NAME

       BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_free, BN_MONT_CTX_set,
       BN_MONT_CTX_copy, BN_from_montgomery, BN_to_montgomery - Montgomery multiplication

SYNOPSIS

        #include <openssl/bn.h>

        BN_MONT_CTX *BN_MONT_CTX_new(void);
        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);

DESCRIPTION

       These functions implement Montgomery multiplication. They are used automatically when
       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 BN_MONT_CTX structure.

       BN_MONT_CTX_set() sets up the mont structure from the modulus m by precomputing its
       inverse and a value R.

       BN_MONT_CTX_copy() copies the BN_MONT_CTX from to to.

       BN_MONT_CTX_free() frees the components of the BN_MONT_CTX, and, if it was created by
       BN_MONT_CTX_new(), also the structure itself.  If mont is NULL, nothing is done.

       BN_mod_mul_montgomery() computes Mont(a,b):=a*b*R^-1 and places the result in r.

       BN_from_montgomery() performs the Montgomery reduction r = a*R^-1.

       BN_to_montgomery() computes Mont(a,R^2), i.e. a*R.  Note that a must be non-negative and
       smaller than the modulus.

       For all functions, ctx is a previously allocated BN_CTX used for temporary variables.

RETURN VALUES

       BN_MONT_CTX_new() returns the newly allocated BN_MONT_CTX, and NULL on error.

       BN_MONT_CTX_free() has no return value.

       For the other functions, 1 is returned for success, 0 on error.  The error codes can be
       obtained by ERR_get_error(3).

WARNING

       The inputs must be reduced modulo m, otherwise the result will be outside the expected
       range.

SEE ALSO

       ERR_get_error(3), BN_add(3), BN_CTX_new(3)

HISTORY

       BN_MONT_CTX_init() was removed in OpenSSL 1.1.0

COPYRIGHT

       Copyright 2000-2017 The OpenSSL Project Authors. All Rights Reserved.

       Licensed under the OpenSSL license (the "License").  You may not use this file except in
       compliance with the License.  You can obtain a copy in the file LICENSE in the source
       distribution or at <https://www.openssl.org/source/license.html>.