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-=pod
-
-=head1 NAME
-
-BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_init,
-BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
-BN_from_montgomery, BN_to_montgomery - Montgomery multiplication
-
-=head1 SYNOPSIS
-
- #include <openssl/bn.h>
-
- BN_MONT_CTX *BN_MONT_CTX_new(void);
- void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
- void BN_MONT_CTX_free(BN_MONT_CTX *mont);
-
- int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
- BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
-
- int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
- BN_MONT_CTX *mont, BN_CTX *ctx);
-
- int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
- BN_CTX *ctx);
-
- int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
- BN_CTX *ctx);
-
-=head1 DESCRIPTION
-
-These functions implement Montgomery multiplication. They are used
-automatically when L<BN_mod_exp(3)|BN_mod_exp(3)> is called with suitable input,
-but they may be useful when several operations are to be performed
-using the same modulus.
-
-BN_MONT_CTX_new() allocates and initializes a B<BN_MONT_CTX> structure.
-BN_MONT_CTX_init() initializes an existing uninitialized B<BN_MONT_CTX>.
-
-BN_MONT_CTX_set() sets up the I<mont> structure from the modulus I<m>
-by precomputing its inverse and a value R.
-
-BN_MONT_CTX_copy() copies the B<BN_MONT_CTX> I<from> to I<to>.
-
-BN_MONT_CTX_free() frees the components of the B<BN_MONT_CTX>, and, if
-it was created by BN_MONT_CTX_new(), also the structure itself.
-
-BN_mod_mul_montgomery() computes Mont(I<a>,I<b>):=I<a>*I<b>*R^-1 and places
-the result in I<r>.
-
-BN_from_montgomery() performs the Montgomery reduction I<r> = I<a>*R^-1.
-
-BN_to_montgomery() computes Mont(I<a>,R^2), i.e. I<a>*R.
-Note that I<a> must be non-negative and smaller than the modulus.
-
-For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
-temporary variables.
-
-The B<BN_MONT_CTX> structure is defined as follows:
-
- typedef struct bn_mont_ctx_st
- {
- int ri; /* number of bits in R */
- BIGNUM RR; /* R^2 (used to convert to Montgomery form) */
- BIGNUM N; /* The modulus */
- BIGNUM Ni; /* R*(1/R mod N) - N*Ni = 1
- * (Ni is only stored for bignum algorithm) */
- BN_ULONG n0; /* least significant word of Ni */
- int flags;
- } BN_MONT_CTX;
-
-BN_to_montgomery() is a macro.
-
-=head1 RETURN VALUES
-
-BN_MONT_CTX_new() returns the newly allocated B<BN_MONT_CTX>, and NULL
-on error.
-
-BN_MONT_CTX_init() and BN_MONT_CTX_free() have no return values.
-
-For the other functions, 1 is returned for success, 0 on error.
-The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>.
-
-=head1 WARNING
-
-The inputs must be reduced modulo B<m>, otherwise the result will be
-outside the expected range.
-
-=head1 SEE ALSO
-
-L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<BN_add(3)|BN_add(3)>,
-L<BN_CTX_new(3)|BN_CTX_new(3)>
-
-=head1 HISTORY
-
-BN_MONT_CTX_new(), BN_MONT_CTX_free(), BN_MONT_CTX_set(),
-BN_mod_mul_montgomery(), BN_from_montgomery() and BN_to_montgomery()
-are available in all versions of SSLeay and OpenSSL.
-
-BN_MONT_CTX_init() and BN_MONT_CTX_copy() were added in SSLeay 0.9.1b.
-
-=cut