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 nonnegative 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).

WARNINGS

       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 2000-2020 The OpenSSL Project Authors. All Rights Reserved.

       Licensed under the Apache License 2.0 (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>.