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.\" ========================================================================
.\"
.IX Title "BN_MOD_MUL_MONTGOMERY 3"
.TH BN_MOD_MUL_MONTGOMERY 3 "2023-09-11" "1.1.1w" "OpenSSL"
.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.nh
.SH "NAME"
BN_mod_mul_montgomery, BN_MONT_CTX_new, BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy, BN_from_montgomery, BN_to_montgomery \- Montgomery multiplication
.SH "SYNOPSIS"
.IX Header "SYNOPSIS"
.Vb 1
\& #include <openssl/bn.h>
\&
\& BN_MONT_CTX *BN_MONT_CTX_new(void);
\& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
\&
\& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
\& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
\&
\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
\& BN_MONT_CTX *mont, BN_CTX *ctx);
\&
\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
\& BN_CTX *ctx);
\&
\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
\& BN_CTX *ctx);
.Ve
.SH "DESCRIPTION"
.IX Header "DESCRIPTION"
These functions implement Montgomery multiplication. They are used
automatically when \fBBN_mod_exp\fR\|(3) is called with suitable input,
but they may be useful when several operations are to be performed
using the same modulus.
.PP
\&\fBBN_MONT_CTX_new()\fR allocates and initializes a \fB\s-1BN_MONT_CTX\s0\fR structure.
.PP
\&\fBBN_MONT_CTX_set()\fR sets up the \fImont\fR structure from the modulus \fIm\fR
by precomputing its inverse and a value R.
.PP
\&\fBBN_MONT_CTX_copy()\fR copies the \fB\s-1BN_MONT_CTX\s0\fR \fIfrom\fR to \fIto\fR.
.PP
\&\fBBN_MONT_CTX_free()\fR frees the components of the \fB\s-1BN_MONT_CTX\s0\fR, and, if
it was created by \fBBN_MONT_CTX_new()\fR, also the structure itself.
If \fBmont\fR is \s-1NULL,\s0 nothing is done.
.PP
\&\fBBN_mod_mul_montgomery()\fR computes Mont(\fIa\fR,\fIb\fR):=\fIa\fR*\fIb\fR*R^\-1 and places
the result in \fIr\fR.
.PP
\&\fBBN_from_montgomery()\fR performs the Montgomery reduction \fIr\fR = \fIa\fR*R^\-1.
.PP
\&\fBBN_to_montgomery()\fR computes Mont(\fIa\fR,R^2), i.e. \fIa\fR*R.
Note that \fIa\fR must be nonnegative and smaller than the modulus.
.PP
For all functions, \fIctx\fR is a previously allocated \fB\s-1BN_CTX\s0\fR used for
temporary variables.
.SH "RETURN VALUES"
.IX Header "RETURN VALUES"
\&\fBBN_MONT_CTX_new()\fR returns the newly allocated \fB\s-1BN_MONT_CTX\s0\fR, and \s-1NULL\s0
on error.
.PP
\&\fBBN_MONT_CTX_free()\fR has no return value.
.PP
For the other functions, 1 is returned for success, 0 on error.
The error codes can be obtained by \fBERR_get_error\fR\|(3).
.SH "WARNINGS"
.IX Header "WARNINGS"
The inputs must be reduced modulo \fBm\fR, otherwise the result will be
outside the expected range.
.SH "SEE ALSO"
.IX Header "SEE ALSO"
\&\fBERR_get_error\fR\|(3), \fBBN_add\fR\|(3),
\&\fBBN_CTX_new\fR\|(3)
.SH "HISTORY"
.IX Header "HISTORY"
\&\fBBN_MONT_CTX_init()\fR was removed in OpenSSL 1.1.0
.SH "COPYRIGHT"
.IX Header "COPYRIGHT"
Copyright 2000\-2020 The OpenSSL Project Authors. All Rights Reserved.
.PP
Licensed under the OpenSSL license (the \*(L"License\*(R"). You may not use
this file except in compliance with the License. You can obtain a copy
in the file \s-1LICENSE\s0 in the source distribution or at
<https://www.openssl.org/source/license.html>.
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