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
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
|
/*
* Copyright 2017-2019 The OpenSSL Project Authors. All Rights Reserved.
* Copyright 2015-2016 Cryptography Research, Inc.
*
* 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 Mike Hamburg
*/
#include <openssl/crypto.h>
#include "word.h"
#include "point_448.h"
static const c448_word_t MONTGOMERY_FACTOR = (c448_word_t) 0x3bd440fae918bc5ULL;
static const curve448_scalar_t sc_p = {
{
{
SC_LIMB(0x2378c292ab5844f3ULL), SC_LIMB(0x216cc2728dc58f55ULL),
SC_LIMB(0xc44edb49aed63690ULL), SC_LIMB(0xffffffff7cca23e9ULL),
SC_LIMB(0xffffffffffffffffULL), SC_LIMB(0xffffffffffffffffULL),
SC_LIMB(0x3fffffffffffffffULL)
}
}
}, sc_r2 = {
{
{
SC_LIMB(0xe3539257049b9b60ULL), SC_LIMB(0x7af32c4bc1b195d9ULL),
SC_LIMB(0x0d66de2388ea1859ULL), SC_LIMB(0xae17cf725ee4d838ULL),
SC_LIMB(0x1a9cc14ba3c47c44ULL), SC_LIMB(0x2052bcb7e4d070afULL),
SC_LIMB(0x3402a939f823b729ULL)
}
}
};
#define WBITS C448_WORD_BITS /* NB this may be different from ARCH_WORD_BITS */
const curve448_scalar_t curve448_scalar_one = {{{1}}};
const curve448_scalar_t curve448_scalar_zero = {{{0}}};
/*
* {extra,accum} - sub +? p
* Must have extra <= 1
*/
static void sc_subx(curve448_scalar_t out,
const c448_word_t accum[C448_SCALAR_LIMBS],
const curve448_scalar_t sub,
const curve448_scalar_t p, c448_word_t extra)
{
c448_dsword_t chain = 0;
unsigned int i;
c448_word_t borrow;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
chain = (chain + accum[i]) - sub->limb[i];
out->limb[i] = (c448_word_t)chain;
chain >>= WBITS;
}
borrow = (c448_word_t)chain + extra; /* = 0 or -1 */
chain = 0;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
chain = (chain + out->limb[i]) + (p->limb[i] & borrow);
out->limb[i] = (c448_word_t)chain;
chain >>= WBITS;
}
}
static void sc_montmul(curve448_scalar_t out, const curve448_scalar_t a,
const curve448_scalar_t b)
{
unsigned int i, j;
c448_word_t accum[C448_SCALAR_LIMBS + 1] = { 0 };
c448_word_t hi_carry = 0;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
c448_word_t mand = a->limb[i];
const c448_word_t *mier = b->limb;
c448_dword_t chain = 0;
for (j = 0; j < C448_SCALAR_LIMBS; j++) {
chain += ((c448_dword_t) mand) * mier[j] + accum[j];
accum[j] = (c448_word_t)chain;
chain >>= WBITS;
}
accum[j] = (c448_word_t)chain;
mand = accum[0] * MONTGOMERY_FACTOR;
chain = 0;
mier = sc_p->limb;
for (j = 0; j < C448_SCALAR_LIMBS; j++) {
chain += (c448_dword_t) mand *mier[j] + accum[j];
if (j)
accum[j - 1] = (c448_word_t)chain;
chain >>= WBITS;
}
chain += accum[j];
chain += hi_carry;
accum[j - 1] = (c448_word_t)chain;
hi_carry = chain >> WBITS;
}
sc_subx(out, accum, sc_p, sc_p, hi_carry);
}
void curve448_scalar_mul(curve448_scalar_t out, const curve448_scalar_t a,
const curve448_scalar_t b)
{
sc_montmul(out, a, b);
sc_montmul(out, out, sc_r2);
}
void curve448_scalar_sub(curve448_scalar_t out, const curve448_scalar_t a,
const curve448_scalar_t b)
{
sc_subx(out, a->limb, b, sc_p, 0);
}
void curve448_scalar_add(curve448_scalar_t out, const curve448_scalar_t a,
const curve448_scalar_t b)
{
c448_dword_t chain = 0;
unsigned int i;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
chain = (chain + a->limb[i]) + b->limb[i];
out->limb[i] = (c448_word_t)chain;
chain >>= WBITS;
}
sc_subx(out, out->limb, sc_p, sc_p, (c448_word_t)chain);
}
static ossl_inline void scalar_decode_short(curve448_scalar_t s,
const unsigned char *ser,
size_t nbytes)
{
size_t i, j, k = 0;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
c448_word_t out = 0;
for (j = 0; j < sizeof(c448_word_t) && k < nbytes; j++, k++)
out |= ((c448_word_t) ser[k]) << (8 * j);
s->limb[i] = out;
}
}
c448_error_t curve448_scalar_decode(
curve448_scalar_t s,
const unsigned char ser[C448_SCALAR_BYTES])
{
unsigned int i;
c448_dsword_t accum = 0;
scalar_decode_short(s, ser, C448_SCALAR_BYTES);
for (i = 0; i < C448_SCALAR_LIMBS; i++)
accum = (accum + s->limb[i] - sc_p->limb[i]) >> WBITS;
/* Here accum == 0 or -1 */
curve448_scalar_mul(s, s, curve448_scalar_one); /* ham-handed reduce */
return c448_succeed_if(~word_is_zero((uint32_t)accum));
}
void curve448_scalar_destroy(curve448_scalar_t scalar)
{
OPENSSL_cleanse(scalar, sizeof(curve448_scalar_t));
}
void curve448_scalar_decode_long(curve448_scalar_t s,
const unsigned char *ser, size_t ser_len)
{
size_t i;
curve448_scalar_t t1, t2;
if (ser_len == 0) {
curve448_scalar_copy(s, curve448_scalar_zero);
return;
}
i = ser_len - (ser_len % C448_SCALAR_BYTES);
if (i == ser_len)
i -= C448_SCALAR_BYTES;
scalar_decode_short(t1, &ser[i], ser_len - i);
if (ser_len == sizeof(curve448_scalar_t)) {
assert(i == 0);
/* ham-handed reduce */
curve448_scalar_mul(s, t1, curve448_scalar_one);
curve448_scalar_destroy(t1);
return;
}
while (i) {
i -= C448_SCALAR_BYTES;
sc_montmul(t1, t1, sc_r2);
(void)curve448_scalar_decode(t2, ser + i);
curve448_scalar_add(t1, t1, t2);
}
curve448_scalar_copy(s, t1);
curve448_scalar_destroy(t1);
curve448_scalar_destroy(t2);
}
void curve448_scalar_encode(unsigned char ser[C448_SCALAR_BYTES],
const curve448_scalar_t s)
{
unsigned int i, j, k = 0;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
for (j = 0; j < sizeof(c448_word_t); j++, k++)
ser[k] = s->limb[i] >> (8 * j);
}
}
void curve448_scalar_halve(curve448_scalar_t out, const curve448_scalar_t a)
{
c448_word_t mask = 0 - (a->limb[0] & 1);
c448_dword_t chain = 0;
unsigned int i;
for (i = 0; i < C448_SCALAR_LIMBS; i++) {
chain = (chain + a->limb[i]) + (sc_p->limb[i] & mask);
out->limb[i] = (c448_word_t)chain;
chain >>= C448_WORD_BITS;
}
for (i = 0; i < C448_SCALAR_LIMBS - 1; i++)
out->limb[i] = out->limb[i] >> 1 | out->limb[i + 1] << (WBITS - 1);
out->limb[i] = out->limb[i] >> 1 | (c448_word_t)(chain << (WBITS - 1));
}
|
