1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
|
=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 <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 non-negative 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 WARNING
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 2000-2017 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<https://www.openssl.org/source/license.html>.
=cut
|
