NAME

       BN_mod_exp_mont, BN_mod_exp_mont_consttime, BN_mod_exp_mont_consttime_x2 - Montgomery exponentiation

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>.