.\" $OpenBSD: BN_mod_mul_reciprocal.3,v 1.12 2022/11/14 18:28:29 schwarze Exp $ .\" full merge up to: OpenSSL 6859cf74 Sep 25 13:33:28 2002 +0000 .\" selective merge up to: OpenSSL e9b77246 Jan 20 19:58:49 2017 +0100 .\" .\" This file is a derived work. .\" The changes are covered by the following Copyright and license: .\" .\" Copyright (c) 2022 Ingo Schwarze .\" .\" Permission to use, copy, modify, and distribute this software for any .\" purpose with or without fee is hereby granted, provided that the above .\" copyright notice and this permission notice appear in all copies. .\" .\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES .\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF .\" MERCHANTABILITY AND FITNESS. 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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: November 14 2022 $ .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 , .Nm BN_reciprocal .Nd modular multiplication using reciprocal .Sh SYNOPSIS .In openssl/bn.h .Ft int .Fo BN_mod_mul_reciprocal .Fa "BIGNUM *r" .Fa "const BIGNUM *a" .Fa "const 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 "const BIGNUM *a" .Fa "BN_RECP_CTX *recp" .Fa "BN_CTX *ctx" .Fc .Ft int .Fo BN_reciprocal .Fa "BIGNUM *r" .Fa "const BIGNUM *m" .Fa "int len" .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. .Pp .Fn BN_RECP_CTX_init initializes an existing uninitialized .Vt BN_RECP_CTX . It is deprecated and dangerous: see .Sx CAVEATS . .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 .Fn BN_reciprocal divides the .Fa len Ap th power of two by .Fa m and places the quotient in .Fa r , rounding it towards zero to the closest integer. .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 .Fn BN_mod_mul_reciprocal , .Fn BN_RECP_CTX_set , and .Fn BN_div_recp return 1 for success or 0 on error. .Pp .Fn BN_reciprocal returns .Fa len for success or \-1 on error. .Pp 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 .Sh HISTORY .Fn BN_mod_mul_reciprocal and .Fn BN_reciprocal first appeared in SSLeay 0.5.1 and have been available since .Ox 2.4 . .Pp .Vt BN_RECP_CTX was added in SSLeay 0.9.0. Before that, the .Fn BN_mod_mul_reciprocal arguments were different. .Pp .Fn BN_RECP_CTX_new , .Fn BN_RECP_CTX_init , .Fn BN_RECP_CTX_free , .Fn BN_RECP_CTX_set , and .Fn BN_div_recp first appeared in SSLeay 0.9.1 and have been available since .Ox 2.6 . .Sh CAVEATS .Fn BN_RECP_CTX_init must not be called on a context that was used previously, or memory used by the embedded .Vt BIGNUM structures is leaked immediately. Besides, it must not be called on a context created with .Fn BN_RECP_CTX_new , or the context itself will likely be leaked later. It can only be used on a static .Vt BN_RECP_CTX structure, on one located on the stack, or on one .Xr malloc 3 Ap ed manually, but all these options are discouraged because they will no longer work once .Vt BN_RECP_CTX is made opaque.