=pod
=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
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 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 structure.
BN_MONT_CTX_set() sets up the I structure from the modulus I
by precomputing its inverse and a value R.
BN_MONT_CTX_copy() copies the B I to I.
BN_MONT_CTX_free() frees the components of the B, and, if
it was created by BN_MONT_CTX_new(), also the structure itself.
If B is NULL, nothing is done.
BN_mod_mul_montgomery() computes Mont(I,I**):=I*****I*****R^-1 and places
the result in I.
BN_from_montgomery() performs the Montgomery reduction I = I*****R^-1.
BN_to_montgomery() computes Mont(I,R^2), i.e. I*R.
Note that I must be nonnegative and smaller than the modulus.
For all functions, I is a previously allocated B used for
temporary variables.
=head1 RETURN VALUES
BN_MONT_CTX_new() returns the newly allocated B, 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.
=head1 WARNINGS
The inputs must be reduced modulo B, otherwise the result will be
outside the expected range.
=head1 SEE ALSO
L, L,
L
=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 OpenSSL license (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.
=cut
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