1=pod 2 3=head1 NAME 4 5BN_mod_exp_mont, BN_mod_exp_mont_consttime, BN_mod_exp_mont_consttime_x2 - 6Montgomery exponentiation 7 8=head1 SYNOPSIS 9 10 #include <openssl/bn.h> 11 12 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 13 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont); 14 15 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p, 16 const BIGNUM *m, BN_CTX *ctx, 17 BN_MONT_CTX *in_mont); 18 19 int BN_mod_exp_mont_consttime_x2(BIGNUM *rr1, const BIGNUM *a1, 20 const BIGNUM *p1, const BIGNUM *m1, 21 BN_MONT_CTX *in_mont1, BIGNUM *rr2, 22 const BIGNUM *a2, const BIGNUM *p2, 23 const BIGNUM *m2, BN_MONT_CTX *in_mont2, 24 BN_CTX *ctx); 25 26=head1 DESCRIPTION 27 28BN_mod_exp_mont() computes I<a> to the I<p>-th power modulo I<m> (C<rr=a^p % m>) 29using Montgomery multiplication. I<in_mont> is a Montgomery context and can be 30NULL. In the case I<in_mont> is NULL, it will be initialized within the 31function, so you can save time on initialization if you provide it in advance. 32 33BN_mod_exp_mont_consttime() computes I<a> to the I<p>-th power modulo I<m> 34(C<rr=a^p % m>) using Montgomery multiplication. It is a variant of 35L<BN_mod_exp_mont(3)> that uses fixed windows and the special precomputation 36memory layout to limit data-dependency to a minimum to protect secret exponents. 37It is called automatically when L<BN_mod_exp_mont(3)> is called with parameters 38I<a>, I<p>, I<m>, any of which have B<BN_FLG_CONSTTIME> flag. 39 40BN_mod_exp_mont_consttime_x2() computes two independent exponentiations I<a1> to 41the I<p1>-th power modulo I<m1> (C<rr1=a1^p1 % m1>) and I<a2> to the I<p2>-th 42power modulo I<m2> (C<rr2=a2^p2 % m2>) using Montgomery multiplication. For some 43fixed and equal modulus sizes I<m1> and I<m2> it uses optimizations that allow 44to speedup two exponentiations. In all other cases the function reduces to two 45calls of L<BN_mod_exp_mont_consttime(3)>. 46 47=head1 RETURN VALUES 48 49For all functions 1 is returned for success, 0 on error. 50The error codes can be obtained by L<ERR_get_error(3)>. 51 52=head1 SEE ALSO 53 54L<ERR_get_error(3)>, L<BN_mod_exp_mont(3)> 55 56=head1 COPYRIGHT 57 58Copyright 2000-2021 The OpenSSL Project Authors. All Rights Reserved. 59 60Licensed under the Apache License 2.0 (the "License"). You may not use 61this file except in compliance with the License. You can obtain a copy 62in the file LICENSE in the source distribution or at 63L<https://www.openssl.org/source/license.html>. 64 65=cut 66
