diff options
Diffstat (limited to 'crypto/bn/bn_prime.c')
| -rw-r--r-- | crypto/bn/bn_prime.c | 745 |
1 files changed, 383 insertions, 362 deletions
diff --git a/crypto/bn/bn_prime.c b/crypto/bn/bn_prime.c index 7b25979dd1c4..1d256874c9d2 100644 --- a/crypto/bn/bn_prime.c +++ b/crypto/bn/bn_prime.c @@ -5,21 +5,21 @@ * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. - * + * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). - * + * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. - * + * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: @@ -34,10 +34,10 @@ * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). - * 4. If you include any Windows specific code (or a derivative thereof) from + * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" - * + * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE @@ -49,7 +49,7 @@ * 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. - * + * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence @@ -63,7 +63,7 @@ * are met: * * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. + * 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 @@ -115,380 +115,401 @@ #include "bn_lcl.h" #include <openssl/rand.h> -/* NB: these functions have been "upgraded", the deprecated versions (which are - * compatibility wrappers using these functions) are in bn_depr.c. - * - Geoff +/* + * NB: these functions have been "upgraded", the deprecated versions (which + * are compatibility wrappers using these functions) are in bn_depr.c. - + * Geoff */ -/* The quick sieve algorithm approach to weeding out primes is - * Philip Zimmermann's, as implemented in PGP. I have had a read of - * his comments and implemented my own version. +/* + * The quick sieve algorithm approach to weeding out primes is Philip + * Zimmermann's, as implemented in PGP. I have had a read of his comments + * and implemented my own version. */ #include "bn_prime.h" static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, - const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); + const BIGNUM *a1_odd, int k, BN_CTX *ctx, + BN_MONT_CTX *mont); static int probable_prime(BIGNUM *rnd, int bits); static int probable_prime_dh(BIGNUM *rnd, int bits, - const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); -static int probable_prime_dh_safe(BIGNUM *rnd, int bits, - const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); + const BIGNUM *add, const BIGNUM *rem, + BN_CTX *ctx); +static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add, + const BIGNUM *rem, BN_CTX *ctx); int BN_GENCB_call(BN_GENCB *cb, int a, int b) - { - /* No callback means continue */ - if(!cb) return 1; - switch(cb->ver) - { - case 1: - /* Deprecated-style callbacks */ - if(!cb->cb.cb_1) - return 1; - cb->cb.cb_1(a, b, cb->arg); - return 1; - case 2: - /* New-style callbacks */ - return cb->cb.cb_2(a, b, cb); - default: - break; - } - /* Unrecognised callback type */ - return 0; - } +{ + /* No callback means continue */ + if (!cb) + return 1; + switch (cb->ver) { + case 1: + /* Deprecated-style callbacks */ + if (!cb->cb.cb_1) + return 1; + cb->cb.cb_1(a, b, cb->arg); + return 1; + case 2: + /* New-style callbacks */ + return cb->cb.cb_2(a, b, cb); + default: + break; + } + /* Unrecognised callback type */ + return 0; +} int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, - const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) - { - BIGNUM *t; - int found=0; - int i,j,c1=0; - BN_CTX *ctx; - int checks = BN_prime_checks_for_size(bits); - - ctx=BN_CTX_new(); - if (ctx == NULL) goto err; - BN_CTX_start(ctx); - t = BN_CTX_get(ctx); - if(!t) goto err; -loop: - /* make a random number and set the top and bottom bits */ - if (add == NULL) - { - if (!probable_prime(ret,bits)) goto err; - } - else - { - if (safe) - { - if (!probable_prime_dh_safe(ret,bits,add,rem,ctx)) - goto err; - } - else - { - if (!probable_prime_dh(ret,bits,add,rem,ctx)) - goto err; - } - } - /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ - if(!BN_GENCB_call(cb, 0, c1++)) - /* aborted */ - goto err; - - if (!safe) - { - i=BN_is_prime_fasttest_ex(ret,checks,ctx,0,cb); - if (i == -1) goto err; - if (i == 0) goto loop; - } - else - { - /* for "safe prime" generation, - * check that (p-1)/2 is prime. - * Since a prime is odd, We just - * need to divide by 2 */ - if (!BN_rshift1(t,ret)) goto err; - - for (i=0; i<checks; i++) - { - j=BN_is_prime_fasttest_ex(ret,1,ctx,0,cb); - if (j == -1) goto err; - if (j == 0) goto loop; - - j=BN_is_prime_fasttest_ex(t,1,ctx,0,cb); - if (j == -1) goto err; - if (j == 0) goto loop; - - if(!BN_GENCB_call(cb, 2, c1-1)) - goto err; - /* We have a safe prime test pass */ - } - } - /* we have a prime :-) */ - found = 1; -err: - if (ctx != NULL) - { - BN_CTX_end(ctx); - BN_CTX_free(ctx); - } - bn_check_top(ret); - return found; - } - -int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) - { - return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); - } + const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) +{ + BIGNUM *t; + int found = 0; + int i, j, c1 = 0; + BN_CTX *ctx; + int checks = BN_prime_checks_for_size(bits); + + ctx = BN_CTX_new(); + if (ctx == NULL) + goto err; + BN_CTX_start(ctx); + t = BN_CTX_get(ctx); + if (!t) + goto err; + loop: + /* make a random number and set the top and bottom bits */ + if (add == NULL) { + if (!probable_prime(ret, bits)) + goto err; + } else { + if (safe) { + if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) + goto err; + } else { + if (!probable_prime_dh(ret, bits, add, rem, ctx)) + goto err; + } + } + /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ + if (!BN_GENCB_call(cb, 0, c1++)) + /* aborted */ + goto err; + + if (!safe) { + i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); + if (i == -1) + goto err; + if (i == 0) + goto loop; + } else { + /* + * for "safe prime" generation, check that (p-1)/2 is prime. Since a + * prime is odd, We just need to divide by 2 + */ + if (!BN_rshift1(t, ret)) + goto err; + + for (i = 0; i < checks; i++) { + j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); + if (j == -1) + goto err; + if (j == 0) + goto loop; + + j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); + if (j == -1) + goto err; + if (j == 0) + goto loop; + + if (!BN_GENCB_call(cb, 2, c1 - 1)) + goto err; + /* We have a safe prime test pass */ + } + } + /* we have a prime :-) */ + found = 1; + err: + if (ctx != NULL) { + BN_CTX_end(ctx); + BN_CTX_free(ctx); + } + bn_check_top(ret); + return found; +} + +int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, + BN_GENCB *cb) +{ + return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); +} int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, - int do_trial_division, BN_GENCB *cb) - { - int i, j, ret = -1; - int k; - BN_CTX *ctx = NULL; - BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ - BN_MONT_CTX *mont = NULL; - const BIGNUM *A = NULL; - - if (BN_cmp(a, BN_value_one()) <= 0) - return 0; - - if (checks == BN_prime_checks) - checks = BN_prime_checks_for_size(BN_num_bits(a)); - - /* first look for small factors */ - if (!BN_is_odd(a)) - /* a is even => a is prime if and only if a == 2 */ - return BN_is_word(a, 2); - if (do_trial_division) - { - for (i = 1; i < NUMPRIMES; i++) - if (BN_mod_word(a, primes[i]) == 0) - return 0; - if(!BN_GENCB_call(cb, 1, -1)) - goto err; - } - - if (ctx_passed != NULL) - ctx = ctx_passed; - else - if ((ctx=BN_CTX_new()) == NULL) - goto err; - BN_CTX_start(ctx); - - /* A := abs(a) */ - if (a->neg) - { - BIGNUM *t; - if ((t = BN_CTX_get(ctx)) == NULL) goto err; - BN_copy(t, a); - t->neg = 0; - A = t; - } - else - A = a; - A1 = BN_CTX_get(ctx); - A1_odd = BN_CTX_get(ctx); - check = BN_CTX_get(ctx); - if (check == NULL) goto err; - - /* compute A1 := A - 1 */ - if (!BN_copy(A1, A)) - goto err; - if (!BN_sub_word(A1, 1)) - goto err; - if (BN_is_zero(A1)) - { - ret = 0; - goto err; - } - - /* write A1 as A1_odd * 2^k */ - k = 1; - while (!BN_is_bit_set(A1, k)) - k++; - if (!BN_rshift(A1_odd, A1, k)) - goto err; - - /* Montgomery setup for computations mod A */ - mont = BN_MONT_CTX_new(); - if (mont == NULL) - goto err; - if (!BN_MONT_CTX_set(mont, A, ctx)) - goto err; - - for (i = 0; i < checks; i++) - { - if (!BN_pseudo_rand_range(check, A1)) - goto err; - if (!BN_add_word(check, 1)) - goto err; - /* now 1 <= check < A */ - - j = witness(check, A, A1, A1_odd, k, ctx, mont); - if (j == -1) goto err; - if (j) - { - ret=0; - goto err; - } - if(!BN_GENCB_call(cb, 1, i)) - goto err; - } - ret=1; -err: - if (ctx != NULL) - { - BN_CTX_end(ctx); - if (ctx_passed == NULL) - BN_CTX_free(ctx); - } - if (mont != NULL) - BN_MONT_CTX_free(mont); - - return(ret); - } + int do_trial_division, BN_GENCB *cb) +{ + int i, j, ret = -1; + int k; + BN_CTX *ctx = NULL; + BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ + BN_MONT_CTX *mont = NULL; + const BIGNUM *A = NULL; + + if (BN_cmp(a, BN_value_one()) <= 0) + return 0; + + if (checks == BN_prime_checks) + checks = BN_prime_checks_for_size(BN_num_bits(a)); + + /* first look for small factors */ + if (!BN_is_odd(a)) + /* a is even => a is prime if and only if a == 2 */ + return BN_is_word(a, 2); + if (do_trial_division) { + for (i = 1; i < NUMPRIMES; i++) + if (BN_mod_word(a, primes[i]) == 0) + return 0; + if (!BN_GENCB_call(cb, 1, -1)) + goto err; + } + + if (ctx_passed != NULL) + ctx = ctx_passed; + else if ((ctx = BN_CTX_new()) == NULL) + goto err; + BN_CTX_start(ctx); + + /* A := abs(a) */ + if (a->neg) { + BIGNUM *t; + if ((t = BN_CTX_get(ctx)) == NULL) + goto err; + BN_copy(t, a); + t->neg = 0; + A = t; + } else + A = a; + A1 = BN_CTX_get(ctx); + A1_odd = BN_CTX_get(ctx); + check = BN_CTX_get(ctx); + if (check == NULL) + goto err; + + /* compute A1 := A - 1 */ + if (!BN_copy(A1, A)) + goto err; + if (!BN_sub_word(A1, 1)) + goto err; + if (BN_is_zero(A1)) { + ret = 0; + goto err; + } + + /* write A1 as A1_odd * 2^k */ + k = 1; + while (!BN_is_bit_set(A1, k)) + k++; + if (!BN_rshift(A1_odd, A1, k)) + goto err; + + /* Montgomery setup for computations mod A */ + mont = BN_MONT_CTX_new(); + if (mont == NULL) + goto err; + if (!BN_MONT_CTX_set(mont, A, ctx)) + goto err; + + for (i = 0; i < checks; i++) { + if (!BN_pseudo_rand_range(check, A1)) + goto err; + if (!BN_add_word(check, 1)) + goto err; + /* now 1 <= check < A */ + + j = witness(check, A, A1, A1_odd, k, ctx, mont); + if (j == -1) + goto err; + if (j) { + ret = 0; + goto err; + } + if (!BN_GENCB_call(cb, 1, i)) + goto err; + } + ret = 1; + err: + if (ctx != NULL) { + BN_CTX_end(ctx); + if (ctx_passed == NULL) + BN_CTX_free(ctx); + } + if (mont != NULL) + BN_MONT_CTX_free(mont); + + return (ret); +} static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, - const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont) - { - if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ - return -1; - if (BN_is_one(w)) - return 0; /* probably prime */ - if (BN_cmp(w, a1) == 0) - return 0; /* w == -1 (mod a), 'a' is probably prime */ - while (--k) - { - if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ - return -1; - if (BN_is_one(w)) - return 1; /* 'a' is composite, otherwise a previous 'w' would - * have been == -1 (mod 'a') */ - if (BN_cmp(w, a1) == 0) - return 0; /* w == -1 (mod a), 'a' is probably prime */ - } - /* If we get here, 'w' is the (a-1)/2-th power of the original 'w', - * and it is neither -1 nor +1 -- so 'a' cannot be prime */ - bn_check_top(w); - return 1; - } + const BIGNUM *a1_odd, int k, BN_CTX *ctx, + BN_MONT_CTX *mont) +{ + if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ + return -1; + if (BN_is_one(w)) + return 0; /* probably prime */ + if (BN_cmp(w, a1) == 0) + return 0; /* w == -1 (mod a), 'a' is probably prime */ + while (--k) { + if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ + return -1; + if (BN_is_one(w)) + return 1; /* 'a' is composite, otherwise a previous 'w' + * would have been == -1 (mod 'a') */ + if (BN_cmp(w, a1) == 0) + return 0; /* w == -1 (mod a), 'a' is probably prime */ + } + /* + * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and + * it is neither -1 nor +1 -- so 'a' cannot be prime + */ + bn_check_top(w); + return 1; +} static int probable_prime(BIGNUM *rnd, int bits) - { - int i; - prime_t mods[NUMPRIMES]; - BN_ULONG delta,maxdelta; - -again: - if (!BN_rand(rnd,bits,1,1)) return(0); - /* we now have a random number 'rand' to test. */ - for (i=1; i<NUMPRIMES; i++) - mods[i]=(prime_t)BN_mod_word(rnd,(BN_ULONG)primes[i]); - maxdelta=BN_MASK2 - primes[NUMPRIMES-1]; - delta=0; - loop: for (i=1; i<NUMPRIMES; i++) - { - /* check that rnd is not a prime and also - * that gcd(rnd-1,primes) == 1 (except for 2) */ - if (((mods[i]+delta)%primes[i]) <= 1) - { - delta+=2; - if (delta > maxdelta) goto again; - goto loop; - } - } - if (!BN_add_word(rnd,delta)) return(0); - bn_check_top(rnd); - return(1); - } +{ + int i; + prime_t mods[NUMPRIMES]; + BN_ULONG delta, maxdelta; + + again: + if (!BN_rand(rnd, bits, 1, 1)) + return (0); + /* we now have a random number 'rand' to test. */ + for (i = 1; i < NUMPRIMES; i++) + mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]); + maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; + delta = 0; + loop:for (i = 1; i < NUMPRIMES; i++) { + /* + * check that rnd is not a prime and also that gcd(rnd-1,primes) == 1 + * (except for 2) + */ + if (((mods[i] + delta) % primes[i]) <= 1) { + delta += 2; + if (delta > maxdelta) + goto again; + goto loop; + } + } + if (!BN_add_word(rnd, delta)) + return (0); + bn_check_top(rnd); + return (1); +} static int probable_prime_dh(BIGNUM *rnd, int bits, - const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx) - { - int i,ret=0; - BIGNUM *t1; - - BN_CTX_start(ctx); - if ((t1 = BN_CTX_get(ctx)) == NULL) goto err; - - if (!BN_rand(rnd,bits,0,1)) goto err; - - /* we need ((rnd-rem) % add) == 0 */ - - if (!BN_mod(t1,rnd,add,ctx)) goto err; - if (!BN_sub(rnd,rnd,t1)) goto err; - if (rem == NULL) - { if (!BN_add_word(rnd,1)) goto err; } - else - { if (!BN_add(rnd,rnd,rem)) goto err; } - - /* we now have a random number 'rand' to test. */ - - loop: for (i=1; i<NUMPRIMES; i++) - { - /* check that rnd is a prime */ - if (BN_mod_word(rnd,(BN_ULONG)primes[i]) <= 1) - { - if (!BN_add(rnd,rnd,add)) goto err; - goto loop; - } - } - ret=1; -err: - BN_CTX_end(ctx); - bn_check_top(rnd); - return(ret); - } + const BIGNUM *add, const BIGNUM *rem, + BN_CTX *ctx) +{ + int i, ret = 0; + BIGNUM *t1; + + BN_CTX_start(ctx); + if ((t1 = BN_CTX_get(ctx)) == NULL) + goto err; + + if (!BN_rand(rnd, bits, 0, 1)) + goto err; + + /* we need ((rnd-rem) % add) == 0 */ + + if (!BN_mod(t1, rnd, add, ctx)) + goto err; + if (!BN_sub(rnd, rnd, t1)) + goto err; + if (rem == NULL) { + if (!BN_add_word(rnd, 1)) + goto err; + } else { + if (!BN_add(rnd, rnd, rem)) + goto err; + } + + /* we now have a random number 'rand' to test. */ + + loop:for (i = 1; i < NUMPRIMES; i++) { + /* check that rnd is a prime */ + if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { + if (!BN_add(rnd, rnd, add)) + goto err; + goto loop; + } + } + ret = 1; + err: + BN_CTX_end(ctx); + bn_check_top(rnd); + return (ret); +} static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, - const BIGNUM *rem, BN_CTX *ctx) - { - int i,ret=0; - BIGNUM *t1,*qadd,*q; - - bits--; - BN_CTX_start(ctx); - t1 = BN_CTX_get(ctx); - q = BN_CTX_get(ctx); - qadd = BN_CTX_get(ctx); - if (qadd == NULL) goto err; - - if (!BN_rshift1(qadd,padd)) goto err; - - if (!BN_rand(q,bits,0,1)) goto err; - - /* we need ((rnd-rem) % add) == 0 */ - if (!BN_mod(t1,q,qadd,ctx)) goto err; - if (!BN_sub(q,q,t1)) goto err; - if (rem == NULL) - { if (!BN_add_word(q,1)) goto err; } - else - { - if (!BN_rshift1(t1,rem)) goto err; - if (!BN_add(q,q,t1)) goto err; - } - - /* we now have a random number 'rand' to test. */ - if (!BN_lshift1(p,q)) goto err; - if (!BN_add_word(p,1)) goto err; - - loop: for (i=1; i<NUMPRIMES; i++) - { - /* check that p and q are prime */ - /* check that for p and q - * gcd(p-1,primes) == 1 (except for 2) */ - if ( (BN_mod_word(p,(BN_ULONG)primes[i]) == 0) || - (BN_mod_word(q,(BN_ULONG)primes[i]) == 0)) - { - if (!BN_add(p,p,padd)) goto err; - if (!BN_add(q,q,qadd)) goto err; - goto loop; - } - } - ret=1; -err: - BN_CTX_end(ctx); - bn_check_top(p); - return(ret); - } + const BIGNUM *rem, BN_CTX *ctx) +{ + int i, ret = 0; + BIGNUM *t1, *qadd, *q; + + bits--; + BN_CTX_start(ctx); + t1 = BN_CTX_get(ctx); + q = BN_CTX_get(ctx); + qadd = BN_CTX_get(ctx); + if (qadd == NULL) + goto err; + + if (!BN_rshift1(qadd, padd)) + goto err; + + if (!BN_rand(q, bits, 0, 1)) + goto err; + + /* we need ((rnd-rem) % add) == 0 */ + if (!BN_mod(t1, q, qadd, ctx)) + goto err; + if (!BN_sub(q, q, t1)) + goto err; + if (rem == NULL) { + if (!BN_add_word(q, 1)) + goto err; + } else { + if (!BN_rshift1(t1, rem)) + goto err; + if (!BN_add(q, q, t1)) + goto err; + } + + /* we now have a random number 'rand' to test. */ + if (!BN_lshift1(p, q)) + goto err; + if (!BN_add_word(p, 1)) + goto err; + + loop:for (i = 1; i < NUMPRIMES; i++) { + /* check that p and q are prime */ + /* + * check that for p and q gcd(p-1,primes) == 1 (except for 2) + */ + if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) || + (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) { + if (!BN_add(p, p, padd)) + goto err; + if (!BN_add(q, q, qadd)) + goto err; + goto loop; + } + } + ret = 1; + err: + BN_CTX_end(ctx); + bn_check_top(p); + return (ret); +} |