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=head1 NAME

BN_mod_mul_reciprocal, BN_div_recp, BN_RECP_CTX_new,

BN_RECP_CTX_free, BN_RECP_CTX_set - modular multiplication using

reciprocal

=head1 SYNOPSIS

 #include <openssl/bn.h>

 BN_RECP_CTX *BN_RECP_CTX_new(void);

 void BN_RECP_CTX_free(BN_RECP_CTX *recp);

 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);

 int BN_div_recp(BIGNUM *dv, BIGNUM *rem, BIGNUM *a, BN_RECP_CTX *recp,

                 BN_CTX *ctx);

 int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,

                           BN_RECP_CTX *recp, BN_CTX *ctx);

=head1 DESCRIPTION

BN_mod_mul_reciprocal() can be used to perform an efficient

L<BN_mod_mul(3)> operation when the operation will be performed

repeatedly with the same modulus. It computes B<r>=(B*B)%B<m>

using B<recp>=1/B<m>, which is set as described below.  B<ctx> is a

previously allocated B<BN_CTX> used for temporary variables.

BN_RECP_CTX_new() allocates and initializes a B<BN_RECP> structure.

BN_RECP_CTX_free() frees the components of the B<BN_RECP>, and, if it

was created by BN_RECP_CTX_new(), also the structure itself.

If B<recp> is NULL, nothing is done.

BN_RECP_CTX_set() stores B<m> in B<recp> and sets it up for computing

1/B<m> and shifting it left by BN_num_bits(B<m>)+1 to make it an

integer. The result and the number of bits it was shifted left will

later be stored in B<recp>.

BN_div_recp() divides B by B<m> using B<recp>. It places the quotient

in B<dv> and the remainder in B<rem>.

The B<BN_RECP_CTX> structure cannot be shared between threads.

=head1 RETURN VALUES

BN_RECP_CTX_new() returns the newly allocated B<BN_RECP_CTX>, and NULL

on error.

BN_RECP_CTX_free() has no return value.

For the other functions, 1 is returned for success, 0 on error.

The error codes can be obtained by L<ERR_get_error(3)>.

=head1 SEE ALSO

L<ERR_get_error(3)>, L<BN_add(3)>,

L<BN_CTX_new(3)>

=head1 HISTORY

BN_RECP_CTX_init() was removed in OpenSSL 1.1.0

=head1 COPYRIGHT

Copyright 2000-2017 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>.

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