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
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
|
/*
* Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2014, Intel Corporation. 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
* https://www.openssl.org/source/license.html
*
* Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1)
* (1) Intel Corporation, Israel Development Center, Haifa, Israel
* (2) University of Haifa, Israel
*
* Reference:
* S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
* 256 Bit Primes"
*/
#ifndef OPENSSL_HEADER_EC_P256_X86_64_H
#define OPENSSL_HEADER_EC_P256_X86_64_H
#include <openssl/base.h>
#include <openssl/bn.h>
#include "../bn/internal.h"
#if defined(__cplusplus)
extern "C" {
#endif
#if !defined(OPENSSL_NO_ASM) && \
(defined(OPENSSL_X86_64) || defined(OPENSSL_AARCH64)) && \
!defined(OPENSSL_SMALL)
// P-256 field operations.
//
// An element mod P in P-256 is represented as a little-endian array of
// |P256_LIMBS| |BN_ULONG|s, spanning the full range of values.
//
// The following functions take fully-reduced inputs mod P and give
// fully-reduced outputs. They may be used in-place.
#define P256_LIMBS (256 / BN_BITS2)
// ecp_nistz256_neg sets |res| to -|a| mod P.
void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
// ecp_nistz256_mul_mont sets |res| to |a| * |b| * 2^-256 mod P.
void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS]);
// ecp_nistz256_sqr_mont sets |res| to |a| * |a| * 2^-256 mod P.
void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS]);
// ecp_nistz256_from_mont sets |res| to |in|, converted from Montgomery domain
// by multiplying with 1.
static inline void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG in[P256_LIMBS]) {
static const BN_ULONG ONE[P256_LIMBS] = { 1 };
ecp_nistz256_mul_mont(res, in, ONE);
}
// P-256 scalar operations.
//
// The following functions compute modulo N, where N is the order of P-256. They
// take fully-reduced inputs and give fully-reduced outputs.
// ecp_nistz256_ord_mul_mont sets |res| to |a| * |b| where inputs and outputs
// are in Montgomery form. That is, |res| is |a| * |b| * 2^-256 mod N.
void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS],
const BN_ULONG b[P256_LIMBS]);
// ecp_nistz256_ord_sqr_mont sets |res| to |a|^(2*|rep|) where inputs and
// outputs are in Montgomery form. That is, |res| is
// (|a| * 2^-256)^(2*|rep|) * 2^256 mod N.
void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
const BN_ULONG a[P256_LIMBS], BN_ULONG rep);
// beeu_mod_inverse_vartime sets out = a^-1 mod p using a Euclidean algorithm.
// Assumption: 0 < a < p < 2^(256) and p is odd.
int beeu_mod_inverse_vartime(BN_ULONG out[P256_LIMBS],
const BN_ULONG a[P256_LIMBS],
const BN_ULONG p[P256_LIMBS]);
// P-256 point operations.
//
// The following functions may be used in-place. All coordinates are in the
// Montgomery domain.
// A P256_POINT represents a P-256 point in Jacobian coordinates.
typedef struct {
BN_ULONG X[P256_LIMBS];
BN_ULONG Y[P256_LIMBS];
BN_ULONG Z[P256_LIMBS];
} P256_POINT;
// A P256_POINT_AFFINE represents a P-256 point in affine coordinates. Infinity
// is encoded as (0, 0).
typedef struct {
BN_ULONG X[P256_LIMBS];
BN_ULONG Y[P256_LIMBS];
} P256_POINT_AFFINE;
// ecp_nistz256_select_w5 sets |*val| to |in_t[index-1]| if 1 <= |index| <= 16
// and all zeros (the point at infinity) if |index| is 0. This is done in
// constant time.
void ecp_nistz256_select_w5(P256_POINT *val, const P256_POINT in_t[16],
int index);
// ecp_nistz256_select_w7 sets |*val| to |in_t[index-1]| if 1 <= |index| <= 64
// and all zeros (the point at infinity) if |index| is 0. This is done in
// constant time.
void ecp_nistz256_select_w7(P256_POINT_AFFINE *val,
const P256_POINT_AFFINE in_t[64], int index);
// ecp_nistz256_point_double sets |r| to |a| doubled.
void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
// ecp_nistz256_point_add adds |a| to |b| and places the result in |r|.
void ecp_nistz256_point_add(P256_POINT *r, const P256_POINT *a,
const P256_POINT *b);
// ecp_nistz256_point_add_affine adds |a| to |b| and places the result in
// |r|. |a| and |b| must not represent the same point unless they are both
// infinity.
void ecp_nistz256_point_add_affine(P256_POINT *r, const P256_POINT *a,
const P256_POINT_AFFINE *b);
#endif /* !defined(OPENSSL_NO_ASM) && \
(defined(OPENSSL_X86_64) || defined(OPENSSL_AARCH64)) && \
!defined(OPENSSL_SMALL) */
#if defined(__cplusplus)
} // extern C++
#endif
#endif // OPENSSL_HEADER_EC_P256_X86_64_H
|
