crypto/ec/ecp_oct.c @@ -0,0 +1,433 @@ +/* crypto/ec/ecp_oct.c */ +/* Includes code written by Lenka Fibikova <fibikova@exp-math.uni-essen.de> + * for the OpenSSL project. + * Includes code written by Bodo Moeller for the OpenSSL project. +*/ +/* ==================================================================== + * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in + * the documentation and/or other materials provided with the + * distribution. + * + * 3. All advertising materials mentioning features or use of this + * software must display the following acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" + * + * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to + * endorse or promote products derived from this software without + * prior written permission. For written permission, please contact + * openssl-core@openssl.org. + * + * 5. Products derived from this software may not be called "OpenSSL" + * nor may "OpenSSL" appear in their names without prior written + * permission of the OpenSSL Project. + * + * 6. Redistributions of any form whatsoever must retain the following + * acknowledgment: + * "This product includes software developed by the OpenSSL Project + * for use in the OpenSSL Toolkit (http://www.openssl.org/)" + * + * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY + * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR + * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, + * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; + * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, + * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED + * OF THE POSSIBILITY OF SUCH DAMAGE. + * ==================================================================== + * + * This product includes cryptographic software written by Eric Young + * (eay@cryptsoft.com). This product includes software written by Tim + * Hudson (tjh@cryptsoft.com). + * + */ +/* ==================================================================== + * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED. + * Portions of this software developed by SUN MICROSYSTEMS, INC., + * and contributed to the OpenSSL project. + */ + +#include <openssl/err.h> +#include <openssl/symhacks.h> + +#include "ec_lcl.h" + +int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, + const BIGNUM *x_, int y_bit, BN_CTX *ctx) + { + BN_CTX *new_ctx = NULL; + BIGNUM *tmp1, *tmp2, *x, *y; + int ret = 0; + + /* clear error queue*/ + ERR_clear_error(); + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + y_bit = (y_bit != 0); + + BN_CTX_start(ctx); + tmp1 = BN_CTX_get(ctx); + tmp2 = BN_CTX_get(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) goto err; + + /* Recover y. We have a Weierstrass equation + * y^2 = x^3 + a*x + b, + * so y is one of the square roots of x^3 + a*x + b. + */ + + /* tmp1 := x^3 */ + if (!BN_nnmod(x, x_, &group->field,ctx)) goto err; + if (group->meth->field_decode == 0) + { + /* field_{sqr,mul} work on standard representation */ + if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err; + if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err; + } + else + { + if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err; + if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err; + } + + /* tmp1 := tmp1 + a*x */ + if (group->a_is_minus3) + { + if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err; + if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err; + if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err; + } + else + { + if (group->meth->field_decode) + { + if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err; + if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err; + } + else + { + /* field_mul works on standard representation */ + if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err; + } + + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; + } + + /* tmp1 := tmp1 + b */ + if (group->meth->field_decode) + { + if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err; + if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; + } + else + { + if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err; + } + + if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) + { + unsigned long err = ERR_peek_last_error(); + + if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) + { + ERR_clear_error(); + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); + } + else + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); + goto err; + } + + if (y_bit != BN_is_odd(y)) + { + if (BN_is_zero(y)) + { + int kron; + + kron = BN_kronecker(x, &group->field, ctx); + if (kron == -2) goto err; + + if (kron == 1) + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT); + else + /* BN_mod_sqrt() should have cought this error (not a square) */ + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); + goto err; + } + if (!BN_usub(y, &group->field, y)) goto err; + } + if (y_bit != BN_is_odd(y)) + { + ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + + +size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, + unsigned char *buf, size_t len, BN_CTX *ctx) + { + size_t ret; + BN_CTX *new_ctx = NULL; + int used_ctx = 0; + BIGNUM *x, *y; + size_t field_len, i, skip; + + if ((form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); + goto err; + } + + if (EC_POINT_is_at_infinity(group, point)) + { + /* encodes to a single 0 octet */ + if (buf != NULL) + { + if (len < 1) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + buf[0] = 0; + } + return 1; + } + + + /* ret := required output buffer length */ + field_len = BN_num_bytes(&group->field); + ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + + /* if 'buf' is NULL, just return required length */ + if (buf != NULL) + { + if (len < ret) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); + goto err; + } + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + used_ctx = 1; + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) goto err; + + if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + + if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y)) + buf[0] = form + 1; + else + buf[0] = form; + + i = 1; + + skip = field_len - BN_num_bytes(x); + if (skip > field_len) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) + { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(x, buf + i); + i += skip; + if (i != 1 + field_len) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + + if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) + { + skip = field_len - BN_num_bytes(y); + if (skip > field_len) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + while (skip > 0) + { + buf[i++] = 0; + skip--; + } + skip = BN_bn2bin(y, buf + i); + i += skip; + } + + if (i != ret) + { + ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); + goto err; + } + } + + if (used_ctx) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + + err: + if (used_ctx) + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return 0; + } + + +int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, + const unsigned char *buf, size_t len, BN_CTX *ctx) + { + point_conversion_form_t form; + int y_bit; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + size_t field_len, enc_len; + int ret = 0; + + if (len == 0) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); + return 0; + } + form = buf[0]; + y_bit = form & 1; + form = form & ~1U; + if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) + && (form != POINT_CONVERSION_UNCOMPRESSED) + && (form != POINT_CONVERSION_HYBRID)) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (form == 0) + { + if (len != 1) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + return EC_POINT_set_to_infinity(group, point); + } + + field_len = BN_num_bytes(&group->field); + enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; + + if (len != enc_len) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + return 0; + } + + if (ctx == NULL) + { + ctx = new_ctx = BN_CTX_new(); + if (ctx == NULL) + return 0; + } + + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) goto err; + + if (!BN_bin2bn(buf + 1, field_len, x)) goto err; + if (BN_ucmp(x, &group->field) >= 0) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + + if (form == POINT_CONVERSION_COMPRESSED) + { + if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err; + } + else + { + if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; + if (BN_ucmp(y, &group->field) >= 0) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + if (form == POINT_CONVERSION_HYBRID) + { + if (y_bit != BN_is_odd(y)) + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); + goto err; + } + } + + if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; + } + + if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ + { + ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); + goto err; + } + + ret = 1; + + err: + BN_CTX_end(ctx); + if (new_ctx != NULL) + BN_CTX_free(new_ctx); + return ret; + } + diff --git a/crypto/ec/ecp_smpl.c b/crypto/ec/ecp_smpl.c index 66a92e2a9005c..7cbb321f9aae4 100644 --- a/crypto/ec/ecp_smpl.c +++ b/crypto/ec/ecp_smpl.c @@ -65,11 +65,19 @@ #include <openssl/err.h> #include <openssl/symhacks.h> +#ifdef OPENSSL_FIPS +#include <openssl/fips.h> +#endif + #include "ec_lcl.h" const EC_METHOD *EC_GFp_simple_method(void) { +#ifdef OPENSSL_FIPS + return fips_ec_gfp_simple_method(); +#else static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, NID_X9_62_prime_field, ec_GFp_simple_group_init, ec_GFp_simple_group_finish, @@ -88,9 +96,7 @@ const EC_METHOD *EC_GFp_simple_method(void) ec_GFp_simple_get_Jprojective_coordinates_GFp, ec_GFp_simple_point_set_affine_coordinates, ec_GFp_simple_point_get_affine_coordinates, - ec_GFp_simple_set_compressed_coordinates, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, + 0,0,0, ec_GFp_simple_add, ec_GFp_simple_dbl, ec_GFp_simple_invert, @@ -110,6 +116,7 @@ const EC_METHOD *EC_GFp_simple_method(void) 0 /* field_set_to_one */ }; return &ret; +#endif } @@ -633,372 +640,6 @@ int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *group, const EC_P return ret; } - -int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *group, EC_POINT *point, - const BIGNUM *x_, int y_bit, BN_CTX *ctx) - { - BN_CTX *new_ctx = NULL; - BIGNUM *tmp1, *tmp2, *x, *y; - int ret = 0; - - /* clear error queue*/ - ERR_clear_error(); - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - y_bit = (y_bit != 0); - - BN_CTX_start(ctx); - tmp1 = BN_CTX_get(ctx); - tmp2 = BN_CTX_get(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - if (y == NULL) goto err; - - /* Recover y. We have a Weierstrass equation - * y^2 = x^3 + a*x + b, - * so y is one of the square roots of x^3 + a*x + b. - */ - - /* tmp1 := x^3 */ - if (!BN_nnmod(x, x_, &group->field,ctx)) goto err; - if (group->meth->field_decode == 0) - { - /* field_{sqr,mul} work on standard representation */ - if (!group->meth->field_sqr(group, tmp2, x_, ctx)) goto err; - if (!group->meth->field_mul(group, tmp1, tmp2, x_, ctx)) goto err; - } - else - { - if (!BN_mod_sqr(tmp2, x_, &group->field, ctx)) goto err; - if (!BN_mod_mul(tmp1, tmp2, x_, &group->field, ctx)) goto err; - } - - /* tmp1 := tmp1 + a*x */ - if (group->a_is_minus3) - { - if (!BN_mod_lshift1_quick(tmp2, x, &group->field)) goto err; - if (!BN_mod_add_quick(tmp2, tmp2, x, &group->field)) goto err; - if (!BN_mod_sub_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, tmp2, &group->a, ctx)) goto err; - if (!BN_mod_mul(tmp2, tmp2, x, &group->field, ctx)) goto err; - } - else - { - /* field_mul works on standard representation */ - if (!group->meth->field_mul(group, tmp2, &group->a, x, ctx)) goto err; - } - - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - - /* tmp1 := tmp1 + b */ - if (group->meth->field_decode) - { - if (!group->meth->field_decode(group, tmp2, &group->b, ctx)) goto err; - if (!BN_mod_add_quick(tmp1, tmp1, tmp2, &group->field)) goto err; - } - else - { - if (!BN_mod_add_quick(tmp1, tmp1, &group->b, &group->field)) goto err; - } - - if (!BN_mod_sqrt(y, tmp1, &group->field, ctx)) - { - unsigned long err = ERR_peek_last_error(); - - if (ERR_GET_LIB(err) == ERR_LIB_BN && ERR_GET_REASON(err) == BN_R_NOT_A_SQUARE) - { - ERR_clear_error(); - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - } - else - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_BN_LIB); - goto err; - } - - if (y_bit != BN_is_odd(y)) - { - if (BN_is_zero(y)) - { - int kron; - - kron = BN_kronecker(x, &group->field, ctx); - if (kron == -2) goto err; - - if (kron == 1) - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSION_BIT); - else - /* BN_mod_sqrt() should have cought this error (not a square) */ - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, EC_R_INVALID_COMPRESSED_POINT); - goto err; - } - if (!BN_usub(y, &group->field, y)) goto err; - } - if (y_bit != BN_is_odd(y)) - { - ECerr(EC_F_EC_GFP_SIMPLE_SET_COMPRESSED_COORDINATES, ERR_R_INTERNAL_ERROR); - goto err; - } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - -size_t ec_GFp_simple_point2oct(const EC_GROUP *group, const EC_POINT *point, point_conversion_form_t form, - unsigned char *buf, size_t len, BN_CTX *ctx) - { - size_t ret; - BN_CTX *new_ctx = NULL; - int used_ctx = 0; - BIGNUM *x, *y; - size_t field_len, i, skip; - - if ((form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_INVALID_FORM); - goto err; - } - - if (EC_POINT_is_at_infinity(group, point)) - { - /* encodes to a single 0 octet */ - if (buf != NULL) - { - if (len < 1) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - buf[0] = 0; - } - return 1; - } - - - /* ret := required output buffer length */ - field_len = BN_num_bytes(&group->field); - ret = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - /* if 'buf' is NULL, just return required length */ - if (buf != NULL) - { - if (len < ret) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, EC_R_BUFFER_TOO_SMALL); - goto err; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - used_ctx = 1; - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - if (y == NULL) goto err; - - if (!EC_POINT_get_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - - if ((form == POINT_CONVERSION_COMPRESSED || form == POINT_CONVERSION_HYBRID) && BN_is_odd(y)) - buf[0] = form + 1; - else - buf[0] = form; - - i = 1; - - skip = field_len - BN_num_bytes(x); - if (skip > field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(x, buf + i); - i += skip; - if (i != 1 + field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - - if (form == POINT_CONVERSION_UNCOMPRESSED || form == POINT_CONVERSION_HYBRID) - { - skip = field_len - BN_num_bytes(y); - if (skip > field_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - while (skip > 0) - { - buf[i++] = 0; - skip--; - } - skip = BN_bn2bin(y, buf + i); - i += skip; - } - - if (i != ret) - { - ECerr(EC_F_EC_GFP_SIMPLE_POINT2OCT, ERR_R_INTERNAL_ERROR); - goto err; - } - } - - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - - err: - if (used_ctx) - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return 0; - } - - -int ec_GFp_simple_oct2point(const EC_GROUP *group, EC_POINT *point, - const unsigned char *buf, size_t len, BN_CTX *ctx) - { - point_conversion_form_t form; - int y_bit; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y; - size_t field_len, enc_len; - int ret = 0; - - if (len == 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_BUFFER_TOO_SMALL); - return 0; - } - form = buf[0]; - y_bit = form & 1; - form = form & ~1U; - if ((form != 0) && (form != POINT_CONVERSION_COMPRESSED) - && (form != POINT_CONVERSION_UNCOMPRESSED) - && (form != POINT_CONVERSION_HYBRID)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - if ((form == 0 || form == POINT_CONVERSION_UNCOMPRESSED) && y_bit) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (form == 0) - { - if (len != 1) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - return EC_POINT_set_to_infinity(group, point); - } - - field_len = BN_num_bytes(&group->field); - enc_len = (form == POINT_CONVERSION_COMPRESSED) ? 1 + field_len : 1 + 2*field_len; - - if (len != enc_len) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - return 0; - } - - if (ctx == NULL) - { - ctx = new_ctx = BN_CTX_new(); - if (ctx == NULL) - return 0; - } - - BN_CTX_start(ctx); - x = BN_CTX_get(ctx); - y = BN_CTX_get(ctx); - if (y == NULL) goto err; - - if (!BN_bin2bn(buf + 1, field_len, x)) goto err; - if (BN_ucmp(x, &group->field) >= 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - - if (form == POINT_CONVERSION_COMPRESSED) - { - if (!EC_POINT_set_compressed_coordinates_GFp(group, point, x, y_bit, ctx)) goto err; - } - else - { - if (!BN_bin2bn(buf + 1 + field_len, field_len, y)) goto err; - if (BN_ucmp(y, &group->field) >= 0) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - if (form == POINT_CONVERSION_HYBRID) - { - if (y_bit != BN_is_odd(y)) - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_INVALID_ENCODING); - goto err; - } - } - - if (!EC_POINT_set_affine_coordinates_GFp(group, point, x, y, ctx)) goto err; - } - - if (!EC_POINT_is_on_curve(group, point, ctx)) /* test required by X9.62 */ - { - ECerr(EC_F_EC_GFP_SIMPLE_OCT2POINT, EC_R_POINT_IS_NOT_ON_CURVE); - goto err; - } - - ret = 1; - - err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - - int ec_GFp_simple_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx) { int (*field_mul)(const EC_GROUP *, BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); diff --git a/crypto/ec/ectest.c b/crypto/ec/ectest.c index 6148d553f9d59..f107782de006d 100644 --- a/crypto/ec/ectest.c +++ b/crypto/ec/ectest.c @@ -94,6 +94,7 @@ int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); retur #include <openssl/objects.h> #include <openssl/rand.h> #include <openssl/bn.h> +#include <openssl/opensslconf.h> #if defined(_MSC_VER) && defined(_MIPS_) && (_MSC_VER/100==12) /* suppress "too big too optimize" warning */ @@ -107,10 +108,6 @@ int main(int argc, char * argv[]) { puts("Elliptic curves are disabled."); retur EXIT(1); \ } while (0) -void prime_field_tests(void); -void char2_field_tests(void); -void internal_curve_test(void); - #define TIMING_BASE_PT 0 #define TIMING_RAND_PT 1 #define TIMING_SIMUL 2 @@ -195,7 +192,50 @@ static void timings(EC_GROUP *group, int type, BN_CTX *ctx) } #endif -void prime_field_tests() +/* test multiplication with group order, long and negative scalars */ +static void group_order_tests(EC_GROUP *group) + { + BIGNUM *n1, *n2, *order; + EC_POINT *P = EC_POINT_new(group); + EC_POINT *Q = EC_POINT_new(group); + BN_CTX *ctx = BN_CTX_new(); + + n1 = BN_new(); n2 = BN_new(); order = BN_new(); + fprintf(stdout, "verify group order ..."); + fflush(stdout); + if (!EC_GROUP_get_order(group, order, ctx)) ABORT; + if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; + if (!EC_POINT_is_at_infinity(group, Q)) ABORT; + fprintf(stdout, "."); + fflush(stdout); + if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; + if (!EC_POINT_mul(group, Q, order, NULL, NULL, ctx)) ABORT; + if (!EC_POINT_is_at_infinity(group, Q)) ABORT; + fprintf(stdout, " ok\n"); + fprintf(stdout, "long/negative scalar tests ... "); + if (!BN_one(n1)) ABORT; + /* n1 = 1 - order */ + if (!BN_sub(n1, n1, order)) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n1, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + /* n2 = 1 + order */ + if (!BN_add(n2, order, BN_value_one())) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + /* n2 = (1 - order) * (1 + order) */ + if (!BN_mul(n2, n1, n2, ctx)) ABORT; + if(!EC_POINT_mul(group, Q, NULL, P, n2, ctx)) ABORT; + if (0 != EC_POINT_cmp(group, Q, P, ctx)) ABORT; + fprintf(stdout, "ok\n"); + EC_POINT_free(P); + EC_POINT_free(Q); + BN_free(n1); + BN_free(n2); + BN_free(order); + BN_CTX_free(ctx); + } + +static void prime_field_tests(void) { BN_CTX *ctx = NULL; BIGNUM *p, *a, *b; @@ -321,21 +361,21 @@ void prime_field_tests() if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "Generator as octect string, compressed form:\n "); + fprintf(stdout, "Generator as octet string, compressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_UNCOMPRESSED, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "\nGenerator as octect string, uncompressed form:\n "); + fprintf(stdout, "\nGenerator as octet string, uncompressed form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); len = EC_POINT_point2oct(group, Q, POINT_CONVERSION_HYBRID, buf, sizeof buf, ctx); if (len == 0) ABORT; if (!EC_POINT_oct2point(group, P, buf, len, ctx)) ABORT; if (0 != EC_POINT_cmp(group, P, Q, ctx)) ABORT; - fprintf(stdout, "\nGenerator as octect string, hybrid form:\n "); + fprintf(stdout, "\nGenerator as octet string, hybrid form:\n "); for (i = 0; i < len; i++) fprintf(stdout, "%02X", buf[i]); if (!EC_POINT_get_Jprojective_coordinates_GFp(group, R, x, y, z, ctx)) ABORT; @@ -381,17 +421,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 160) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_160 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_160, group)) ABORT; @@ -425,19 +455,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 192) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); -#if 0 - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; -#endif - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_192 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_192, group)) ABORT; @@ -471,19 +489,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 224) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); -#if 0 - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; -#endif - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_224 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_224, group)) ABORT; @@ -518,19 +524,7 @@ void prime_field_tests() if (EC_GROUP_get_degree(group) != 256) ABORT; fprintf(stdout, " ok\n"); - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); -#if 0 - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; -#endif - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + group_order_tests(group); if (!(P_256 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_256, group)) ABORT; @@ -569,20 +563,8 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 384) ABORT; fprintf(stdout, " ok\n"); - - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); -#if 0 - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; -#endif - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + + group_order_tests(group); if (!(P_384 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_384, group)) ABORT; @@ -627,20 +609,8 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); if (EC_GROUP_get_degree(group) != 521) ABORT; fprintf(stdout, " ok\n"); - - fprintf(stdout, "verify group order ..."); - fflush(stdout); - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, "."); - fflush(stdout); -#if 0 - if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; -#endif - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; - fprintf(stdout, " ok\n"); + + group_order_tests(group); if (!(P_521 = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; if (!EC_GROUP_copy(P_521, group)) ABORT; @@ -669,6 +639,7 @@ void prime_field_tests() points[2] = Q; points[3] = Q; + if (!EC_GROUP_get_order(group, z, ctx)) ABORT; if (!BN_add(y, z, BN_value_one())) ABORT; if (BN_is_odd(y)) ABORT; if (!BN_rshift1(y, y)) ABORT; @@ -802,22 +773,14 @@ void prime_field_tests() fprintf(stdout, "verify degree ..."); \ if (EC_GROUP_get_degree(group) != _degree) ABORT; \ fprintf(stdout, " ok\n"); \ - fprintf(stdout, "verify group order ..."); \ - fflush(stdout); \ - if (!EC_GROUP_get_order(group, z, ctx)) ABORT; \ - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \ - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \ - fprintf(stdout, "."); \ - fflush(stdout); \ - /* if (!EC_GROUP_precompute_mult(group, ctx)) ABORT; */ \ - if (!EC_POINT_mul(group, Q, z, NULL, NULL, ctx)) ABORT; \ - if (!EC_POINT_is_at_infinity(group, Q)) ABORT; \ - fprintf(stdout, " ok\n"); \ + group_order_tests(group); \ if (!(_variable = EC_GROUP_new(EC_GROUP_method_of(group)))) ABORT; \ - if (!EC_GROUP_copy(_variable, group)) ABORT; + if (!EC_GROUP_copy(_variable, group)) ABORT; \ -void char2_field_tests() - { +#ifndef OPENSSL_NO_EC2M + +static void char2_field_tests(void) + { BN_CTX *ctx = NULL; BIGNUM *p, *a, *b; EC_GROUP *group; @@ -1249,8 +1212,9 @@ void char2_field_tests() if (C2_B571) EC_GROUP_free(C2_B571); } +#endif -void internal_curve_test(void) +static void internal_curve_test(void) { EC_builtin_curve *curves = NULL; size_t crv_len = 0, n = 0; @@ -1297,13 +1261,189 @@ void internal_curve_test(void) EC_GROUP_free(group); } if (ok) - fprintf(stdout, " ok\n"); + fprintf(stdout, " ok\n\n"); else - fprintf(stdout, " failed\n"); + { + fprintf(stdout, " failed\n\n"); + ABORT; + } OPENSSL_free(curves); return; } +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 +/* nistp_test_params contains magic numbers for testing our optimized + * implementations of several NIST curves with characteristic > 3. */ +struct nistp_test_params + { + const EC_METHOD* (*meth) (); + int degree; + /* Qx, Qy and D are taken from + * http://csrc.nist.gov/groups/ST/toolkit/documents/Examples/ECDSA_Prime.pdf + * Otherwise, values are standard curve parameters from FIPS 180-3 */ + const char *p, *a, *b, *Qx, *Qy, *Gx, *Gy, *order, *d; + }; + +static const struct nistp_test_params nistp_tests_params[] = + { + { + /* P-224 */ + EC_GFp_nistp224_method, + 224, + "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* p */ + "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* a */ + "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* b */ + "E84FB0B8E7000CB657D7973CF6B42ED78B301674276DF744AF130B3E", /* Qx */ + "4376675C6FC5612C21A0FF2D2A89D2987DF7A2BC52183B5982298555", /* Qy */ + "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gx */ + "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* Gy */ + "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* order */ + "3F0C488E987C80BE0FEE521F8D90BE6034EC69AE11CA72AA777481E8", /* d */ + }, + { + /* P-256 */ + EC_GFp_nistp256_method, + 256, + "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff", /* p */ + "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", /* a */ + "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", /* b */ + "b7e08afdfe94bad3f1dc8c734798ba1c62b3a0ad1e9ea2a38201cd0889bc7a19", /* Qx */ + "3603f747959dbf7a4bb226e41928729063adc7ae43529e61b563bbc606cc5e09", /* Qy */ + "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", /* Gx */ + "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", /* Gy */ + "ffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551", /* order */ + "c477f9f65c22cce20657faa5b2d1d8122336f851a508a1ed04e479c34985bf96", /* d */ + }, + { + /* P-521 */ + EC_GFp_nistp521_method, + 521, + "1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff", /* p */ + "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc", /* a */ + "051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", /* b */ + "0098e91eef9a68452822309c52fab453f5f117c1da8ed796b255e9ab8f6410cca16e59df403a6bdc6ca467a37056b1e54b3005d8ac030decfeb68df18b171885d5c4", /* Qx */ + "0164350c321aecfc1cca1ba4364c9b15656150b4b78d6a48d7d28e7f31985ef17be8554376b72900712c4b83ad668327231526e313f5f092999a4632fd50d946bc2e", /* Qy */ + "c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", /* Gx */ + "11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", /* Gy */ + "1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409", /* order */ + "0100085f47b8e1b8b11b7eb33028c0b2888e304bfc98501955b45bba1478dc184eeedf09b86a5f7c21994406072787205e69a63709fe35aa93ba333514b24f961722", /* d */ + }, + }; + +void nistp_single_test(const struct nistp_test_params *test) + { + BN_CTX *ctx; + BIGNUM *p, *a, *b, *x, *y, *n, *m, *order; + EC_GROUP *NISTP; + EC_POINT *G, *P, *Q, *Q_CHECK; + + fprintf(stdout, "\nNIST curve P-%d (optimised implementation):\n", test->degree); + ctx = BN_CTX_new(); + p = BN_new(); + a = BN_new(); + b = BN_new(); + x = BN_new(); y = BN_new(); + m = BN_new(); n = BN_new(); order = BN_new(); + + NISTP = EC_GROUP_new(test->meth()); + if(!NISTP) ABORT; + if (!BN_hex2bn(&p, test->p)) ABORT; + if (1 != BN_is_prime_ex(p, BN_prime_checks, ctx, NULL)) ABORT; + if (!BN_hex2bn(&a, test->a)) ABORT; + if (!BN_hex2bn(&b, test->b)) ABORT; + if (!EC_GROUP_set_curve_GFp(NISTP, p, a, b, ctx)) ABORT; + G = EC_POINT_new(NISTP); + P = EC_POINT_new(NISTP); + Q = EC_POINT_new(NISTP); + Q_CHECK = EC_POINT_new(NISTP); + if(!BN_hex2bn(&x, test->Qx)) ABORT; + if(!BN_hex2bn(&y, test->Qy)) ABORT; + if(!EC_POINT_set_affine_coordinates_GFp(NISTP, Q_CHECK, x, y, ctx)) ABORT; + if (!BN_hex2bn(&x, test->Gx)) ABORT; + if (!BN_hex2bn(&y, test->Gy)) ABORT; + if (!EC_POINT_set_affine_coordinates_GFp(NISTP, G, x, y, ctx)) ABORT; + if (!BN_hex2bn(&order, test->order)) ABORT; + if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT; + + fprintf(stdout, "verify degree ... "); + if (EC_GROUP_get_degree(NISTP) != test->degree) ABORT; + fprintf(stdout, "ok\n"); + + fprintf(stdout, "NIST test vectors ... "); + if (!BN_hex2bn(&n, test->d)) ABORT; + /* fixed point multiplication */ + EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + /* random point multiplication */ + EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + + /* set generator to P = 2*G, where G is the standard generator */ + if (!EC_POINT_dbl(NISTP, P, G, ctx)) ABORT; + if (!EC_GROUP_set_generator(NISTP, P, order, BN_value_one())) ABORT; + /* set the scalar to m=n/2, where n is the NIST test scalar */ + if (!BN_rshift(m, n, 1)) ABORT; + + /* test the non-standard generator */ + /* fixed point multiplication */ + EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + /* random point multiplication */ + EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + + /* now repeat all tests with precomputation */ + if (!EC_GROUP_precompute_mult(NISTP, ctx)) ABORT; + + /* fixed point multiplication */ + EC_POINT_mul(NISTP, Q, m, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + /* random point multiplication */ + EC_POINT_mul(NISTP, Q, NULL, P, m, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + + /* reset generator */ + if (!EC_GROUP_set_generator(NISTP, G, order, BN_value_one())) ABORT; + /* fixed point multiplication */ + EC_POINT_mul(NISTP, Q, n, NULL, NULL, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + /* random point multiplication */ + EC_POINT_mul(NISTP, Q, NULL, G, n, ctx); + if (0 != EC_POINT_cmp(NISTP, Q, Q_CHECK, ctx)) ABORT; + + fprintf(stdout, "ok\n"); + group_order_tests(NISTP); +#if 0 + timings(NISTP, TIMING_BASE_PT, ctx); + timings(NISTP, TIMING_RAND_PT, ctx); +#endif + EC_GROUP_free(NISTP); + EC_POINT_free(G); + EC_POINT_free(P); + EC_POINT_free(Q); + EC_POINT_free(Q_CHECK); + BN_free(n); + BN_free(m); + BN_free(p); + BN_free(a); + BN_free(b); + BN_free(x); + BN_free(y); + BN_free(order); + BN_CTX_free(ctx); + } + +void nistp_tests() + { + unsigned i; + + for (i = 0; i < sizeof(nistp_tests_params) / sizeof(struct nistp_test_params); i++) + { + nistp_single_test(&nistp_tests_params[i]); + } + } +#endif + static const char rnd_seed[] = "string to make the random number generator think it has entropy"; int main(int argc, char *argv[]) @@ -1327,7 +1467,12 @@ int main(int argc, char *argv[]) prime_field_tests(); puts(""); +#ifndef OPENSSL_NO_EC2M char2_field_tests(); +#endif +#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128 + nistp_tests(); +#endif /* test the internal curves */ internal_curve_test(); @@ -1336,7 +1481,7 @@ int main(int argc, char *argv[]) #endif CRYPTO_cleanup_all_ex_data(); ERR_free_strings(); - ERR_remove_state(0); + ERR_remove_thread_state(NULL); CRYPTO_mem_leaks_fp(stderr); return 0; |