=pod

=head1 NAME

BN_mod_mul_reciprocal, BN_RECP_CTX_new, BN_RECP_CTX_init,
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_init(BN_RECP_CTX *recp);
 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_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
BN_mod_mul(3) operation when the operation will be performed
repeatedly with the same modulus. It computes B<r>=(B<a>*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_init() initializes an existing uninitialized B<BN_RECP>.

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.

BN_RECP_CTX_set() computes 1/B<m> and shifts 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 are stored in B<recp>.

The B<BN_RECP_CTX> structure is defined as follows:

 typedef struct bn_recp_ctx_st
	{
	BIGNUM N;	/* the divisor */
	BIGNUM Nr;	/* the reciprocal */
	int num_bits;
	int shift;
	int flags;
	} BN_RECP_CTX;

It 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_init() and BN_RECP_CTX_free() have no return values.

For the other functions, 1 is returned for success, 0 on error.
The error codes can be obtained by ERR_get_error(3).

=head1 SEE ALSO

bn(3), err(3), BN_add(3), BN_CTX_new(3)

=head1 HISTORY

B<BN_RECP_CTX> was added in SSLeay 0.9.0. Before that, the function
BN_reciprocal() was used instead, and the BN_mod_mul_reciprocal()
arguments werde different.

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