mirror of
https://github.com/openssl/openssl.git
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146 lines
5.0 KiB
Plaintext
146 lines
5.0 KiB
Plaintext
=pod
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=head1 NAME
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BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
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BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_mod_sqrt, BN_exp, BN_mod_exp, BN_gcd -
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arithmetic operations on BIGNUMs
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=head1 SYNOPSIS
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#include <openssl/bn.h>
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int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx);
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int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
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BN_CTX *ctx);
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int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx);
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int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx);
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int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
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BN_CTX *ctx);
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int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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BIGNUM *BN_mod_sqrt(BIGNUM *in, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
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int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
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int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
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const BIGNUM *m, BN_CTX *ctx);
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int BN_gcd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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=head1 DESCRIPTION
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BN_add() adds I<a> and I<b> and places the result in I<r> (C<r=a+b>).
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I<r> may be the same B<BIGNUM> as I<a> or I<b>.
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BN_sub() subtracts I<b> from I<a> and places the result in I<r> (C<r=a-b>).
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I<r> may be the same B<BIGNUM> as I<a> or I<b>.
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BN_mul() multiplies I<a> and I<b> and places the result in I<r> (C<r=a*b>).
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I<r> may be the same B<BIGNUM> as I<a> or I<b>.
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For multiplication by powers of 2, use L<BN_lshift(3)>.
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BN_sqr() takes the square of I<a> and places the result in I<r>
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(C<r=a^2>). I<r> and I<a> may be the same B<BIGNUM>.
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This function is faster than BN_mul(r,a,a).
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BN_div() divides I<a> by I<d> and places the result in I<dv> and the
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remainder in I<rem> (C<dv=a/d, rem=a%d>). Either of I<dv> and I<rem> may
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be B<NULL>, in which case the respective value is not returned.
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The result is rounded towards zero; thus if I<a> is negative, the
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remainder will be zero or negative.
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For division by powers of 2, use BN_rshift(3).
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BN_mod() corresponds to BN_div() with I<dv> set to B<NULL>.
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BN_nnmod() reduces I<a> modulo I<m> and places the nonnegative
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remainder in I<r>.
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BN_mod_add() adds I<a> to I<b> modulo I<m> and places the nonnegative
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result in I<r>.
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BN_mod_sub() subtracts I<b> from I<a> modulo I<m> and places the
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nonnegative result in I<r>.
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BN_mod_mul() multiplies I<a> by I<b> and finds the nonnegative
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remainder respective to modulus I<m> (C<r=(a*b) mod m>). I<r> may be
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the same B<BIGNUM> as I<a> or I<b>. For more efficient algorithms for
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repeated computations using the same modulus, see
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L<BN_mod_mul_montgomery(3)> and
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L<BN_mod_mul_reciprocal(3)>.
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BN_mod_sqr() takes the square of I<a> modulo B<m> and places the
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result in I<r>.
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BN_mod_sqrt() returns the modular square root of I<a> such that
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C<in^2 = a (mod p)>. The modulus I<p> must be a
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prime, otherwise an error or an incorrect "result" will be returned.
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The result is stored into I<in> which can be NULL. The result will be
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newly allocated in that case.
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BN_exp() raises I<a> to the I<p>-th power and places the result in I<r>
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(C<r=a^p>). This function is faster than repeated applications of
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BN_mul().
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BN_mod_exp() computes I<a> to the I<p>-th power modulo I<m> (C<r=a^p %
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m>). This function uses less time and space than BN_exp(). Do not call this
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function when B<m> is even and any of the parameters have the
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B<BN_FLG_CONSTTIME> flag set.
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BN_gcd() computes the greatest common divisor of I<a> and I<b> and
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places the result in I<r>. I<r> may be the same B<BIGNUM> as I<a> or
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I<b>.
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For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
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temporary variables; see L<BN_CTX_new(3)>.
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Unless noted otherwise, the result B<BIGNUM> must be different from
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the arguments.
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=head1 NOTES
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For modular operations such as BN_nnmod() or BN_mod_exp() it is an error
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to use the same B<BIGNUM> object for the modulus as for the output.
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=head1 RETURN VALUES
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The BN_mod_sqrt() returns the result (possibly incorrect if I<p> is
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not a prime), or NULL.
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For all remaining functions, 1 is returned for success, 0 on error. The return
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value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>).
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The error codes can be obtained by L<ERR_get_error(3)>.
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=head1 SEE ALSO
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L<ERR_get_error(3)>, L<BN_CTX_new(3)>,
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L<BN_add_word(3)>, L<BN_set_bit(3)>
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=head1 COPYRIGHT
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Copyright 2000-2024 The OpenSSL Project Authors. All Rights Reserved.
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Licensed under the Apache License 2.0 (the "License"). You may not use
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this file except in compliance with the License. You can obtain a copy
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in the file LICENSE in the source distribution or at
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L<https://www.openssl.org/source/license.html>.
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=cut
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