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=head1 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

=head1 SYNOPSIS

 #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);

=head1 DESCRIPTION

These functions implement Montgomery multiplication. They are used
automatically when L<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.

BN_MONT_CTX_new() allocates and initializes a B<BN_MONT_CTX> structure.

BN_MONT_CTX_set() sets up the I<mont> structure from the modulus I<m>
by precomputing its inverse and a value R.

BN_MONT_CTX_copy() copies the B<BN_MONT_CTX> I<from> to I<to>.

BN_MONT_CTX_free() frees the components of the B<BN_MONT_CTX>, and, if
it was created by BN_MONT_CTX_new(), also the structure itself.
If B<mont> is NULL, nothing is done.

BN_mod_mul_montgomery() computes Mont(I<a>,I<b>):=I<a>*I<b>*R^-1 and places
the result in I<r>.

BN_from_montgomery() performs the Montgomery reduction I<r> = I<a>*R^-1.

BN_to_montgomery() computes Mont(I<a>,R^2), i.e. I<a>*R.
Note that I<a> must be nonnegative and smaller than the modulus.

For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
temporary variables.

=head1 RETURN VALUES

BN_MONT_CTX_new() returns the newly allocated B<BN_MONT_CTX>, and NULL
on error.

BN_MONT_CTX_free() has no return value.

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

=head1 WARNINGS

The inputs must be reduced modulo B<m>, otherwise the result will be
outside the expected range.

=head1 SEE ALSO

L<ERR_get_error(3)>, L<BN_add(3)>,
L<BN_CTX_new(3)>

=head1 HISTORY

BN_MONT_CTX_init() was removed in OpenSSL 1.1.0

=head1 COPYRIGHT

Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the Apache License 2.0 (the "License").  You may not use
this file except in compliance with the License.  You can obtain a copy
in the file LICENSE in the source distribution or at
L<https://www.openssl.org/source/license.html>.

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