1=pod 2 3=head1 NAME 4 5BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add, 6BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd - 7arithmetic operations on BIGNUMs 8 9=head1 SYNOPSIS 10 11 #include <openssl/bn.h> 12 13 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 14 15 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); 16 17 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); 18 19 int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); 20 21 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, 22 BN_CTX *ctx); 23 24 int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); 25 26 int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); 27 28 int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, 29 BN_CTX *ctx); 30 31 int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, 32 BN_CTX *ctx); 33 34 int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, 35 BN_CTX *ctx); 36 37 int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); 38 39 int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx); 40 41 int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, 42 const BIGNUM *m, BN_CTX *ctx); 43 44 int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); 45 46=head1 DESCRIPTION 47 48BN_add() adds I<a> and I<b> and places the result in I<r> (C<r=a+b>). 49I<r> may be the same B<BIGNUM> as I<a> or I<b>. 50 51BN_sub() subtracts I<b> from I<a> and places the result in I<r> (C<r=a-b>). 52I<r> may be the same B<BIGNUM> as I<a> or I<b>. 53 54BN_mul() multiplies I<a> and I<b> and places the result in I<r> (C<r=a*b>). 55I<r> may be the same B<BIGNUM> as I<a> or I<b>. 56For multiplication by powers of 2, use L<BN_lshift(3)>. 57 58BN_sqr() takes the square of I<a> and places the result in I<r> 59(C<r=a^2>). I<r> and I<a> may be the same B<BIGNUM>. 60This function is faster than BN_mul(r,a,a). 61 62BN_div() divides I<a> by I<d> and places the result in I<dv> and the 63remainder in I<rem> (C<dv=a/d, rem=a%d>). Either of I<dv> and I<rem> may 64be B<NULL>, in which case the respective value is not returned. 65The result is rounded towards zero; thus if I<a> is negative, the 66remainder will be zero or negative. 67For division by powers of 2, use BN_rshift(3). 68 69BN_mod() corresponds to BN_div() with I<dv> set to B<NULL>. 70 71BN_nnmod() reduces I<a> modulo I<m> and places the nonnegative 72remainder in I<r>. 73 74BN_mod_add() adds I<a> to I<b> modulo I<m> and places the nonnegative 75result in I<r>. 76 77BN_mod_sub() subtracts I<b> from I<a> modulo I<m> and places the 78nonnegative result in I<r>. 79 80BN_mod_mul() multiplies I<a> by I<b> and finds the nonnegative 81remainder respective to modulus I<m> (C<r=(a*b) mod m>). I<r> may be 82the same B<BIGNUM> as I<a> or I<b>. For more efficient algorithms for 83repeated computations using the same modulus, see 84L<BN_mod_mul_montgomery(3)> and 85L<BN_mod_mul_reciprocal(3)>. 86 87BN_mod_sqr() takes the square of I<a> modulo B<m> and places the 88result in I<r>. 89 90BN_exp() raises I<a> to the I<p>-th power and places the result in I<r> 91(C<r=a^p>). This function is faster than repeated applications of 92BN_mul(). 93 94BN_mod_exp() computes I<a> to the I<p>-th power modulo I<m> (C<r=a^p % 95m>). This function uses less time and space than BN_exp(). Do not call this 96function when B<m> is even and any of the parameters have the 97B<BN_FLG_CONSTTIME> flag set. 98 99BN_gcd() computes the greatest common divisor of I<a> and I<b> and 100places the result in I<r>. I<r> may be the same B<BIGNUM> as I<a> or 101I<b>. 102 103For all functions, I<ctx> is a previously allocated B<BN_CTX> used for 104temporary variables; see L<BN_CTX_new(3)>. 105 106Unless noted otherwise, the result B<BIGNUM> must be different from 107the arguments. 108 109=head1 RETURN VALUES 110 111For all functions, 1 is returned for success, 0 on error. The return 112value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>). 113The error codes can be obtained by L<ERR_get_error(3)>. 114 115=head1 SEE ALSO 116 117L<ERR_get_error(3)>, L<BN_CTX_new(3)>, 118L<BN_add_word(3)>, L<BN_set_bit(3)> 119 120=head1 COPYRIGHT 121 122Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved. 123 124Licensed under the OpenSSL license (the "License"). You may not use 125this file except in compliance with the License. You can obtain a copy 126in the file LICENSE in the source distribution or at 127L<https://www.openssl.org/source/license.html>. 128 129=cut 130