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BN_mod_exp_mont(3)                  OpenSSL                 BN_mod_exp_mont(3)



NAME
       BN_mod_exp_mont, BN_mod_exp_mont_consttime,
       BN_mod_exp_mont_consttime_x2 - Montgomery exponentiation

LIBRARY
       libcrypto, -lcrypto

SYNOPSIS
        #include <openssl/bn.h>

        int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
                            const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont);

        int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
                                      const BIGNUM *m, BN_CTX *ctx,
                                      BN_MONT_CTX *in_mont);

        int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1,
                                         const BIGNUM *p1, const BIGNUM *m1,
                                         BN_MONT_CTX *in_mont1, BIGNUM *rr2,
                                         const BIGNUM *a2, const BIGNUM *p2,
                                         const BIGNUM *m2, BN_MONT_CTX *in_mont2,
                                         BN_CTX *ctx);

DESCRIPTION
       BN_mod_exp_mont() computes a to the p-th power modulo m ("rr=a^p % m")
       using Montgomery multiplication. in_mont is a Montgomery context and
       can be NULL. In the case in_mont is NULL, it will be initialized within
       the function, so you can save time on initialization if you provide it
       in advance.

       BN_mod_exp_mont_consttime() computes a to the p-th power modulo m
       ("rr=a^p % m") using Montgomery multiplication. It is a variant of
       BN_mod_exp_mont(3) that uses fixed windows and the special
       precomputation memory layout to limit data-dependency to a minimum to
       protect secret exponents.  It is called automatically when
       BN_mod_exp_mont(3) is called with parameters a, p, m, any of which have
       BN_FLG_CONSTTIME flag.

       BN_mod_exp_mont_consttime_x2() computes two independent exponentiations
       a1 to the p1-th power modulo m1 ("rr1=a1^p1 % m1") and a2 to the p2-th
       power modulo m2 ("rr2=a2^p2 % m2") using Montgomery multiplication. For
       some fixed and equal modulus sizes m1 and m2 it uses optimizations that
       allow to speedup two exponentiations. In all other cases the function
       reduces to two calls of BN_mod_exp_mont_consttime(3).

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

SEE ALSO
       ERR_get_error(3), BN_mod_exp_mont(3)

COPYRIGHT
       Copyright 2000-2021 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>.



3.0.12                            2023-05-07                BN_mod_exp_mont(3)