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>.