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 |
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. |
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. |
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 | |