1 /*
2 * Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved.
3 * Copyright (c) 2014, Intel Corporation. All Rights Reserved.
4 *
5 * Licensed under the OpenSSL license (the "License"). You may not use
6 * this file except in compliance with the License. You can obtain a copy
7 * in the file LICENSE in the source distribution or at
8 * https://www.openssl.org/source/license.html
9 *
10 * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1)
11 * (1) Intel Corporation, Israel Development Center, Haifa, Israel
12 * (2) University of Haifa, Israel
13 *
14 * Reference:
15 * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
16 * 256 Bit Primes"
17 */
18
19 #ifndef OPENSSL_HEADER_EC_P256_X86_64_H
20 #define OPENSSL_HEADER_EC_P256_X86_64_H
21
22 #include <openssl/base.h>
23
24 #include <openssl/bn.h>
25
26 #include "../bn/internal.h"
27
28 #if defined(__cplusplus)
29 extern "C" {
30 #endif
31
32
33 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
34 !defined(OPENSSL_SMALL)
35
36 // P-256 field operations.
37 //
38 // An element mod P in P-256 is represented as a little-endian array of
39 // |P256_LIMBS| |BN_ULONG|s, spanning the full range of values.
40 //
41 // The following functions take fully-reduced inputs mod P and give
42 // fully-reduced outputs. They may be used in-place.
43
44 #define P256_LIMBS (256 / BN_BITS2)
45
46 // ecp_nistz256_neg sets |res| to -|a| mod P.
47 void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
48
49 // ecp_nistz256_mul_mont sets |res| to |a| * |b| * 2^-256 mod P.
50 void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
51 const BN_ULONG a[P256_LIMBS],
52 const BN_ULONG b[P256_LIMBS]);
53
54 // ecp_nistz256_sqr_mont sets |res| to |a| * |a| * 2^-256 mod P.
55 void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
56 const BN_ULONG a[P256_LIMBS]);
57
58 // ecp_nistz256_from_mont sets |res| to |in|, converted from Montgomery domain
59 // by multiplying with 1.
ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],const BN_ULONG in[P256_LIMBS])60 static inline void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
61 const BN_ULONG in[P256_LIMBS]) {
62 static const BN_ULONG ONE[P256_LIMBS] = { 1 };
63 ecp_nistz256_mul_mont(res, in, ONE);
64 }
65
66 // ecp_nistz256_to_mont sets |res| to |in|, converted to Montgomery domain
67 // by multiplying with RR = 2^512 mod P precomputed for NIST P256 curve.
ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],const BN_ULONG in[P256_LIMBS])68 static inline void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
69 const BN_ULONG in[P256_LIMBS]) {
70 static const BN_ULONG RR[P256_LIMBS] = {
71 TOBN(0x00000000, 0x00000003), TOBN(0xfffffffb, 0xffffffff),
72 TOBN(0xffffffff, 0xfffffffe), TOBN(0x00000004, 0xfffffffd)};
73 ecp_nistz256_mul_mont(res, in, RR);
74 }
75
76
77 // P-256 scalar operations.
78 //
79 // The following functions compute modulo N, where N is the order of P-256. They
80 // take fully-reduced inputs and give fully-reduced outputs.
81
82 // ecp_nistz256_ord_mul_mont sets |res| to |a| * |b| where inputs and outputs
83 // are in Montgomery form. That is, |res| is |a| * |b| * 2^-256 mod N.
84 void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
85 const BN_ULONG a[P256_LIMBS],
86 const BN_ULONG b[P256_LIMBS]);
87
88 // ecp_nistz256_ord_sqr_mont sets |res| to |a|^(2*|rep|) where inputs and
89 // outputs are in Montgomery form. That is, |res| is
90 // (|a| * 2^-256)^(2*|rep|) * 2^256 mod N.
91 void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
92 const BN_ULONG a[P256_LIMBS], BN_ULONG rep);
93
94 // beeu_mod_inverse_vartime sets out = a^-1 mod p using a Euclidean algorithm.
95 // Assumption: 0 < a < p < 2^(256) and p is odd.
96 int beeu_mod_inverse_vartime(BN_ULONG out[P256_LIMBS],
97 const BN_ULONG a[P256_LIMBS],
98 const BN_ULONG p[P256_LIMBS]);
99
100
101 // P-256 point operations.
102 //
103 // The following functions may be used in-place. All coordinates are in the
104 // Montgomery domain.
105
106 // A P256_POINT represents a P-256 point in Jacobian coordinates.
107 typedef struct {
108 BN_ULONG X[P256_LIMBS];
109 BN_ULONG Y[P256_LIMBS];
110 BN_ULONG Z[P256_LIMBS];
111 } P256_POINT;
112
113 // A P256_POINT_AFFINE represents a P-256 point in affine coordinates. Infinity
114 // is encoded as (0, 0).
115 typedef struct {
116 BN_ULONG X[P256_LIMBS];
117 BN_ULONG Y[P256_LIMBS];
118 } P256_POINT_AFFINE;
119
120 // ecp_nistz256_select_w5 sets |*val| to |in_t[index-1]| if 1 <= |index| <= 16
121 // and all zeros (the point at infinity) if |index| is 0. This is done in
122 // constant time.
123 void ecp_nistz256_select_w5(P256_POINT *val, const P256_POINT in_t[16],
124 int index);
125
126 // ecp_nistz256_select_w7 sets |*val| to |in_t[index-1]| if 1 <= |index| <= 64
127 // and all zeros (the point at infinity) if |index| is 0. This is done in
128 // constant time.
129 void ecp_nistz256_select_w7(P256_POINT_AFFINE *val,
130 const P256_POINT_AFFINE in_t[64], int index);
131
132 // ecp_nistz256_point_double sets |r| to |a| doubled.
133 void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
134
135 // ecp_nistz256_point_add adds |a| to |b| and places the result in |r|.
136 void ecp_nistz256_point_add(P256_POINT *r, const P256_POINT *a,
137 const P256_POINT *b);
138
139 // ecp_nistz256_point_add_affine adds |a| to |b| and places the result in
140 // |r|. |a| and |b| must not represent the same point unless they are both
141 // infinity.
142 void ecp_nistz256_point_add_affine(P256_POINT *r, const P256_POINT *a,
143 const P256_POINT_AFFINE *b);
144
145 #endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
146 !defined(OPENSSL_SMALL) */
147
148
149 #if defined(__cplusplus)
150 } // extern C++
151 #endif
152
153 #endif // OPENSSL_HEADER_EC_P256_X86_64_H
154