| =pod |
| |
| =head1 NAME |
| |
| BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add, |
| BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_mod_sqrt, BN_exp, BN_mod_exp, BN_gcd - |
| arithmetic operations on BIGNUMs |
| |
| =head1 SYNOPSIS |
| |
| #include <openssl/bn.h> |
| |
| int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); |
| |
| int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); |
| |
| int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); |
| |
| int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); |
| |
| int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, |
| BN_CTX *ctx); |
| |
| int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); |
| |
| int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); |
| |
| int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, |
| BN_CTX *ctx); |
| |
| int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, |
| BN_CTX *ctx); |
| |
| int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, |
| BN_CTX *ctx); |
| |
| int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); |
| |
| BIGNUM *BN_mod_sqrt(BIGNUM *in, BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); |
| |
| int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx); |
| |
| int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, |
| const BIGNUM *m, BN_CTX *ctx); |
| |
| int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); |
| |
| =head1 DESCRIPTION |
| |
| BN_add() adds I<a> and I<b> and places the result in I<r> (C<r=a+b>). |
| I<r> may be the same B<BIGNUM> as I<a> or I<b>. |
| |
| BN_sub() subtracts I<b> from I<a> and places the result in I<r> (C<r=a-b>). |
| I<r> may be the same B<BIGNUM> as I<a> or I<b>. |
| |
| BN_mul() multiplies I<a> and I<b> and places the result in I<r> (C<r=a*b>). |
| I<r> may be the same B<BIGNUM> as I<a> or I<b>. |
| For multiplication by powers of 2, use L<BN_lshift(3)>. |
| |
| BN_sqr() takes the square of I<a> and places the result in I<r> |
| (C<r=a^2>). I<r> and I<a> may be the same B<BIGNUM>. |
| This function is faster than BN_mul(r,a,a). |
| |
| BN_div() divides I<a> by I<d> and places the result in I<dv> and the |
| remainder in I<rem> (C<dv=a/d, rem=a%d>). Either of I<dv> and I<rem> may |
| be B<NULL>, in which case the respective value is not returned. |
| The result is rounded towards zero; thus if I<a> is negative, the |
| remainder will be zero or negative. |
| For division by powers of 2, use BN_rshift(3). |
| |
| BN_mod() corresponds to BN_div() with I<dv> set to B<NULL>. |
| |
| BN_nnmod() reduces I<a> modulo I<m> and places the nonnegative |
| remainder in I<r>. |
| |
| BN_mod_add() adds I<a> to I<b> modulo I<m> and places the nonnegative |
| result in I<r>. |
| |
| BN_mod_sub() subtracts I<b> from I<a> modulo I<m> and places the |
| nonnegative result in I<r>. |
| |
| BN_mod_mul() multiplies I<a> by I<b> and finds the nonnegative |
| remainder respective to modulus I<m> (C<r=(a*b) mod m>). I<r> may be |
| the same B<BIGNUM> as I<a> or I<b>. For more efficient algorithms for |
| repeated computations using the same modulus, see |
| L<BN_mod_mul_montgomery(3)> and |
| L<BN_mod_mul_reciprocal(3)>. |
| |
| BN_mod_sqr() takes the square of I<a> modulo B<m> and places the |
| result in I<r>. |
| |
| BN_mod_sqrt() returns the modular square root of I<a> such that |
| C<in^2 = a (mod p)>. The modulus I<p> must be a |
| prime, otherwise an error or an incorrect "result" will be returned. |
| The result is stored into I<in> which can be NULL. The result will be |
| newly allocated in that case. |
| |
| BN_exp() raises I<a> to the I<p>-th power and places the result in I<r> |
| (C<r=a^p>). This function is faster than repeated applications of |
| BN_mul(). |
| |
| BN_mod_exp() computes I<a> to the I<p>-th power modulo I<m> (C<r=a^p % |
| m>). This function uses less time and space than BN_exp(). Do not call this |
| function when B<m> is even and any of the parameters have the |
| B<BN_FLG_CONSTTIME> flag set. |
| |
| BN_gcd() computes the greatest common divisor of I<a> and I<b> and |
| places the result in I<r>. I<r> may be the same B<BIGNUM> as I<a> or |
| I<b>. |
| |
| For all functions, I<ctx> is a previously allocated B<BN_CTX> used for |
| temporary variables; see L<BN_CTX_new(3)>. |
| |
| Unless noted otherwise, the result B<BIGNUM> must be different from |
| the arguments. |
| |
| =head1 RETURN VALUES |
| |
| The BN_mod_sqrt() returns the result (possibly incorrect if I<p> is |
| not a prime), or NULL. |
| |
| For all remaining functions, 1 is returned for success, 0 on error. The return |
| value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>). |
| The error codes can be obtained by L<ERR_get_error(3)>. |
| |
| =head1 SEE ALSO |
| |
| L<ERR_get_error(3)>, L<BN_CTX_new(3)>, |
| L<BN_add_word(3)>, L<BN_set_bit(3)> |
| |
| =head1 COPYRIGHT |
| |
| Copyright 2000-2022 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 |
| L<https://www.openssl.org/source/license.html>. |
| |
| =cut |