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_mod_sqrt, 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 BIGNUM *BN_mod_sqrt(BIGNUM *in, BIGNUM *a, const BIGNUM *p, BN_CTX *ctx); 40 41 int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx); 42 43 int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, 44 const BIGNUM *m, BN_CTX *ctx); 45 46 int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); 47 48=head1 DESCRIPTION 49 50BN_add() adds I<a> and I<b> and places the result in I<r> (C<r=a+b>). 51I<r> may be the same B<BIGNUM> as I<a> or I<b>. 52 53BN_sub() subtracts I<b> from I<a> and places the result in I<r> (C<r=a-b>). 54I<r> may be the same B<BIGNUM> as I<a> or I<b>. 55 56BN_mul() multiplies I<a> and I<b> and places the result in I<r> (C<r=a*b>). 57I<r> may be the same B<BIGNUM> as I<a> or I<b>. 58For multiplication by powers of 2, use L<BN_lshift(3)>. 59 60BN_sqr() takes the square of I<a> and places the result in I<r> 61(C<r=a^2>). I<r> and I<a> may be the same B<BIGNUM>. 62This function is faster than BN_mul(r,a,a). 63 64BN_div() divides I<a> by I<d> and places the result in I<dv> and the 65remainder in I<rem> (C<dv=a/d, rem=a%d>). Either of I<dv> and I<rem> may 66be B<NULL>, in which case the respective value is not returned. 67The result is rounded towards zero; thus if I<a> is negative, the 68remainder will be zero or negative. 69For division by powers of 2, use BN_rshift(3). 70 71BN_mod() corresponds to BN_div() with I<dv> set to B<NULL>. 72 73BN_nnmod() reduces I<a> modulo I<m> and places the nonnegative 74remainder in I<r>. 75 76BN_mod_add() adds I<a> to I<b> modulo I<m> and places the nonnegative 77result in I<r>. 78 79BN_mod_sub() subtracts I<b> from I<a> modulo I<m> and places the 80nonnegative result in I<r>. 81 82BN_mod_mul() multiplies I<a> by I<b> and finds the nonnegative 83remainder respective to modulus I<m> (C<r=(a*b) mod m>). I<r> may be 84the same B<BIGNUM> as I<a> or I<b>. For more efficient algorithms for 85repeated computations using the same modulus, see 86L<BN_mod_mul_montgomery(3)> and 87L<BN_mod_mul_reciprocal(3)>. 88 89BN_mod_sqr() takes the square of I<a> modulo B<m> and places the 90result in I<r>. 91 92BN_mod_sqrt() returns the modular square root of I<a> such that 93C<in^2 = a (mod p)>. The modulus I<p> must be a 94prime, otherwise an error or an incorrect "result" will be returned. 95The result is stored into I<in> which can be NULL. The result will be 96newly allocated in that case. 97 98BN_exp() raises I<a> to the I<p>-th power and places the result in I<r> 99(C<r=a^p>). This function is faster than repeated applications of 100BN_mul(). 101 102BN_mod_exp() computes I<a> to the I<p>-th power modulo I<m> (C<r=a^p % 103m>). This function uses less time and space than BN_exp(). Do not call this 104function when B<m> is even and any of the parameters have the 105B<BN_FLG_CONSTTIME> flag set. 106 107BN_gcd() computes the greatest common divisor of I<a> and I<b> and 108places the result in I<r>. I<r> may be the same B<BIGNUM> as I<a> or 109I<b>. 110 111For all functions, I<ctx> is a previously allocated B<BN_CTX> used for 112temporary variables; see L<BN_CTX_new(3)>. 113 114Unless noted otherwise, the result B<BIGNUM> must be different from 115the arguments. 116 117=head1 NOTES 118 119For modular operations such as BN_nnmod() or BN_mod_exp() it is an error 120to use the same B<BIGNUM> object for the modulus as for the output. 121 122=head1 RETURN VALUES 123 124The BN_mod_sqrt() returns the result (possibly incorrect if I<p> is 125not a prime), or NULL. 126 127For all remaining functions, 1 is returned for success, 0 on error. The return 128value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>). 129The error codes can be obtained by L<ERR_get_error(3)>. 130 131=head1 SEE ALSO 132 133L<ERR_get_error(3)>, L<BN_CTX_new(3)>, 134L<BN_add_word(3)>, L<BN_set_bit(3)> 135 136=head1 COPYRIGHT 137 138Copyright 2000-2022 The OpenSSL Project Authors. All Rights Reserved. 139 140Licensed under the Apache License 2.0 (the "License"). You may not use 141this file except in compliance with the License. You can obtain a copy 142in the file LICENSE in the source distribution or at 143L<https://www.openssl.org/source/license.html>. 144 145=cut 146