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-.\"     $OpenBSD: BN_mod_mul_montgomery.3,v 1.11 2018/03/27 17:35:50 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,
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-.\"
-.Dd $Mdocdate: March 27 2018 $
-.Dt BN_MOD_MUL_MONTGOMERY 3
-.Os
-.Sh NAME
-.Nm BN_MONT_CTX_new ,
-.Nm BN_MONT_CTX_init ,
-.Nm BN_MONT_CTX_free ,
-.Nm BN_MONT_CTX_set ,
-.Nm BN_MONT_CTX_copy ,
-.Nm BN_mod_mul_montgomery ,
-.Nm BN_from_montgomery ,
-.Nm BN_to_montgomery
-.Nd Montgomery multiplication
-.Sh SYNOPSIS
-.In openssl/bn.h
-.Ft BN_MONT_CTX *
-.Fo BN_MONT_CTX_new
-.Fa void
-.Fc
-.Ft void
-.Fo BN_MONT_CTX_init
-.Fa "BN_MONT_CTX *ctx"
-.Fc
-.Ft void
-.Fo BN_MONT_CTX_free
-.Fa "BN_MONT_CTX *mont"
-.Fc
-.Ft int
-.Fo BN_MONT_CTX_set
-.Fa "BN_MONT_CTX *mont"
-.Fa "const BIGNUM *m"
-.Fa "BN_CTX *ctx"
-.Fc
-.Ft BN_MONT_CTX *
-.Fo BN_MONT_CTX_copy
-.Fa "BN_MONT_CTX *to"
-.Fa "BN_MONT_CTX *from"
-.Fc
-.Ft int
-.Fo BN_mod_mul_montgomery
-.Fa "BIGNUM *r"
-.Fa "BIGNUM *a"
-.Fa "BIGNUM *b"
-.Fa "BN_MONT_CTX *mont"
-.Fa "BN_CTX *ctx"
-.Fc
-.Ft int
-.Fo BN_from_montgomery
-.Fa "BIGNUM *r"
-.Fa "BIGNUM *a"
-.Fa "BN_MONT_CTX *mont"
-.Fa "BN_CTX *ctx"
-.Fc
-.Ft int
-.Fo BN_to_montgomery
-.Fa "BIGNUM *r"
-.Fa "BIGNUM *a"
-.Fa "BN_MONT_CTX *mont"
-.Fa "BN_CTX *ctx"
-.Fc
-.Sh DESCRIPTION
-These functions implement Montgomery multiplication.
-They are used automatically when
-.Xr BN_mod_exp 3
-is called with suitable input, but they may be useful when several
-operations are to be performed using the same modulus.
-.Pp
-.Fn BN_MONT_CTX_new
-allocates and initializes a
-.Vt BN_MONT_CTX
-structure.
-.Pp
-.Fn BN_MONT_CTX_init
-initializes an existing uninitialized
-.Vt BN_MONT_CTX .
-It is deprecated and dangerous: see
-.Sx CAVEATS .
-.Pp
-.Fn BN_MONT_CTX_set
-sets up the
-.Fa mont
-structure from the modulus
-.Fa m
-by precomputing its inverse and a value R.
-.Pp
-.Fn BN_MONT_CTX_copy
-copies the
-.Vt BN_MONT_CTX
-.Fa from
-to
-.Fa to .
-.Pp
-.Fn BN_MONT_CTX_free
-frees the components of the
-.Vt BN_MONT_CTX ,
-and, if it was created by
-.Fn BN_MONT_CTX_new ,
-also the structure itself.
-If
-.Fa mont
-is a
-.Dv NULL
-pointer, no action occurs.
-.Pp
-.Fn BN_mod_mul_montgomery
-computes
-.Pp
-.D1 Mont Ns Po Fa a , Fa b Pc := Fa a No * Fa b No * R^-1
-.Pp
-and places the result in
-.Fa r .
-.Pp
-.Fn BN_from_montgomery
-performs the Montgomery reduction
-.Pp
-.D1 Fa r No = Fa a No * R^-1
-.Pp
-.Fn BN_to_montgomery
-computes
-.Pp
-.D1 Mont Ns Po Fa a , No R^2 Pc = Fa a No * R
-.Pp
-Note that
-.Fa a
-must be non-negative and smaller than the modulus.
-.Pp
-For all functions,
-.Fa ctx
-is a previously allocated
-.Vt BN_CTX
-used for temporary variables.
-.Pp
-The
-.Vt BN_MONT_CTX
-structure is defined as follows:
-.Bd -literal
-typedef struct bn_mont_ctx_st {
-        int ri;         /* number of bits in R */
-        BIGNUM RR;      /* R^2 (used to convert to Montgomery form) */
-        BIGNUM N;       /* The modulus */
-        BIGNUM Ni;      /* R*(1/R mod N) - N*Ni = 1
-                         * (Ni is only stored for bignum algorithm) */
-        BN_ULONG n0;    /* least significant word of Ni */
-        int flags;
-} BN_MONT_CTX;
-.Ed
-.Pp
-.Fn BN_to_montgomery
-is a macro.
-.Pp
-.Sy Warning :
-The inputs must be reduced modulo
-.Fa m ,
-otherwise the result will be outside the expected range.
-.Sh RETURN VALUES
-.Fn BN_MONT_CTX_new
-returns the newly allocated
-.Vt BN_MONT_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
-.Sh HISTORY
-.Fn BN_MONT_CTX_new ,
-.Fn BN_MONT_CTX_free ,
-.Fn BN_MONT_CTX_set ,
-.Fn BN_mod_mul_montgomery ,
-.Fn BN_from_montgomery ,
-and
-.Fn BN_to_montgomery
-first appeared in SSLeay 0.6.1 and have been available since
-.Ox 2.4 .
-.Pp
-.Fn BN_MONT_CTX_init
-and
-.Fn BN_MONT_CTX_copy
-first appeared in SSLeay 0.9.1 and have been available since
-.Ox 2.6 .
-.Sh CAVEATS
-.Fn BN_MONT_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_MONT_CTX_new ,
-or the context itself will likely be leaked later.
-It can only be used on a static
-.Vt BN_MONT_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_MONT_CTX
-is made opaque.