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.\" $OpenBSD: BN_mod_mul_reciprocal.3,v 1.5 2016/12/10 21:13:25 schwarze Exp $
.\" OpenSSL 6859cf74 Sep 25 13:33:28 2002 +0000
.\"
.\" This file was written by Ulf Moeller <ulf@openssl.org>.
.\" Copyright (c) 2000 The OpenSSL Project. All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\"
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\"
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in
.\" the documentation and/or other materials provided with the
.\" distribution.
.\"
.\" 3. All advertising materials mentioning features or use of this
.\" software must display the following acknowledgment:
.\" "This product includes software developed by the OpenSSL Project
.\" for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
.\"
.\" 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
.\" endorse or promote products derived from this software without
.\" prior written permission. For written permission, please contact
.\" openssl-core@openssl.org.
.\"
.\" 5. Products derived from this software may not be called "OpenSSL"
.\" nor may "OpenSSL" appear in their names without prior written
.\" permission of the OpenSSL Project.
.\"
.\" 6. Redistributions of any form whatsoever must retain the following
.\" acknowledgment:
.\" "This product includes software developed by the OpenSSL Project
.\" for use in the OpenSSL Toolkit (http://www.openssl.org/)"
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
.\" EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
.\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
.\" ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
.\" SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
.\" NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
.\" LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
.\" STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
.\" OF THE POSSIBILITY OF SUCH DAMAGE.
.\"
.Dd $Mdocdate: December 10 2016 $
.Dt BN_MOD_MUL_RECIPROCAL 3
.Os
.Sh NAME
.Nm BN_mod_mul_reciprocal ,
.Nm BN_RECP_CTX_new ,
.Nm BN_RECP_CTX_init ,
.Nm BN_RECP_CTX_free ,
.Nm BN_RECP_CTX_set ,
.Nm BN_div_recp
.Nd modular multiplication using reciprocal
.Sh SYNOPSIS
.In openssl/bn.h
.Ft int
.Fo BN_mod_mul_reciprocal
.Fa "BIGNUM *r"
.Fa "BIGNUM *a"
.Fa "BIGNUM *b"
.Fa "BN_RECP_CTX *recp"
.Fa "BN_CTX *ctx"
.Fc
.Ft BN_RECP_CTX *
.Fo BN_RECP_CTX_new
.Fa void
.Fc
.Ft void
.Fo BN_RECP_CTX_init
.Fa "BN_RECP_CTX *recp"
.Fc
.Ft void
.Fo BN_RECP_CTX_free
.Fa "BN_RECP_CTX *recp"
.Fc
.Ft int
.Fo BN_RECP_CTX_set
.Fa "BN_RECP_CTX *recp"
.Fa "const BIGNUM *m"
.Fa "BN_CTX *ctx"
.Fc
.Ft int
.Fo BN_div_recp
.Fa "BIGNUM *dv"
.Fa "BIGNUM *rem"
.Fa "BIGNUM *a"
.Fa "BN_RECP_CTX *recp"
.Fa "BN_CTX *ctx"
.Fc
.Sh DESCRIPTION
.Fn BN_mod_mul_reciprocal
can be used to perform an efficient
.Xr BN_mod_mul 3
operation when the operation will be performed repeatedly with the same
modulus.
It computes
.Fa r Ns =( Ns Fa a Ns * Ns Fa b Ns )% Ns Fa m
using
.Fa recp Ns =1/ Ns Fa m ,
which is set as described below.
.Fa ctx
is a previously allocated
.Vt BN_CTX
used for temporary variables.
.Pp
.Fn BN_RECP_CTX_new
allocates and initializes a
.Vt BN_RECP_CTX
structure.
.Fn BN_RECP_CTX_init
initializes an existing uninitialized
.Vt BN_RECP_CTX .
.Pp
.Fn BN_RECP_CTX_free
frees the components of the
.Vt BN_RECP_CTX ,
and, if it was created by
.Fn BN_RECP_CTX_new ,
also the structure itself.
If
.Fa recp
is a
.Dv NULL
pointer, no action occurs.
.Pp
.Fn BN_RECP_CTX_set
stores
.Fa m
in
.Fa recp
and sets it up for computing
.Pf 1/ Fa m
and shifting it left by
.Fn BN_num_bits m Ns +1
to make it an integer.
The result and the number of bits it was shifted left will later be
stored in
.Fa recp .
.Pp
.Fn BN_div_recp
divides
.Fa a
by
.Fa m
using
.Fa recp .
It places the quotient in
.Fa dv
and the remainder in
.Fa rem .
.Pp
The
.Vt BN_RECP_CTX
structure is defined as follows:
.Bd -literal
typedef struct bn_recp_ctx_st {
BIGNUM N; /* the divisor */
BIGNUM Nr; /* the reciprocal */
int num_bits;
int shift;
int flags;
} BN_RECP_CTX;
.Ed
.Pp
It cannot be shared between threads.
.Sh RETURN VALUES
.Fn BN_RECP_CTX_new
returns the newly allocated
.Vt BN_RECP_CTX
or
.Dv NULL
on error.
.Pp
For the other functions, 1 is returned for success or 0 on error.
The error codes can be obtained by
.Xr ERR_get_error 3 .
.Sh SEE ALSO
.Xr BN_add 3 ,
.Xr BN_CTX_new 3 ,
.Xr BN_new 3 ,
.Xr ERR_get_error 3
.Sh HISTORY
.Vt BN_RECP_CTX
was added in SSLeay 0.9.0.
Before that, a function
.Fn BN_reciprocal
was used instead, and the
.Fn BN_mod_mul_reciprocal
arguments were different.
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