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
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
|
/*
version 20081011
Matthew Dempsky
Public domain.
Derived from public domain code by D. J. Bernstein.
20140216 tweak: Mask top bit of point input.
*/
#include "config.h"
static void add (unsigned int out[32],
const unsigned int a[32],
const unsigned int b[32])
{
unsigned int j;
unsigned int u;
u = 0;
for (j = 0; j < 31; ++j) {
u += a[j] + b[j];
out[j] = u & 255;
u >>= 8;
}
u += a[31] + b[31];
out[31] = u;
}
static void curve25519_ref_sub (unsigned int out[32],
const unsigned int a[32],
const unsigned int b[32])
{
unsigned int j;
unsigned int u;
u = 218;
for (j = 0; j < 31; ++j) {
u += a[j] + 65280 - b[j];
out[j] = u & 255;
u >>= 8;
}
u += a[31] - b[31];
out[31] = u;
}
static void curve25519_ref_squeeze (unsigned int a[32])
{
unsigned int j;
unsigned int u;
u = 0;
for (j = 0; j < 31; ++j) {
u += a[j];
a[j] = u & 255;
u >>= 8;
}
u += a[31];
a[31] = u & 127;
u = 19 * (u >> 7);
for (j = 0; j < 31; ++j) {
u += a[j];
a[j] = u & 255;
u >>= 8;
}
u += a[31];
a[31] = u;
}
static const unsigned int minusp[32] = {
19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 128
};
static void curve25519_ref_freeze (unsigned int a[32])
{
unsigned int aorig[32];
unsigned int j;
unsigned int negative;
for (j = 0; j < 32; ++j)
aorig[j] = a[j];
add (a, a, minusp);
negative = -((a[31] >> 7) & 1);
for (j = 0; j < 32; ++j)
a[j] ^= negative & (aorig[j] ^ a[j]);
}
static void curve25519_ref_mult (unsigned int out[32],
const unsigned int a[32],
const unsigned int b[32])
{
unsigned int i;
unsigned int j;
unsigned int u;
for (i = 0; i < 32; ++i) {
u = 0;
for (j = 0; j <= i; ++j)
u += a[j] * b[i - j];
for (j = i + 1; j < 32; ++j)
u += 38 * a[j] * b[i + 32 - j];
out[i] = u;
}
curve25519_ref_squeeze (out);
}
static void curve25519_ref_mult121665 (unsigned int out[32], const unsigned int a[32])
{
unsigned int j;
unsigned int u;
u = 0;
for (j = 0; j < 31; ++j) {
u += 121665 * a[j];
out[j] = u & 255;
u >>= 8;
}
u += 121665 * a[31];
out[31] = u & 127;
u = 19 * (u >> 7);
for (j = 0; j < 31; ++j) {
u += out[j];
out[j] = u & 255;
u >>= 8;
}
u += out[j];
out[j] = u;
}
static void curve25519_ref_square (unsigned int out[32], const unsigned int a[32])
{
unsigned int i;
unsigned int j;
unsigned int u;
for (i = 0; i < 32; ++i) {
u = 0;
for (j = 0; j < i - j; ++j)
u += a[j] * a[i - j];
for (j = i + 1; j < i + 32 - j; ++j)
u += 38 * a[j] * a[i + 32 - j];
u *= 2;
if ((i & 1) == 0) {
u += a[i / 2] * a[i / 2];
u += 38 * a[i / 2 + 16] * a[i / 2 + 16];
}
out[i] = u;
}
curve25519_ref_squeeze (out);
}
static void curve25519_ref_select (unsigned int p[64],
unsigned int q[64],
const unsigned int r[64],
const unsigned int s[64],
unsigned int b)
{
unsigned int j;
unsigned int t;
unsigned int bminus1;
bminus1 = b - 1;
for (j = 0; j < 64; ++j) {
t = bminus1 & (r[j] ^ s[j]);
p[j] = s[j] ^ t;
q[j] = r[j] ^ t;
}
}
static void mainloop (unsigned int work[64], const unsigned char e[32])
{
unsigned int xzm1[64];
unsigned int xzm[64];
unsigned int xzmb[64];
unsigned int xzm1b[64];
unsigned int xznb[64];
unsigned int xzn1b[64];
unsigned int a0[64];
unsigned int a1[64];
unsigned int b0[64];
unsigned int b1[64];
unsigned int c1[64];
unsigned int r[32];
unsigned int s[32];
unsigned int t[32];
unsigned int u[32];
unsigned int i;
unsigned int j;
unsigned int b;
int pos;
for (j = 0; j < 32; ++j)
xzm1[j] = work[j];
xzm1[32] = 1;
for (j = 33; j < 64; ++j)
xzm1[j] = 0;
xzm[0] = 1;
for (j = 1; j < 64; ++j)
xzm[j] = 0;
for (pos = 254; pos >= 0; --pos) {
b = e[pos / 8] >> (pos & 7);
b &= 1;
curve25519_ref_select (xzmb, xzm1b, xzm, xzm1, b);
add (a0, xzmb, xzmb + 32);
curve25519_ref_sub (a0 + 32, xzmb, xzmb + 32);
add (a1, xzm1b, xzm1b + 32);
curve25519_ref_sub (a1 + 32, xzm1b, xzm1b + 32);
curve25519_ref_square (b0, a0);
curve25519_ref_square (b0 + 32, a0 + 32);
curve25519_ref_mult (b1, a1, a0 + 32);
curve25519_ref_mult (b1 + 32, a1 + 32, a0);
add (c1, b1, b1 + 32);
curve25519_ref_sub (c1 + 32, b1, b1 + 32);
curve25519_ref_square (r, c1 + 32);
curve25519_ref_sub (s, b0, b0 + 32);
curve25519_ref_mult121665 (t, s);
add (u, t, b0);
curve25519_ref_mult (xznb, b0, b0 + 32);
curve25519_ref_mult (xznb + 32, s, u);
curve25519_ref_square (xzn1b, c1);
curve25519_ref_mult (xzn1b + 32, r, work);
curve25519_ref_select (xzm, xzm1, xznb, xzn1b, b);
}
for (j = 0; j < 64; ++j)
work[j] = xzm[j];
}
static void recip (unsigned int out[32], const unsigned int z[32])
{
unsigned int z2[32];
unsigned int z9[32];
unsigned int z11[32];
unsigned int z2_5_0[32];
unsigned int z2_10_0[32];
unsigned int z2_20_0[32];
unsigned int z2_50_0[32];
unsigned int z2_100_0[32];
unsigned int t0[32];
unsigned int t1[32];
int i;
/* 2 */ curve25519_ref_square (z2, z);
/* 4 */ curve25519_ref_square (t1, z2);
/* 8 */ curve25519_ref_square (t0, t1);
/* 9 */ curve25519_ref_mult (z9, t0, z);
/* 11 */ curve25519_ref_mult (z11, z9, z2);
/* 22 */ curve25519_ref_square (t0, z11);
/* 2^5 - 2^0 = 31 */ curve25519_ref_mult (z2_5_0, t0, z9);
/* 2^6 - 2^1 */ curve25519_ref_square (t0, z2_5_0);
/* 2^7 - 2^2 */ curve25519_ref_square (t1, t0);
/* 2^8 - 2^3 */ curve25519_ref_square (t0, t1);
/* 2^9 - 2^4 */ curve25519_ref_square (t1, t0);
/* 2^10 - 2^5 */ curve25519_ref_square (t0, t1);
/* 2^10 - 2^0 */ curve25519_ref_mult (z2_10_0, t0, z2_5_0);
/* 2^11 - 2^1 */ curve25519_ref_square (t0, z2_10_0);
/* 2^12 - 2^2 */ curve25519_ref_square (t1, t0);
/* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) {
curve25519_ref_square (t0, t1);
curve25519_ref_square (t1, t0);
}
/* 2^20 - 2^0 */ curve25519_ref_mult (z2_20_0, t1, z2_10_0);
/* 2^21 - 2^1 */ curve25519_ref_square (t0, z2_20_0);
/* 2^22 - 2^2 */ curve25519_ref_square (t1, t0);
/* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) {
curve25519_ref_square (t0, t1);
curve25519_ref_square (t1, t0);
}
/* 2^40 - 2^0 */ curve25519_ref_mult (t0, t1, z2_20_0);
/* 2^41 - 2^1 */ curve25519_ref_square (t1, t0);
/* 2^42 - 2^2 */ curve25519_ref_square (t0, t1);
/* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) {
curve25519_ref_square (t1, t0);
curve25519_ref_square (t0, t1);
}
/* 2^50 - 2^0 */ curve25519_ref_mult (z2_50_0, t0, z2_10_0);
/* 2^51 - 2^1 */ curve25519_ref_square (t0, z2_50_0);
/* 2^52 - 2^2 */ curve25519_ref_square (t1, t0);
/* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) {
curve25519_ref_square (t0, t1);
curve25519_ref_square (t1, t0);
}
/* 2^100 - 2^0 */ curve25519_ref_mult (z2_100_0, t1, z2_50_0);
/* 2^101 - 2^1 */ curve25519_ref_square (t1, z2_100_0);
/* 2^102 - 2^2 */ curve25519_ref_square (t0, t1);
/* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) {
curve25519_ref_square (t1, t0);
curve25519_ref_square (t0, t1);
}
/* 2^200 - 2^0 */ curve25519_ref_mult (t1, t0, z2_100_0);
/* 2^201 - 2^1 */ curve25519_ref_square (t0, t1);
/* 2^202 - 2^2 */ curve25519_ref_square (t1, t0);
/* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) {
curve25519_ref_square (t0, t1);
curve25519_ref_square (t1, t0);
}
/* 2^250 - 2^0 */ curve25519_ref_mult (t0, t1, z2_50_0);
/* 2^251 - 2^1 */ curve25519_ref_square (t1, t0);
/* 2^252 - 2^2 */ curve25519_ref_square (t0, t1);
/* 2^253 - 2^3 */ curve25519_ref_square (t1, t0);
/* 2^254 - 2^4 */ curve25519_ref_square (t0, t1);
/* 2^255 - 2^5 */ curve25519_ref_square (t1, t0);
/* 2^255 - 21 */ curve25519_ref_mult (out, t1, z11);
}
int scalarmult_ref (unsigned char *q,
const unsigned char *n,
const unsigned char *p)
{
unsigned int work[96];
unsigned char e[32];
unsigned int i;
for (i = 0; i < 32; ++i)
e[i] = n[i];
e[0] &= 248;
e[31] &= 127;
e[31] |= 64;
for (i = 0; i < 32; ++i)
work[i] = p[i];
work[31] &= 127;
mainloop (work, e);
recip (work + 32, work + 32);
curve25519_ref_mult (work + 64, work, work + 32);
curve25519_ref_freeze (work + 64);
for (i = 0; i < 32; ++i)
q[i] = work[64 + i];
return 0;
}
|
