1=pod
2
3=head1 NAME
4
5BN_mod_mul_montgomery, BN_MONT_CTX_new,
6BN_MONT_CTX_free, BN_MONT_CTX_set, BN_MONT_CTX_copy,
7BN_from_montgomery, BN_to_montgomery - Montgomery multiplication
8
9=head1 SYNOPSIS
10
11 #include <openssl/bn.h>
12
13 BN_MONT_CTX *BN_MONT_CTX_new(void);
14 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
15
16 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
17 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
18
19 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
20                           BN_MONT_CTX *mont, BN_CTX *ctx);
21
22 int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
23                        BN_CTX *ctx);
24
25 int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
26                      BN_CTX *ctx);
27
28=head1 DESCRIPTION
29
30These functions implement Montgomery multiplication. They are used
31automatically when L<BN_mod_exp(3)> is called with suitable input,
32but they may be useful when several operations are to be performed
33using the same modulus.
34
35BN_MONT_CTX_new() allocates and initializes a B<BN_MONT_CTX> structure.
36
37BN_MONT_CTX_set() sets up the I<mont> structure from the modulus I<m>
38by precomputing its inverse and a value R.
39
40BN_MONT_CTX_copy() copies the B<BN_MONT_CTX> I<from> to I<to>.
41
42BN_MONT_CTX_free() frees the components of the B<BN_MONT_CTX>, and, if
43it was created by BN_MONT_CTX_new(), also the structure itself.
44If B<mont> is NULL, nothing is done.
45
46BN_mod_mul_montgomery() computes Mont(I<a>,I<b>):=I<a>*I<b>*R^-1 and places
47the result in I<r>.
48
49BN_from_montgomery() performs the Montgomery reduction I<r> = I<a>*R^-1.
50
51BN_to_montgomery() computes Mont(I<a>,R^2), i.e. I<a>*R.
52Note that I<a> must be nonnegative and smaller than the modulus.
53
54For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
55temporary variables.
56
57=head1 RETURN VALUES
58
59BN_MONT_CTX_new() returns the newly allocated B<BN_MONT_CTX>, and NULL
60on error.
61
62BN_MONT_CTX_free() has no return value.
63
64For the other functions, 1 is returned for success, 0 on error.
65The error codes can be obtained by L<ERR_get_error(3)>.
66
67=head1 WARNINGS
68
69The inputs must be reduced modulo B<m>, otherwise the result will be
70outside the expected range.
71
72=head1 SEE ALSO
73
74L<ERR_get_error(3)>, L<BN_add(3)>,
75L<BN_CTX_new(3)>
76
77=head1 HISTORY
78
79BN_MONT_CTX_init() was removed in OpenSSL 1.1.0
80
81=head1 COPYRIGHT
82
83Copyright 2000-2020 The OpenSSL Project Authors. All Rights Reserved.
84
85Licensed under the Apache License 2.0 (the "License").  You may not use
86this file except in compliance with the License.  You can obtain a copy
87in the file LICENSE in the source distribution or at
88L<https://www.openssl.org/source/license.html>.
89
90=cut
91