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BN_mod_mul_montgomery(3)            OpenSSL           BN_mod_mul_montgomery(3)

       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

       libcrypto, -lcrypto

        #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);

       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.

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

       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).

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

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

       BN_MONT_CTX_init() was removed in OpenSSL 1.1.0

       Copyright 2000-2020 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

1.1.1i                            2020-12-10          BN_mod_mul_montgomery(3)