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BN_add.pod
=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 OpenSSL license (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