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aa6bb135 | 1 | /* |
3a86f1db | 2 | * Copyright 2016-2019 The OpenSSL Project Authors. All Rights Reserved. |
df3bde67 | 3 | * |
a7f182b7 | 4 | * Licensed under the Apache License 2.0 (the "License"). You may not use |
aa6bb135 RS |
5 | * this file except in compliance with the License. You can obtain a copy |
6 | * in the file LICENSE in the source distribution or at | |
7 | * https://www.openssl.org/source/license.html | |
df3bde67 | 8 | */ |
a90def6b | 9 | |
a90def6b | 10 | #include <string.h> |
706457b7 | 11 | #include "ec_local.h" |
06c6d05f | 12 | #include <openssl/sha.h> |
a90def6b | 13 | |
3c849bc9 AP |
14 | #if defined(X25519_ASM) && (defined(__x86_64) || defined(__x86_64__) || \ |
15 | defined(_M_AMD64) || defined(_M_X64)) | |
cfc32a1e | 16 | |
3c849bc9 | 17 | # define BASE_2_64_IMPLEMENTED |
c521e439 AP |
18 | |
19 | typedef uint64_t fe64[4]; | |
20 | ||
91860165 | 21 | int x25519_fe64_eligible(void); |
c521e439 AP |
22 | |
23 | /* | |
3c849bc9 AP |
24 | * Following subroutines perform corresponding operations modulo |
25 | * 2^256-38, i.e. double the curve modulus. However, inputs and | |
26 | * outputs are permitted to be partially reduced, i.e. to remain | |
27 | * in [0..2^256) range. It's all tied up in final fe64_tobytes | |
28 | * that performs full reduction modulo 2^255-19. | |
29 | * | |
30 | * There are no reference C implementations for these. | |
c521e439 AP |
31 | */ |
32 | void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g); | |
33 | void x25519_fe64_sqr(fe64 h, const fe64 f); | |
34 | void x25519_fe64_mul121666(fe64 h, fe64 f); | |
35 | void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g); | |
36 | void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g); | |
37 | void x25519_fe64_tobytes(uint8_t *s, const fe64 f); | |
3c849bc9 AP |
38 | # define fe64_mul x25519_fe64_mul |
39 | # define fe64_sqr x25519_fe64_sqr | |
40 | # define fe64_mul121666 x25519_fe64_mul121666 | |
41 | # define fe64_add x25519_fe64_add | |
42 | # define fe64_sub x25519_fe64_sub | |
43 | # define fe64_tobytes x25519_fe64_tobytes | |
c521e439 AP |
44 | |
45 | static uint64_t load_8(const uint8_t *in) | |
46 | { | |
47 | uint64_t result; | |
48 | ||
49 | result = in[0]; | |
50 | result |= ((uint64_t)in[1]) << 8; | |
51 | result |= ((uint64_t)in[2]) << 16; | |
52 | result |= ((uint64_t)in[3]) << 24; | |
53 | result |= ((uint64_t)in[4]) << 32; | |
54 | result |= ((uint64_t)in[5]) << 40; | |
55 | result |= ((uint64_t)in[6]) << 48; | |
56 | result |= ((uint64_t)in[7]) << 56; | |
57 | ||
58 | return result; | |
59 | } | |
60 | ||
61 | static void fe64_frombytes(fe64 h, const uint8_t *s) | |
62 | { | |
63 | h[0] = load_8(s); | |
64 | h[1] = load_8(s + 8); | |
65 | h[2] = load_8(s + 16); | |
66 | h[3] = load_8(s + 24) & 0x7fffffffffffffff; | |
67 | } | |
68 | ||
69 | static void fe64_0(fe64 h) | |
70 | { | |
71 | h[0] = 0; | |
72 | h[1] = 0; | |
73 | h[2] = 0; | |
74 | h[3] = 0; | |
75 | } | |
76 | ||
77 | static void fe64_1(fe64 h) | |
78 | { | |
79 | h[0] = 1; | |
80 | h[1] = 0; | |
81 | h[2] = 0; | |
82 | h[3] = 0; | |
83 | } | |
84 | ||
85 | static void fe64_copy(fe64 h, const fe64 f) | |
86 | { | |
87 | h[0] = f[0]; | |
88 | h[1] = f[1]; | |
89 | h[2] = f[2]; | |
90 | h[3] = f[3]; | |
91 | } | |
92 | ||
93 | static void fe64_cswap(fe64 f, fe64 g, unsigned int b) | |
94 | { | |
95 | int i; | |
96 | uint64_t mask = 0 - (uint64_t)b; | |
97 | ||
98 | for (i = 0; i < 4; i++) { | |
99 | uint64_t x = f[i] ^ g[i]; | |
100 | x &= mask; | |
101 | f[i] ^= x; | |
102 | g[i] ^= x; | |
103 | } | |
104 | } | |
105 | ||
106 | static void fe64_invert(fe64 out, const fe64 z) | |
107 | { | |
108 | fe64 t0; | |
109 | fe64 t1; | |
110 | fe64 t2; | |
111 | fe64 t3; | |
112 | int i; | |
113 | ||
114 | /* | |
115 | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as | |
116 | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. | |
117 | */ | |
118 | ||
119 | /* t0 = z ** 2 */ | |
120 | fe64_sqr(t0, z); | |
121 | ||
122 | /* t1 = t0 ** (2 ** 2) = z ** 8 */ | |
123 | fe64_sqr(t1, t0); | |
124 | fe64_sqr(t1, t1); | |
125 | ||
126 | /* t1 = z * t1 = z ** 9 */ | |
127 | fe64_mul(t1, z, t1); | |
128 | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ | |
129 | fe64_mul(t0, t0, t1); | |
130 | ||
131 | /* t2 = t0 ** 2 = z ** 22 */ | |
132 | fe64_sqr(t2, t0); | |
133 | ||
134 | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ | |
135 | fe64_mul(t1, t1, t2); | |
136 | ||
137 | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ | |
138 | fe64_sqr(t2, t1); | |
139 | for (i = 1; i < 5; ++i) | |
140 | fe64_sqr(t2, t2); | |
141 | ||
142 | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ | |
143 | fe64_mul(t1, t2, t1); | |
144 | ||
145 | /* Continuing similarly... */ | |
146 | ||
147 | /* t2 = z ** (2 ** 20 - 1) */ | |
148 | fe64_sqr(t2, t1); | |
149 | for (i = 1; i < 10; ++i) | |
150 | fe64_sqr(t2, t2); | |
151 | ||
152 | fe64_mul(t2, t2, t1); | |
153 | ||
154 | /* t2 = z ** (2 ** 40 - 1) */ | |
155 | fe64_sqr(t3, t2); | |
156 | for (i = 1; i < 20; ++i) | |
157 | fe64_sqr(t3, t3); | |
158 | ||
159 | fe64_mul(t2, t3, t2); | |
160 | ||
161 | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ | |
162 | for (i = 0; i < 10; ++i) | |
163 | fe64_sqr(t2, t2); | |
164 | ||
165 | /* t1 = z ** (2 ** 50 - 1) */ | |
166 | fe64_mul(t1, t2, t1); | |
167 | ||
168 | /* t2 = z ** (2 ** 100 - 1) */ | |
169 | fe64_sqr(t2, t1); | |
170 | for (i = 1; i < 50; ++i) | |
171 | fe64_sqr(t2, t2); | |
172 | ||
173 | fe64_mul(t2, t2, t1); | |
174 | ||
175 | /* t2 = z ** (2 ** 200 - 1) */ | |
176 | fe64_sqr(t3, t2); | |
177 | for (i = 1; i < 100; ++i) | |
178 | fe64_sqr(t3, t3); | |
179 | ||
180 | fe64_mul(t2, t3, t2); | |
181 | ||
182 | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ | |
183 | for (i = 0; i < 50; ++i) | |
184 | fe64_sqr(t2, t2); | |
185 | ||
186 | /* t1 = z ** (2 ** 250 - 1) */ | |
187 | fe64_mul(t1, t2, t1); | |
188 | ||
189 | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ | |
190 | for (i = 0; i < 5; ++i) | |
191 | fe64_sqr(t1, t1); | |
192 | ||
193 | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ | |
194 | fe64_mul(out, t1, t0); | |
195 | } | |
196 | ||
197 | /* | |
198 | * Duplicate of original x25519_scalar_mult_generic, but using | |
199 | * fe64_* subroutines. | |
200 | */ | |
201 | static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32], | |
202 | const uint8_t point[32]) | |
203 | { | |
204 | fe64 x1, x2, z2, x3, z3, tmp0, tmp1; | |
205 | uint8_t e[32]; | |
206 | unsigned swap = 0; | |
207 | int pos; | |
208 | ||
209 | memcpy(e, scalar, 32); | |
210 | e[0] &= 0xf8; | |
211 | e[31] &= 0x7f; | |
212 | e[31] |= 0x40; | |
213 | fe64_frombytes(x1, point); | |
214 | fe64_1(x2); | |
215 | fe64_0(z2); | |
216 | fe64_copy(x3, x1); | |
217 | fe64_1(z3); | |
218 | ||
219 | for (pos = 254; pos >= 0; --pos) { | |
220 | unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); | |
221 | ||
222 | swap ^= b; | |
223 | fe64_cswap(x2, x3, swap); | |
224 | fe64_cswap(z2, z3, swap); | |
225 | swap = b; | |
226 | fe64_sub(tmp0, x3, z3); | |
227 | fe64_sub(tmp1, x2, z2); | |
228 | fe64_add(x2, x2, z2); | |
229 | fe64_add(z2, x3, z3); | |
230 | fe64_mul(z3, x2, tmp0); | |
231 | fe64_mul(z2, z2, tmp1); | |
232 | fe64_sqr(tmp0, tmp1); | |
233 | fe64_sqr(tmp1, x2); | |
234 | fe64_add(x3, z3, z2); | |
235 | fe64_sub(z2, z3, z2); | |
236 | fe64_mul(x2, tmp1, tmp0); | |
237 | fe64_sub(tmp1, tmp1, tmp0); | |
238 | fe64_sqr(z2, z2); | |
239 | fe64_mul121666(z3, tmp1); | |
240 | fe64_sqr(x3, x3); | |
241 | fe64_add(tmp0, tmp0, z3); | |
242 | fe64_mul(z3, x1, z2); | |
243 | fe64_mul(z2, tmp1, tmp0); | |
244 | } | |
245 | ||
246 | fe64_invert(z2, z2); | |
247 | fe64_mul(x2, x2, z2); | |
248 | fe64_tobytes(out, x2); | |
249 | ||
250 | OPENSSL_cleanse(e, sizeof(e)); | |
251 | } | |
3c849bc9 | 252 | #endif |
c521e439 | 253 | |
3c849bc9 AP |
254 | #if defined(X25519_ASM) \ |
255 | || ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \ | |
256 | && !defined(__sparc__) \ | |
3a86f1db | 257 | && (!defined(__SIZEOF_LONG__) || (__SIZEOF_LONG__ == 8)) \ |
3c849bc9 AP |
258 | && !(defined(__ANDROID__) && !defined(__clang__)) ) |
259 | /* | |
260 | * Base 2^51 implementation. It's virtually no different from reference | |
261 | * base 2^25.5 implementation in respect to lax boundary conditions for | |
262 | * intermediate values and even individual limbs. So that whatever you | |
263 | * know about the reference, applies even here... | |
264 | */ | |
265 | # define BASE_2_51_IMPLEMENTED | |
266 | ||
267 | typedef uint64_t fe51[5]; | |
268 | ||
269 | static const uint64_t MASK51 = 0x7ffffffffffff; | |
270 | ||
271 | static uint64_t load_7(const uint8_t *in) | |
272 | { | |
273 | uint64_t result; | |
274 | ||
275 | result = in[0]; | |
276 | result |= ((uint64_t)in[1]) << 8; | |
277 | result |= ((uint64_t)in[2]) << 16; | |
278 | result |= ((uint64_t)in[3]) << 24; | |
279 | result |= ((uint64_t)in[4]) << 32; | |
280 | result |= ((uint64_t)in[5]) << 40; | |
281 | result |= ((uint64_t)in[6]) << 48; | |
282 | ||
283 | return result; | |
284 | } | |
285 | ||
286 | static uint64_t load_6(const uint8_t *in) | |
287 | { | |
288 | uint64_t result; | |
289 | ||
290 | result = in[0]; | |
291 | result |= ((uint64_t)in[1]) << 8; | |
292 | result |= ((uint64_t)in[2]) << 16; | |
293 | result |= ((uint64_t)in[3]) << 24; | |
294 | result |= ((uint64_t)in[4]) << 32; | |
295 | result |= ((uint64_t)in[5]) << 40; | |
296 | ||
297 | return result; | |
298 | } | |
299 | ||
300 | static void fe51_frombytes(fe51 h, const uint8_t *s) | |
301 | { | |
302 | uint64_t h0 = load_7(s); /* 56 bits */ | |
303 | uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */ | |
304 | uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */ | |
305 | uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */ | |
306 | uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */ | |
307 | ||
308 | h1 |= h0 >> 51; h0 &= MASK51; | |
309 | h2 |= h1 >> 51; h1 &= MASK51; | |
310 | h3 |= h2 >> 51; h2 &= MASK51; | |
311 | h4 |= h3 >> 51; h3 &= MASK51; | |
312 | ||
313 | h[0] = h0; | |
314 | h[1] = h1; | |
315 | h[2] = h2; | |
316 | h[3] = h3; | |
317 | h[4] = h4; | |
318 | } | |
319 | ||
320 | static void fe51_tobytes(uint8_t *s, const fe51 h) | |
321 | { | |
322 | uint64_t h0 = h[0]; | |
323 | uint64_t h1 = h[1]; | |
324 | uint64_t h2 = h[2]; | |
325 | uint64_t h3 = h[3]; | |
326 | uint64_t h4 = h[4]; | |
327 | uint64_t q; | |
328 | ||
329 | /* compare to modulus */ | |
330 | q = (h0 + 19) >> 51; | |
331 | q = (h1 + q) >> 51; | |
332 | q = (h2 + q) >> 51; | |
333 | q = (h3 + q) >> 51; | |
334 | q = (h4 + q) >> 51; | |
335 | ||
336 | /* full reduce */ | |
337 | h0 += 19 * q; | |
338 | h1 += h0 >> 51; h0 &= MASK51; | |
339 | h2 += h1 >> 51; h1 &= MASK51; | |
340 | h3 += h2 >> 51; h2 &= MASK51; | |
341 | h4 += h3 >> 51; h3 &= MASK51; | |
342 | h4 &= MASK51; | |
343 | ||
344 | /* smash */ | |
345 | s[0] = (uint8_t)(h0 >> 0); | |
346 | s[1] = (uint8_t)(h0 >> 8); | |
347 | s[2] = (uint8_t)(h0 >> 16); | |
348 | s[3] = (uint8_t)(h0 >> 24); | |
349 | s[4] = (uint8_t)(h0 >> 32); | |
350 | s[5] = (uint8_t)(h0 >> 40); | |
351 | s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3)); | |
352 | s[7] = (uint8_t)(h1 >> 5); | |
353 | s[8] = (uint8_t)(h1 >> 13); | |
354 | s[9] = (uint8_t)(h1 >> 21); | |
355 | s[10] = (uint8_t)(h1 >> 29); | |
356 | s[11] = (uint8_t)(h1 >> 37); | |
357 | s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6)); | |
358 | s[13] = (uint8_t)(h2 >> 2); | |
359 | s[14] = (uint8_t)(h2 >> 10); | |
360 | s[15] = (uint8_t)(h2 >> 18); | |
361 | s[16] = (uint8_t)(h2 >> 26); | |
362 | s[17] = (uint8_t)(h2 >> 34); | |
363 | s[18] = (uint8_t)(h2 >> 42); | |
364 | s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1)); | |
365 | s[20] = (uint8_t)(h3 >> 7); | |
366 | s[21] = (uint8_t)(h3 >> 15); | |
367 | s[22] = (uint8_t)(h3 >> 23); | |
368 | s[23] = (uint8_t)(h3 >> 31); | |
369 | s[24] = (uint8_t)(h3 >> 39); | |
370 | s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4)); | |
371 | s[26] = (uint8_t)(h4 >> 4); | |
372 | s[27] = (uint8_t)(h4 >> 12); | |
373 | s[28] = (uint8_t)(h4 >> 20); | |
374 | s[29] = (uint8_t)(h4 >> 28); | |
375 | s[30] = (uint8_t)(h4 >> 36); | |
376 | s[31] = (uint8_t)(h4 >> 44); | |
377 | } | |
378 | ||
379 | # if defined(X25519_ASM) | |
380 | void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g); | |
381 | void x25519_fe51_sqr(fe51 h, const fe51 f); | |
382 | void x25519_fe51_mul121666(fe51 h, fe51 f); | |
383 | # define fe51_mul x25519_fe51_mul | |
384 | # define fe51_sq x25519_fe51_sqr | |
385 | # define fe51_mul121666 x25519_fe51_mul121666 | |
c521e439 AP |
386 | # else |
387 | ||
3c849bc9 AP |
388 | typedef __uint128_t u128; |
389 | ||
cfc32a1e AP |
390 | static void fe51_mul(fe51 h, const fe51 f, const fe51 g) |
391 | { | |
392 | u128 h0, h1, h2, h3, h4; | |
393 | uint64_t f_i, g0, g1, g2, g3, g4; | |
394 | ||
395 | f_i = f[0]; | |
396 | h0 = (u128)f_i * (g0 = g[0]); | |
397 | h1 = (u128)f_i * (g1 = g[1]); | |
398 | h2 = (u128)f_i * (g2 = g[2]); | |
399 | h3 = (u128)f_i * (g3 = g[3]); | |
400 | h4 = (u128)f_i * (g4 = g[4]); | |
401 | ||
402 | f_i = f[1]; | |
403 | h0 += (u128)f_i * (g4 *= 19); | |
404 | h1 += (u128)f_i * g0; | |
405 | h2 += (u128)f_i * g1; | |
406 | h3 += (u128)f_i * g2; | |
407 | h4 += (u128)f_i * g3; | |
408 | ||
409 | f_i = f[2]; | |
410 | h0 += (u128)f_i * (g3 *= 19); | |
411 | h1 += (u128)f_i * g4; | |
412 | h2 += (u128)f_i * g0; | |
413 | h3 += (u128)f_i * g1; | |
414 | h4 += (u128)f_i * g2; | |
415 | ||
416 | f_i = f[3]; | |
417 | h0 += (u128)f_i * (g2 *= 19); | |
418 | h1 += (u128)f_i * g3; | |
419 | h2 += (u128)f_i * g4; | |
420 | h3 += (u128)f_i * g0; | |
421 | h4 += (u128)f_i * g1; | |
422 | ||
423 | f_i = f[4]; | |
424 | h0 += (u128)f_i * (g1 *= 19); | |
425 | h1 += (u128)f_i * g2; | |
426 | h2 += (u128)f_i * g3; | |
427 | h3 += (u128)f_i * g4; | |
428 | h4 += (u128)f_i * g0; | |
429 | ||
430 | /* partial [lazy] reduction */ | |
431 | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; | |
432 | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; | |
433 | ||
434 | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; | |
435 | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; | |
436 | ||
437 | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; | |
438 | g3 += g2 >> 51; g2 &= MASK51; | |
439 | g1 += g0 >> 51; g0 &= MASK51; | |
440 | ||
441 | h[0] = g0; | |
442 | h[1] = g1; | |
443 | h[2] = g2; | |
444 | h[3] = g3; | |
445 | h[4] = g4; | |
446 | } | |
447 | ||
448 | static void fe51_sq(fe51 h, const fe51 f) | |
449 | { | |
c521e439 | 450 | # if defined(OPENSSL_SMALL_FOOTPRINT) |
cfc32a1e | 451 | fe51_mul(h, f, f); |
c521e439 | 452 | # else |
cfc32a1e AP |
453 | /* dedicated squaring gives 16-25% overall improvement */ |
454 | uint64_t g0 = f[0]; | |
455 | uint64_t g1 = f[1]; | |
456 | uint64_t g2 = f[2]; | |
457 | uint64_t g3 = f[3]; | |
458 | uint64_t g4 = f[4]; | |
459 | u128 h0, h1, h2, h3, h4; | |
460 | ||
461 | h0 = (u128)g0 * g0; g0 *= 2; | |
462 | h1 = (u128)g0 * g1; | |
463 | h2 = (u128)g0 * g2; | |
464 | h3 = (u128)g0 * g3; | |
465 | h4 = (u128)g0 * g4; | |
466 | ||
467 | g0 = g4; /* borrow g0 */ | |
468 | h3 += (u128)g0 * (g4 *= 19); | |
469 | ||
470 | h2 += (u128)g1 * g1; g1 *= 2; | |
471 | h3 += (u128)g1 * g2; | |
472 | h4 += (u128)g1 * g3; | |
473 | h0 += (u128)g1 * g4; | |
474 | ||
475 | g0 = g3; /* borrow g0 */ | |
476 | h1 += (u128)g0 * (g3 *= 19); | |
477 | h2 += (u128)(g0 * 2) * g4; | |
478 | ||
479 | h4 += (u128)g2 * g2; g2 *= 2; | |
480 | h0 += (u128)g2 * g3; | |
481 | h1 += (u128)g2 * g4; | |
482 | ||
483 | /* partial [lazy] reduction */ | |
484 | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; | |
485 | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; | |
486 | ||
487 | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; | |
488 | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; | |
489 | ||
490 | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; | |
491 | g3 += g2 >> 51; g2 &= MASK51; | |
492 | g1 += g0 >> 51; g0 &= MASK51; | |
493 | ||
494 | h[0] = g0; | |
495 | h[1] = g1; | |
496 | h[2] = g2; | |
497 | h[3] = g3; | |
498 | h[4] = g4; | |
c521e439 | 499 | # endif |
cfc32a1e AP |
500 | } |
501 | ||
c521e439 AP |
502 | static void fe51_mul121666(fe51 h, fe51 f) |
503 | { | |
504 | u128 h0 = f[0] * (u128)121666; | |
505 | u128 h1 = f[1] * (u128)121666; | |
506 | u128 h2 = f[2] * (u128)121666; | |
507 | u128 h3 = f[3] * (u128)121666; | |
508 | u128 h4 = f[4] * (u128)121666; | |
509 | uint64_t g0, g1, g2, g3, g4; | |
510 | ||
511 | h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; | |
512 | h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; | |
513 | ||
514 | h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; | |
515 | g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; | |
516 | ||
517 | g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; | |
518 | g3 += g2 >> 51; g2 &= MASK51; | |
519 | g1 += g0 >> 51; g0 &= MASK51; | |
520 | ||
521 | h[0] = g0; | |
522 | h[1] = g1; | |
523 | h[2] = g2; | |
524 | h[3] = g3; | |
525 | h[4] = g4; | |
526 | } | |
527 | # endif | |
528 | ||
cfc32a1e AP |
529 | static void fe51_add(fe51 h, const fe51 f, const fe51 g) |
530 | { | |
531 | h[0] = f[0] + g[0]; | |
532 | h[1] = f[1] + g[1]; | |
533 | h[2] = f[2] + g[2]; | |
534 | h[3] = f[3] + g[3]; | |
535 | h[4] = f[4] + g[4]; | |
536 | } | |
537 | ||
538 | static void fe51_sub(fe51 h, const fe51 f, const fe51 g) | |
539 | { | |
540 | /* | |
541 | * Add 2*modulus to ensure that result remains positive | |
542 | * even if subtrahend is partially reduced. | |
543 | */ | |
544 | h[0] = (f[0] + 0xfffffffffffda) - g[0]; | |
545 | h[1] = (f[1] + 0xffffffffffffe) - g[1]; | |
546 | h[2] = (f[2] + 0xffffffffffffe) - g[2]; | |
547 | h[3] = (f[3] + 0xffffffffffffe) - g[3]; | |
548 | h[4] = (f[4] + 0xffffffffffffe) - g[4]; | |
549 | } | |
550 | ||
551 | static void fe51_0(fe51 h) | |
552 | { | |
553 | h[0] = 0; | |
554 | h[1] = 0; | |
555 | h[2] = 0; | |
556 | h[3] = 0; | |
557 | h[4] = 0; | |
558 | } | |
559 | ||
560 | static void fe51_1(fe51 h) | |
561 | { | |
562 | h[0] = 1; | |
563 | h[1] = 0; | |
564 | h[2] = 0; | |
565 | h[3] = 0; | |
566 | h[4] = 0; | |
567 | } | |
568 | ||
569 | static void fe51_copy(fe51 h, const fe51 f) | |
570 | { | |
571 | h[0] = f[0]; | |
572 | h[1] = f[1]; | |
573 | h[2] = f[2]; | |
574 | h[3] = f[3]; | |
575 | h[4] = f[4]; | |
576 | } | |
577 | ||
578 | static void fe51_cswap(fe51 f, fe51 g, unsigned int b) | |
579 | { | |
580 | int i; | |
581 | uint64_t mask = 0 - (uint64_t)b; | |
582 | ||
583 | for (i = 0; i < 5; i++) { | |
584 | int64_t x = f[i] ^ g[i]; | |
585 | x &= mask; | |
586 | f[i] ^= x; | |
587 | g[i] ^= x; | |
588 | } | |
589 | } | |
590 | ||
591 | static void fe51_invert(fe51 out, const fe51 z) | |
592 | { | |
593 | fe51 t0; | |
594 | fe51 t1; | |
595 | fe51 t2; | |
596 | fe51 t3; | |
597 | int i; | |
598 | ||
599 | /* | |
600 | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as | |
601 | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. | |
602 | */ | |
603 | ||
604 | /* t0 = z ** 2 */ | |
605 | fe51_sq(t0, z); | |
606 | ||
607 | /* t1 = t0 ** (2 ** 2) = z ** 8 */ | |
608 | fe51_sq(t1, t0); | |
609 | fe51_sq(t1, t1); | |
610 | ||
611 | /* t1 = z * t1 = z ** 9 */ | |
612 | fe51_mul(t1, z, t1); | |
613 | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ | |
614 | fe51_mul(t0, t0, t1); | |
615 | ||
616 | /* t2 = t0 ** 2 = z ** 22 */ | |
617 | fe51_sq(t2, t0); | |
618 | ||
619 | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ | |
620 | fe51_mul(t1, t1, t2); | |
621 | ||
622 | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ | |
623 | fe51_sq(t2, t1); | |
624 | for (i = 1; i < 5; ++i) | |
625 | fe51_sq(t2, t2); | |
626 | ||
627 | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ | |
628 | fe51_mul(t1, t2, t1); | |
629 | ||
630 | /* Continuing similarly... */ | |
631 | ||
632 | /* t2 = z ** (2 ** 20 - 1) */ | |
633 | fe51_sq(t2, t1); | |
634 | for (i = 1; i < 10; ++i) | |
635 | fe51_sq(t2, t2); | |
636 | ||
637 | fe51_mul(t2, t2, t1); | |
638 | ||
639 | /* t2 = z ** (2 ** 40 - 1) */ | |
640 | fe51_sq(t3, t2); | |
641 | for (i = 1; i < 20; ++i) | |
642 | fe51_sq(t3, t3); | |
643 | ||
644 | fe51_mul(t2, t3, t2); | |
645 | ||
646 | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ | |
647 | for (i = 0; i < 10; ++i) | |
648 | fe51_sq(t2, t2); | |
649 | ||
650 | /* t1 = z ** (2 ** 50 - 1) */ | |
651 | fe51_mul(t1, t2, t1); | |
652 | ||
653 | /* t2 = z ** (2 ** 100 - 1) */ | |
654 | fe51_sq(t2, t1); | |
655 | for (i = 1; i < 50; ++i) | |
656 | fe51_sq(t2, t2); | |
657 | ||
658 | fe51_mul(t2, t2, t1); | |
659 | ||
660 | /* t2 = z ** (2 ** 200 - 1) */ | |
661 | fe51_sq(t3, t2); | |
662 | for (i = 1; i < 100; ++i) | |
663 | fe51_sq(t3, t3); | |
664 | ||
665 | fe51_mul(t2, t3, t2); | |
666 | ||
667 | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ | |
668 | for (i = 0; i < 50; ++i) | |
669 | fe51_sq(t2, t2); | |
670 | ||
671 | /* t1 = z ** (2 ** 250 - 1) */ | |
672 | fe51_mul(t1, t2, t1); | |
673 | ||
674 | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ | |
675 | for (i = 0; i < 5; ++i) | |
676 | fe51_sq(t1, t1); | |
677 | ||
678 | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ | |
679 | fe51_mul(out, t1, t0); | |
680 | } | |
681 | ||
cfc32a1e AP |
682 | /* |
683 | * Duplicate of original x25519_scalar_mult_generic, but using | |
684 | * fe51_* subroutines. | |
685 | */ | |
686 | static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], | |
687 | const uint8_t point[32]) | |
688 | { | |
689 | fe51 x1, x2, z2, x3, z3, tmp0, tmp1; | |
690 | uint8_t e[32]; | |
691 | unsigned swap = 0; | |
692 | int pos; | |
693 | ||
c521e439 AP |
694 | # ifdef BASE_2_64_IMPLEMENTED |
695 | if (x25519_fe64_eligible()) { | |
696 | x25519_scalar_mulx(out, scalar, point); | |
697 | return; | |
698 | } | |
699 | # endif | |
700 | ||
cfc32a1e AP |
701 | memcpy(e, scalar, 32); |
702 | e[0] &= 0xf8; | |
703 | e[31] &= 0x7f; | |
704 | e[31] |= 0x40; | |
705 | fe51_frombytes(x1, point); | |
706 | fe51_1(x2); | |
707 | fe51_0(z2); | |
708 | fe51_copy(x3, x1); | |
709 | fe51_1(z3); | |
710 | ||
711 | for (pos = 254; pos >= 0; --pos) { | |
712 | unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); | |
713 | ||
714 | swap ^= b; | |
715 | fe51_cswap(x2, x3, swap); | |
716 | fe51_cswap(z2, z3, swap); | |
717 | swap = b; | |
718 | fe51_sub(tmp0, x3, z3); | |
719 | fe51_sub(tmp1, x2, z2); | |
720 | fe51_add(x2, x2, z2); | |
721 | fe51_add(z2, x3, z3); | |
722 | fe51_mul(z3, tmp0, x2); | |
723 | fe51_mul(z2, z2, tmp1); | |
724 | fe51_sq(tmp0, tmp1); | |
725 | fe51_sq(tmp1, x2); | |
726 | fe51_add(x3, z3, z2); | |
727 | fe51_sub(z2, z3, z2); | |
728 | fe51_mul(x2, tmp1, tmp0); | |
729 | fe51_sub(tmp1, tmp1, tmp0); | |
730 | fe51_sq(z2, z2); | |
731 | fe51_mul121666(z3, tmp1); | |
732 | fe51_sq(x3, x3); | |
733 | fe51_add(tmp0, tmp0, z3); | |
734 | fe51_mul(z3, x1, z2); | |
735 | fe51_mul(z2, tmp1, tmp0); | |
736 | } | |
cfc32a1e AP |
737 | |
738 | fe51_invert(z2, z2); | |
739 | fe51_mul(x2, x2, z2); | |
740 | fe51_tobytes(out, x2); | |
741 | ||
742 | OPENSSL_cleanse(e, sizeof(e)); | |
743 | } | |
744 | #endif | |
745 | ||
746 | /* | |
747 | * Reference base 2^25.5 implementation. | |
3a17b9a4 | 748 | * |
cfc32a1e AP |
749 | * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP |
750 | * 20141124 (http://bench.cr.yp.to/supercop.html). | |
751 | * | |
752 | * The field functions are shared by Ed25519 and X25519 where possible. | |
753 | */ | |
a90def6b | 754 | |
3a17b9a4 DMSP |
755 | /* |
756 | * fe means field element. Here the field is \Z/(2^255-19). An element t, | |
a90def6b DSH |
757 | * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 |
758 | * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on | |
3a17b9a4 DMSP |
759 | * context. |
760 | */ | |
a90def6b DSH |
761 | typedef int32_t fe[10]; |
762 | ||
425dde5d | 763 | static const int64_t kBottom21Bits = 0x1fffffLL; |
5b7af0dd EK |
764 | static const int64_t kBottom25Bits = 0x1ffffffLL; |
765 | static const int64_t kBottom26Bits = 0x3ffffffLL; | |
766 | static const int64_t kTop39Bits = 0xfffffffffe000000LL; | |
767 | static const int64_t kTop38Bits = 0xfffffffffc000000LL; | |
b9577984 | 768 | |
3a17b9a4 DMSP |
769 | static uint64_t load_3(const uint8_t *in) |
770 | { | |
771 | uint64_t result; | |
772 | ||
425dde5d | 773 | result = ((uint64_t)in[0]); |
3a17b9a4 DMSP |
774 | result |= ((uint64_t)in[1]) << 8; |
775 | result |= ((uint64_t)in[2]) << 16; | |
776 | return result; | |
a90def6b DSH |
777 | } |
778 | ||
3a17b9a4 DMSP |
779 | static uint64_t load_4(const uint8_t *in) |
780 | { | |
781 | uint64_t result; | |
782 | ||
425dde5d | 783 | result = ((uint64_t)in[0]); |
3a17b9a4 DMSP |
784 | result |= ((uint64_t)in[1]) << 8; |
785 | result |= ((uint64_t)in[2]) << 16; | |
786 | result |= ((uint64_t)in[3]) << 24; | |
787 | return result; | |
a90def6b DSH |
788 | } |
789 | ||
3a17b9a4 DMSP |
790 | static void fe_frombytes(fe h, const uint8_t *s) |
791 | { | |
792 | /* Ignores top bit of h. */ | |
425dde5d DMSP |
793 | int64_t h0 = load_4(s); |
794 | int64_t h1 = load_3(s + 4) << 6; | |
795 | int64_t h2 = load_3(s + 7) << 5; | |
796 | int64_t h3 = load_3(s + 10) << 3; | |
797 | int64_t h4 = load_3(s + 13) << 2; | |
798 | int64_t h5 = load_4(s + 16); | |
799 | int64_t h6 = load_3(s + 20) << 7; | |
800 | int64_t h7 = load_3(s + 23) << 5; | |
801 | int64_t h8 = load_3(s + 26) << 4; | |
802 | int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2; | |
3a17b9a4 DMSP |
803 | int64_t carry0; |
804 | int64_t carry1; | |
805 | int64_t carry2; | |
806 | int64_t carry3; | |
807 | int64_t carry4; | |
808 | int64_t carry5; | |
809 | int64_t carry6; | |
810 | int64_t carry7; | |
811 | int64_t carry8; | |
812 | int64_t carry9; | |
813 | ||
814 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; | |
815 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; | |
816 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; | |
817 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
818 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
819 | ||
820 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
821 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; | |
822 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
823 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
824 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
825 | ||
826 | h[0] = (int32_t)h0; | |
827 | h[1] = (int32_t)h1; | |
828 | h[2] = (int32_t)h2; | |
829 | h[3] = (int32_t)h3; | |
830 | h[4] = (int32_t)h4; | |
831 | h[5] = (int32_t)h5; | |
832 | h[6] = (int32_t)h6; | |
833 | h[7] = (int32_t)h7; | |
834 | h[8] = (int32_t)h8; | |
835 | h[9] = (int32_t)h9; | |
a90def6b DSH |
836 | } |
837 | ||
3a17b9a4 DMSP |
838 | /* |
839 | * Preconditions: | |
840 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. | |
a90def6b DSH |
841 | * |
842 | * Write p=2^255-19; q=floor(h/p). | |
843 | * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). | |
844 | * | |
845 | * Proof: | |
846 | * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. | |
847 | * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. | |
848 | * | |
849 | * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). | |
850 | * Then 0<y<1. | |
851 | * | |
852 | * Write r=h-pq. | |
853 | * Have 0<=r<=p-1=2^255-20. | |
854 | * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. | |
855 | * | |
856 | * Write x=r+19(2^-255)r+y. | |
857 | * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. | |
858 | * | |
859 | * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) | |
3a17b9a4 DMSP |
860 | * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. |
861 | */ | |
862 | static void fe_tobytes(uint8_t *s, const fe h) | |
863 | { | |
864 | int32_t h0 = h[0]; | |
865 | int32_t h1 = h[1]; | |
866 | int32_t h2 = h[2]; | |
867 | int32_t h3 = h[3]; | |
868 | int32_t h4 = h[4]; | |
869 | int32_t h5 = h[5]; | |
870 | int32_t h6 = h[6]; | |
871 | int32_t h7 = h[7]; | |
872 | int32_t h8 = h[8]; | |
873 | int32_t h9 = h[9]; | |
874 | int32_t q; | |
875 | ||
876 | q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; | |
877 | q = (h0 + q) >> 26; | |
878 | q = (h1 + q) >> 25; | |
879 | q = (h2 + q) >> 26; | |
880 | q = (h3 + q) >> 25; | |
881 | q = (h4 + q) >> 26; | |
882 | q = (h5 + q) >> 25; | |
883 | q = (h6 + q) >> 26; | |
884 | q = (h7 + q) >> 25; | |
885 | q = (h8 + q) >> 26; | |
886 | q = (h9 + q) >> 25; | |
887 | ||
888 | /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ | |
889 | h0 += 19 * q; | |
890 | /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ | |
891 | ||
892 | h1 += h0 >> 26; h0 &= kBottom26Bits; | |
893 | h2 += h1 >> 25; h1 &= kBottom25Bits; | |
894 | h3 += h2 >> 26; h2 &= kBottom26Bits; | |
895 | h4 += h3 >> 25; h3 &= kBottom25Bits; | |
896 | h5 += h4 >> 26; h4 &= kBottom26Bits; | |
897 | h6 += h5 >> 25; h5 &= kBottom25Bits; | |
898 | h7 += h6 >> 26; h6 &= kBottom26Bits; | |
899 | h8 += h7 >> 25; h7 &= kBottom25Bits; | |
900 | h9 += h8 >> 26; h8 &= kBottom26Bits; | |
901 | h9 &= kBottom25Bits; | |
902 | /* h10 = carry9 */ | |
903 | ||
904 | /* | |
905 | * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. | |
906 | * Have h0+...+2^230 h9 between 0 and 2^255-1; | |
907 | * evidently 2^255 h10-2^255 q = 0. | |
908 | * Goal: Output h0+...+2^230 h9. | |
909 | */ | |
425dde5d DMSP |
910 | s[ 0] = (uint8_t) (h0 >> 0); |
911 | s[ 1] = (uint8_t) (h0 >> 8); | |
912 | s[ 2] = (uint8_t) (h0 >> 16); | |
913 | s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2)); | |
914 | s[ 4] = (uint8_t) (h1 >> 6); | |
915 | s[ 5] = (uint8_t) (h1 >> 14); | |
916 | s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3)); | |
917 | s[ 7] = (uint8_t) (h2 >> 5); | |
918 | s[ 8] = (uint8_t) (h2 >> 13); | |
919 | s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5)); | |
920 | s[10] = (uint8_t) (h3 >> 3); | |
921 | s[11] = (uint8_t) (h3 >> 11); | |
3a17b9a4 | 922 | s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6)); |
425dde5d DMSP |
923 | s[13] = (uint8_t) (h4 >> 2); |
924 | s[14] = (uint8_t) (h4 >> 10); | |
925 | s[15] = (uint8_t) (h4 >> 18); | |
926 | s[16] = (uint8_t) (h5 >> 0); | |
927 | s[17] = (uint8_t) (h5 >> 8); | |
928 | s[18] = (uint8_t) (h5 >> 16); | |
3a17b9a4 | 929 | s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1)); |
425dde5d DMSP |
930 | s[20] = (uint8_t) (h6 >> 7); |
931 | s[21] = (uint8_t) (h6 >> 15); | |
3a17b9a4 | 932 | s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3)); |
425dde5d DMSP |
933 | s[23] = (uint8_t) (h7 >> 5); |
934 | s[24] = (uint8_t) (h7 >> 13); | |
3a17b9a4 | 935 | s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4)); |
425dde5d DMSP |
936 | s[26] = (uint8_t) (h8 >> 4); |
937 | s[27] = (uint8_t) (h8 >> 12); | |
3a17b9a4 | 938 | s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6)); |
425dde5d DMSP |
939 | s[29] = (uint8_t) (h9 >> 2); |
940 | s[30] = (uint8_t) (h9 >> 10); | |
941 | s[31] = (uint8_t) (h9 >> 18); | |
a90def6b DSH |
942 | } |
943 | ||
944 | /* h = f */ | |
3a17b9a4 DMSP |
945 | static void fe_copy(fe h, const fe f) |
946 | { | |
947 | memmove(h, f, sizeof(int32_t) * 10); | |
a90def6b DSH |
948 | } |
949 | ||
950 | /* h = 0 */ | |
3a17b9a4 DMSP |
951 | static void fe_0(fe h) |
952 | { | |
953 | memset(h, 0, sizeof(int32_t) * 10); | |
954 | } | |
a90def6b DSH |
955 | |
956 | /* h = 1 */ | |
3a17b9a4 DMSP |
957 | static void fe_1(fe h) |
958 | { | |
959 | memset(h, 0, sizeof(int32_t) * 10); | |
960 | h[0] = 1; | |
a90def6b DSH |
961 | } |
962 | ||
3a17b9a4 DMSP |
963 | /* |
964 | * h = f + g | |
965 | * | |
a90def6b DSH |
966 | * Can overlap h with f or g. |
967 | * | |
968 | * Preconditions: | |
969 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
970 | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
971 | * | |
972 | * Postconditions: | |
3a17b9a4 DMSP |
973 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
974 | */ | |
975 | static void fe_add(fe h, const fe f, const fe g) | |
976 | { | |
977 | unsigned i; | |
978 | ||
979 | for (i = 0; i < 10; i++) { | |
980 | h[i] = f[i] + g[i]; | |
981 | } | |
a90def6b DSH |
982 | } |
983 | ||
3a17b9a4 DMSP |
984 | /* |
985 | * h = f - g | |
986 | * | |
a90def6b DSH |
987 | * Can overlap h with f or g. |
988 | * | |
989 | * Preconditions: | |
990 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
991 | * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
992 | * | |
993 | * Postconditions: | |
3a17b9a4 DMSP |
994 | * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
995 | */ | |
996 | static void fe_sub(fe h, const fe f, const fe g) | |
997 | { | |
998 | unsigned i; | |
999 | ||
1000 | for (i = 0; i < 10; i++) { | |
1001 | h[i] = f[i] - g[i]; | |
1002 | } | |
a90def6b DSH |
1003 | } |
1004 | ||
3a17b9a4 DMSP |
1005 | /* |
1006 | * h = f * g | |
1007 | * | |
a90def6b DSH |
1008 | * Can overlap h with f or g. |
1009 | * | |
1010 | * Preconditions: | |
1011 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. | |
1012 | * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. | |
1013 | * | |
1014 | * Postconditions: | |
1015 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. | |
1016 | * | |
1017 | * Notes on implementation strategy: | |
1018 | * | |
1019 | * Using schoolbook multiplication. | |
1020 | * Karatsuba would save a little in some cost models. | |
1021 | * | |
1022 | * Most multiplications by 2 and 19 are 32-bit precomputations; | |
1023 | * cheaper than 64-bit postcomputations. | |
1024 | * | |
1025 | * There is one remaining multiplication by 19 in the carry chain; | |
1026 | * one *19 precomputation can be merged into this, | |
1027 | * but the resulting data flow is considerably less clean. | |
1028 | * | |
1029 | * There are 12 carries below. | |
1030 | * 10 of them are 2-way parallelizable and vectorizable. | |
1031 | * Can get away with 11 carries, but then data flow is much deeper. | |
1032 | * | |
3a17b9a4 DMSP |
1033 | * With tighter constraints on inputs can squeeze carries into int32. |
1034 | */ | |
1035 | static void fe_mul(fe h, const fe f, const fe g) | |
1036 | { | |
1037 | int32_t f0 = f[0]; | |
1038 | int32_t f1 = f[1]; | |
1039 | int32_t f2 = f[2]; | |
1040 | int32_t f3 = f[3]; | |
1041 | int32_t f4 = f[4]; | |
1042 | int32_t f5 = f[5]; | |
1043 | int32_t f6 = f[6]; | |
1044 | int32_t f7 = f[7]; | |
1045 | int32_t f8 = f[8]; | |
1046 | int32_t f9 = f[9]; | |
1047 | int32_t g0 = g[0]; | |
1048 | int32_t g1 = g[1]; | |
1049 | int32_t g2 = g[2]; | |
1050 | int32_t g3 = g[3]; | |
1051 | int32_t g4 = g[4]; | |
1052 | int32_t g5 = g[5]; | |
1053 | int32_t g6 = g[6]; | |
1054 | int32_t g7 = g[7]; | |
1055 | int32_t g8 = g[8]; | |
1056 | int32_t g9 = g[9]; | |
1057 | int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ | |
1058 | int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ | |
1059 | int32_t g3_19 = 19 * g3; | |
1060 | int32_t g4_19 = 19 * g4; | |
1061 | int32_t g5_19 = 19 * g5; | |
1062 | int32_t g6_19 = 19 * g6; | |
1063 | int32_t g7_19 = 19 * g7; | |
1064 | int32_t g8_19 = 19 * g8; | |
1065 | int32_t g9_19 = 19 * g9; | |
1066 | int32_t f1_2 = 2 * f1; | |
1067 | int32_t f3_2 = 2 * f3; | |
1068 | int32_t f5_2 = 2 * f5; | |
1069 | int32_t f7_2 = 2 * f7; | |
1070 | int32_t f9_2 = 2 * f9; | |
1071 | int64_t f0g0 = f0 * (int64_t) g0; | |
1072 | int64_t f0g1 = f0 * (int64_t) g1; | |
1073 | int64_t f0g2 = f0 * (int64_t) g2; | |
1074 | int64_t f0g3 = f0 * (int64_t) g3; | |
1075 | int64_t f0g4 = f0 * (int64_t) g4; | |
1076 | int64_t f0g5 = f0 * (int64_t) g5; | |
1077 | int64_t f0g6 = f0 * (int64_t) g6; | |
1078 | int64_t f0g7 = f0 * (int64_t) g7; | |
1079 | int64_t f0g8 = f0 * (int64_t) g8; | |
1080 | int64_t f0g9 = f0 * (int64_t) g9; | |
1081 | int64_t f1g0 = f1 * (int64_t) g0; | |
1082 | int64_t f1g1_2 = f1_2 * (int64_t) g1; | |
1083 | int64_t f1g2 = f1 * (int64_t) g2; | |
1084 | int64_t f1g3_2 = f1_2 * (int64_t) g3; | |
1085 | int64_t f1g4 = f1 * (int64_t) g4; | |
1086 | int64_t f1g5_2 = f1_2 * (int64_t) g5; | |
1087 | int64_t f1g6 = f1 * (int64_t) g6; | |
1088 | int64_t f1g7_2 = f1_2 * (int64_t) g7; | |
1089 | int64_t f1g8 = f1 * (int64_t) g8; | |
1090 | int64_t f1g9_38 = f1_2 * (int64_t) g9_19; | |
1091 | int64_t f2g0 = f2 * (int64_t) g0; | |
1092 | int64_t f2g1 = f2 * (int64_t) g1; | |
1093 | int64_t f2g2 = f2 * (int64_t) g2; | |
1094 | int64_t f2g3 = f2 * (int64_t) g3; | |
1095 | int64_t f2g4 = f2 * (int64_t) g4; | |
1096 | int64_t f2g5 = f2 * (int64_t) g5; | |
1097 | int64_t f2g6 = f2 * (int64_t) g6; | |
1098 | int64_t f2g7 = f2 * (int64_t) g7; | |
1099 | int64_t f2g8_19 = f2 * (int64_t) g8_19; | |
1100 | int64_t f2g9_19 = f2 * (int64_t) g9_19; | |
1101 | int64_t f3g0 = f3 * (int64_t) g0; | |
1102 | int64_t f3g1_2 = f3_2 * (int64_t) g1; | |
1103 | int64_t f3g2 = f3 * (int64_t) g2; | |
1104 | int64_t f3g3_2 = f3_2 * (int64_t) g3; | |
1105 | int64_t f3g4 = f3 * (int64_t) g4; | |
1106 | int64_t f3g5_2 = f3_2 * (int64_t) g5; | |
1107 | int64_t f3g6 = f3 * (int64_t) g6; | |
1108 | int64_t f3g7_38 = f3_2 * (int64_t) g7_19; | |
1109 | int64_t f3g8_19 = f3 * (int64_t) g8_19; | |
1110 | int64_t f3g9_38 = f3_2 * (int64_t) g9_19; | |
1111 | int64_t f4g0 = f4 * (int64_t) g0; | |
1112 | int64_t f4g1 = f4 * (int64_t) g1; | |
1113 | int64_t f4g2 = f4 * (int64_t) g2; | |
1114 | int64_t f4g3 = f4 * (int64_t) g3; | |
1115 | int64_t f4g4 = f4 * (int64_t) g4; | |
1116 | int64_t f4g5 = f4 * (int64_t) g5; | |
1117 | int64_t f4g6_19 = f4 * (int64_t) g6_19; | |
1118 | int64_t f4g7_19 = f4 * (int64_t) g7_19; | |
1119 | int64_t f4g8_19 = f4 * (int64_t) g8_19; | |
1120 | int64_t f4g9_19 = f4 * (int64_t) g9_19; | |
1121 | int64_t f5g0 = f5 * (int64_t) g0; | |
1122 | int64_t f5g1_2 = f5_2 * (int64_t) g1; | |
1123 | int64_t f5g2 = f5 * (int64_t) g2; | |
1124 | int64_t f5g3_2 = f5_2 * (int64_t) g3; | |
1125 | int64_t f5g4 = f5 * (int64_t) g4; | |
1126 | int64_t f5g5_38 = f5_2 * (int64_t) g5_19; | |
1127 | int64_t f5g6_19 = f5 * (int64_t) g6_19; | |
1128 | int64_t f5g7_38 = f5_2 * (int64_t) g7_19; | |
1129 | int64_t f5g8_19 = f5 * (int64_t) g8_19; | |
1130 | int64_t f5g9_38 = f5_2 * (int64_t) g9_19; | |
1131 | int64_t f6g0 = f6 * (int64_t) g0; | |
1132 | int64_t f6g1 = f6 * (int64_t) g1; | |
1133 | int64_t f6g2 = f6 * (int64_t) g2; | |
1134 | int64_t f6g3 = f6 * (int64_t) g3; | |
1135 | int64_t f6g4_19 = f6 * (int64_t) g4_19; | |
1136 | int64_t f6g5_19 = f6 * (int64_t) g5_19; | |
1137 | int64_t f6g6_19 = f6 * (int64_t) g6_19; | |
1138 | int64_t f6g7_19 = f6 * (int64_t) g7_19; | |
1139 | int64_t f6g8_19 = f6 * (int64_t) g8_19; | |
1140 | int64_t f6g9_19 = f6 * (int64_t) g9_19; | |
1141 | int64_t f7g0 = f7 * (int64_t) g0; | |
1142 | int64_t f7g1_2 = f7_2 * (int64_t) g1; | |
1143 | int64_t f7g2 = f7 * (int64_t) g2; | |
1144 | int64_t f7g3_38 = f7_2 * (int64_t) g3_19; | |
1145 | int64_t f7g4_19 = f7 * (int64_t) g4_19; | |
1146 | int64_t f7g5_38 = f7_2 * (int64_t) g5_19; | |
1147 | int64_t f7g6_19 = f7 * (int64_t) g6_19; | |
1148 | int64_t f7g7_38 = f7_2 * (int64_t) g7_19; | |
1149 | int64_t f7g8_19 = f7 * (int64_t) g8_19; | |
1150 | int64_t f7g9_38 = f7_2 * (int64_t) g9_19; | |
1151 | int64_t f8g0 = f8 * (int64_t) g0; | |
1152 | int64_t f8g1 = f8 * (int64_t) g1; | |
1153 | int64_t f8g2_19 = f8 * (int64_t) g2_19; | |
1154 | int64_t f8g3_19 = f8 * (int64_t) g3_19; | |
1155 | int64_t f8g4_19 = f8 * (int64_t) g4_19; | |
1156 | int64_t f8g5_19 = f8 * (int64_t) g5_19; | |
1157 | int64_t f8g6_19 = f8 * (int64_t) g6_19; | |
1158 | int64_t f8g7_19 = f8 * (int64_t) g7_19; | |
1159 | int64_t f8g8_19 = f8 * (int64_t) g8_19; | |
1160 | int64_t f8g9_19 = f8 * (int64_t) g9_19; | |
1161 | int64_t f9g0 = f9 * (int64_t) g0; | |
1162 | int64_t f9g1_38 = f9_2 * (int64_t) g1_19; | |
1163 | int64_t f9g2_19 = f9 * (int64_t) g2_19; | |
1164 | int64_t f9g3_38 = f9_2 * (int64_t) g3_19; | |
1165 | int64_t f9g4_19 = f9 * (int64_t) g4_19; | |
1166 | int64_t f9g5_38 = f9_2 * (int64_t) g5_19; | |
1167 | int64_t f9g6_19 = f9 * (int64_t) g6_19; | |
1168 | int64_t f9g7_38 = f9_2 * (int64_t) g7_19; | |
1169 | int64_t f9g8_19 = f9 * (int64_t) g8_19; | |
1170 | int64_t f9g9_38 = f9_2 * (int64_t) g9_19; | |
425dde5d DMSP |
1171 | int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; |
1172 | int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19; | |
1173 | int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38; | |
1174 | int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19; | |
1175 | int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38; | |
1176 | int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19; | |
1177 | int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38; | |
1178 | int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19; | |
1179 | int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38; | |
1180 | int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ; | |
3a17b9a4 DMSP |
1181 | int64_t carry0; |
1182 | int64_t carry1; | |
1183 | int64_t carry2; | |
1184 | int64_t carry3; | |
1185 | int64_t carry4; | |
1186 | int64_t carry5; | |
1187 | int64_t carry6; | |
1188 | int64_t carry7; | |
1189 | int64_t carry8; | |
1190 | int64_t carry9; | |
1191 | ||
1192 | /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) | |
1193 | * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 | |
1194 | * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) | |
1195 | * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ | |
1196 | ||
1197 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
1198 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
1199 | /* |h0| <= 2^25 */ | |
1200 | /* |h4| <= 2^25 */ | |
1201 | /* |h1| <= 1.71*2^59 */ | |
1202 | /* |h5| <= 1.71*2^59 */ | |
1203 | ||
1204 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; | |
1205 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
1206 | /* |h1| <= 2^24; from now on fits into int32 */ | |
1207 | /* |h5| <= 2^24; from now on fits into int32 */ | |
1208 | /* |h2| <= 1.41*2^60 */ | |
1209 | /* |h6| <= 1.41*2^60 */ | |
1210 | ||
1211 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; | |
1212 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
1213 | /* |h2| <= 2^25; from now on fits into int32 unchanged */ | |
1214 | /* |h6| <= 2^25; from now on fits into int32 unchanged */ | |
1215 | /* |h3| <= 1.71*2^59 */ | |
1216 | /* |h7| <= 1.71*2^59 */ | |
1217 | ||
1218 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; | |
1219 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
1220 | /* |h3| <= 2^24; from now on fits into int32 unchanged */ | |
1221 | /* |h7| <= 2^24; from now on fits into int32 unchanged */ | |
1222 | /* |h4| <= 1.72*2^34 */ | |
1223 | /* |h8| <= 1.41*2^60 */ | |
1224 | ||
1225 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
1226 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
1227 | /* |h4| <= 2^25; from now on fits into int32 unchanged */ | |
1228 | /* |h8| <= 2^25; from now on fits into int32 unchanged */ | |
1229 | /* |h5| <= 1.01*2^24 */ | |
1230 | /* |h9| <= 1.71*2^59 */ | |
1231 | ||
1232 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; | |
1233 | /* |h9| <= 2^24; from now on fits into int32 unchanged */ | |
1234 | /* |h0| <= 1.1*2^39 */ | |
1235 | ||
1236 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
1237 | /* |h0| <= 2^25; from now on fits into int32 unchanged */ | |
1238 | /* |h1| <= 1.01*2^24 */ | |
1239 | ||
1240 | h[0] = (int32_t)h0; | |
1241 | h[1] = (int32_t)h1; | |
1242 | h[2] = (int32_t)h2; | |
1243 | h[3] = (int32_t)h3; | |
1244 | h[4] = (int32_t)h4; | |
1245 | h[5] = (int32_t)h5; | |
1246 | h[6] = (int32_t)h6; | |
1247 | h[7] = (int32_t)h7; | |
1248 | h[8] = (int32_t)h8; | |
1249 | h[9] = (int32_t)h9; | |
a90def6b DSH |
1250 | } |
1251 | ||
3a17b9a4 DMSP |
1252 | /* |
1253 | * h = f * f | |
1254 | * | |
a90def6b DSH |
1255 | * Can overlap h with f. |
1256 | * | |
1257 | * Preconditions: | |
1258 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. | |
1259 | * | |
1260 | * Postconditions: | |
1261 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. | |
1262 | * | |
3a17b9a4 DMSP |
1263 | * See fe_mul.c for discussion of implementation strategy. |
1264 | */ | |
1265 | static void fe_sq(fe h, const fe f) | |
1266 | { | |
1267 | int32_t f0 = f[0]; | |
1268 | int32_t f1 = f[1]; | |
1269 | int32_t f2 = f[2]; | |
1270 | int32_t f3 = f[3]; | |
1271 | int32_t f4 = f[4]; | |
1272 | int32_t f5 = f[5]; | |
1273 | int32_t f6 = f[6]; | |
1274 | int32_t f7 = f[7]; | |
1275 | int32_t f8 = f[8]; | |
1276 | int32_t f9 = f[9]; | |
1277 | int32_t f0_2 = 2 * f0; | |
1278 | int32_t f1_2 = 2 * f1; | |
1279 | int32_t f2_2 = 2 * f2; | |
1280 | int32_t f3_2 = 2 * f3; | |
1281 | int32_t f4_2 = 2 * f4; | |
1282 | int32_t f5_2 = 2 * f5; | |
1283 | int32_t f6_2 = 2 * f6; | |
1284 | int32_t f7_2 = 2 * f7; | |
1285 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ | |
1286 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ | |
1287 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ | |
1288 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ | |
1289 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ | |
1290 | int64_t f0f0 = f0 * (int64_t) f0; | |
1291 | int64_t f0f1_2 = f0_2 * (int64_t) f1; | |
1292 | int64_t f0f2_2 = f0_2 * (int64_t) f2; | |
1293 | int64_t f0f3_2 = f0_2 * (int64_t) f3; | |
1294 | int64_t f0f4_2 = f0_2 * (int64_t) f4; | |
1295 | int64_t f0f5_2 = f0_2 * (int64_t) f5; | |
1296 | int64_t f0f6_2 = f0_2 * (int64_t) f6; | |
1297 | int64_t f0f7_2 = f0_2 * (int64_t) f7; | |
1298 | int64_t f0f8_2 = f0_2 * (int64_t) f8; | |
1299 | int64_t f0f9_2 = f0_2 * (int64_t) f9; | |
1300 | int64_t f1f1_2 = f1_2 * (int64_t) f1; | |
1301 | int64_t f1f2_2 = f1_2 * (int64_t) f2; | |
1302 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; | |
1303 | int64_t f1f4_2 = f1_2 * (int64_t) f4; | |
1304 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; | |
1305 | int64_t f1f6_2 = f1_2 * (int64_t) f6; | |
1306 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; | |
1307 | int64_t f1f8_2 = f1_2 * (int64_t) f8; | |
1308 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; | |
1309 | int64_t f2f2 = f2 * (int64_t) f2; | |
1310 | int64_t f2f3_2 = f2_2 * (int64_t) f3; | |
1311 | int64_t f2f4_2 = f2_2 * (int64_t) f4; | |
1312 | int64_t f2f5_2 = f2_2 * (int64_t) f5; | |
1313 | int64_t f2f6_2 = f2_2 * (int64_t) f6; | |
1314 | int64_t f2f7_2 = f2_2 * (int64_t) f7; | |
1315 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; | |
1316 | int64_t f2f9_38 = f2 * (int64_t) f9_38; | |
1317 | int64_t f3f3_2 = f3_2 * (int64_t) f3; | |
1318 | int64_t f3f4_2 = f3_2 * (int64_t) f4; | |
1319 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; | |
1320 | int64_t f3f6_2 = f3_2 * (int64_t) f6; | |
1321 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; | |
1322 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; | |
1323 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; | |
1324 | int64_t f4f4 = f4 * (int64_t) f4; | |
1325 | int64_t f4f5_2 = f4_2 * (int64_t) f5; | |
1326 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; | |
1327 | int64_t f4f7_38 = f4 * (int64_t) f7_38; | |
1328 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; | |
1329 | int64_t f4f9_38 = f4 * (int64_t) f9_38; | |
1330 | int64_t f5f5_38 = f5 * (int64_t) f5_38; | |
1331 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; | |
1332 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; | |
1333 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; | |
1334 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; | |
1335 | int64_t f6f6_19 = f6 * (int64_t) f6_19; | |
1336 | int64_t f6f7_38 = f6 * (int64_t) f7_38; | |
1337 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; | |
1338 | int64_t f6f9_38 = f6 * (int64_t) f9_38; | |
1339 | int64_t f7f7_38 = f7 * (int64_t) f7_38; | |
1340 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; | |
1341 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; | |
1342 | int64_t f8f8_19 = f8 * (int64_t) f8_19; | |
1343 | int64_t f8f9_38 = f8 * (int64_t) f9_38; | |
1344 | int64_t f9f9_38 = f9 * (int64_t) f9_38; | |
425dde5d DMSP |
1345 | int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; |
1346 | int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; | |
1347 | int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; | |
1348 | int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; | |
1349 | int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; | |
1350 | int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; | |
1351 | int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; | |
1352 | int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; | |
1353 | int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; | |
1354 | int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; | |
3a17b9a4 DMSP |
1355 | int64_t carry0; |
1356 | int64_t carry1; | |
1357 | int64_t carry2; | |
1358 | int64_t carry3; | |
1359 | int64_t carry4; | |
1360 | int64_t carry5; | |
1361 | int64_t carry6; | |
1362 | int64_t carry7; | |
1363 | int64_t carry8; | |
1364 | int64_t carry9; | |
1365 | ||
1366 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
1367 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
1368 | ||
1369 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; | |
1370 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
1371 | ||
1372 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; | |
1373 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
1374 | ||
1375 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; | |
1376 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
1377 | ||
1378 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
1379 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
1380 | ||
1381 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; | |
1382 | ||
1383 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
1384 | ||
1385 | h[0] = (int32_t)h0; | |
1386 | h[1] = (int32_t)h1; | |
1387 | h[2] = (int32_t)h2; | |
1388 | h[3] = (int32_t)h3; | |
1389 | h[4] = (int32_t)h4; | |
1390 | h[5] = (int32_t)h5; | |
1391 | h[6] = (int32_t)h6; | |
1392 | h[7] = (int32_t)h7; | |
1393 | h[8] = (int32_t)h8; | |
1394 | h[9] = (int32_t)h9; | |
a90def6b DSH |
1395 | } |
1396 | ||
3a17b9a4 DMSP |
1397 | static void fe_invert(fe out, const fe z) |
1398 | { | |
1399 | fe t0; | |
1400 | fe t1; | |
1401 | fe t2; | |
1402 | fe t3; | |
1403 | int i; | |
1404 | ||
1405 | /* | |
1406 | * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as | |
1407 | * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. | |
1408 | */ | |
1409 | ||
1410 | /* t0 = z ** 2 */ | |
1411 | fe_sq(t0, z); | |
1412 | ||
1413 | /* t1 = t0 ** (2 ** 2) = z ** 8 */ | |
1414 | fe_sq(t1, t0); | |
1415 | fe_sq(t1, t1); | |
1416 | ||
1417 | /* t1 = z * t1 = z ** 9 */ | |
1418 | fe_mul(t1, z, t1); | |
1419 | /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ | |
1420 | fe_mul(t0, t0, t1); | |
a90def6b | 1421 | |
3a17b9a4 DMSP |
1422 | /* t2 = t0 ** 2 = z ** 22 */ |
1423 | fe_sq(t2, t0); | |
0eadff03 | 1424 | |
3a17b9a4 DMSP |
1425 | /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ |
1426 | fe_mul(t1, t1, t2); | |
0eadff03 | 1427 | |
3a17b9a4 DMSP |
1428 | /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ |
1429 | fe_sq(t2, t1); | |
1430 | for (i = 1; i < 5; ++i) { | |
1431 | fe_sq(t2, t2); | |
1432 | } | |
0eadff03 | 1433 | |
3a17b9a4 DMSP |
1434 | /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ |
1435 | fe_mul(t1, t2, t1); | |
0eadff03 | 1436 | |
3a17b9a4 | 1437 | /* Continuing similarly... */ |
0eadff03 | 1438 | |
3a17b9a4 DMSP |
1439 | /* t2 = z ** (2 ** 20 - 1) */ |
1440 | fe_sq(t2, t1); | |
1441 | for (i = 1; i < 10; ++i) { | |
1442 | fe_sq(t2, t2); | |
1443 | } | |
1444 | fe_mul(t2, t2, t1); | |
0eadff03 | 1445 | |
3a17b9a4 DMSP |
1446 | /* t2 = z ** (2 ** 40 - 1) */ |
1447 | fe_sq(t3, t2); | |
1448 | for (i = 1; i < 20; ++i) { | |
1449 | fe_sq(t3, t3); | |
1450 | } | |
1451 | fe_mul(t2, t3, t2); | |
0eadff03 | 1452 | |
3a17b9a4 DMSP |
1453 | /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ |
1454 | for (i = 0; i < 10; ++i) { | |
1455 | fe_sq(t2, t2); | |
1456 | } | |
1457 | /* t1 = z ** (2 ** 50 - 1) */ | |
1458 | fe_mul(t1, t2, t1); | |
0eadff03 | 1459 | |
3a17b9a4 DMSP |
1460 | /* t2 = z ** (2 ** 100 - 1) */ |
1461 | fe_sq(t2, t1); | |
1462 | for (i = 1; i < 50; ++i) { | |
1463 | fe_sq(t2, t2); | |
1464 | } | |
1465 | fe_mul(t2, t2, t1); | |
0eadff03 | 1466 | |
3a17b9a4 DMSP |
1467 | /* t2 = z ** (2 ** 200 - 1) */ |
1468 | fe_sq(t3, t2); | |
1469 | for (i = 1; i < 100; ++i) { | |
1470 | fe_sq(t3, t3); | |
1471 | } | |
1472 | fe_mul(t2, t3, t2); | |
0eadff03 | 1473 | |
3a17b9a4 | 1474 | /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ |
a90def6b | 1475 | fe_sq(t2, t2); |
3a17b9a4 DMSP |
1476 | for (i = 1; i < 50; ++i) { |
1477 | fe_sq(t2, t2); | |
1478 | } | |
0eadff03 | 1479 | |
3a17b9a4 DMSP |
1480 | /* t1 = z ** (2 ** 250 - 1) */ |
1481 | fe_mul(t1, t2, t1); | |
0eadff03 | 1482 | |
3a17b9a4 | 1483 | /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ |
a90def6b | 1484 | fe_sq(t1, t1); |
3a17b9a4 DMSP |
1485 | for (i = 1; i < 5; ++i) { |
1486 | fe_sq(t1, t1); | |
1487 | } | |
0eadff03 | 1488 | |
3a17b9a4 DMSP |
1489 | /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ |
1490 | fe_mul(out, t1, t0); | |
a90def6b DSH |
1491 | } |
1492 | ||
3a17b9a4 DMSP |
1493 | /* |
1494 | * h = -f | |
a90def6b DSH |
1495 | * |
1496 | * Preconditions: | |
1497 | * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. | |
1498 | * | |
1499 | * Postconditions: | |
3a17b9a4 DMSP |
1500 | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
1501 | */ | |
1502 | static void fe_neg(fe h, const fe f) | |
1503 | { | |
1504 | unsigned i; | |
1505 | ||
1506 | for (i = 0; i < 10; i++) { | |
1507 | h[i] = -f[i]; | |
1508 | } | |
a90def6b DSH |
1509 | } |
1510 | ||
3a17b9a4 DMSP |
1511 | /* |
1512 | * Replace (f,g) with (g,g) if b == 1; | |
a90def6b DSH |
1513 | * replace (f,g) with (f,g) if b == 0. |
1514 | * | |
3a17b9a4 DMSP |
1515 | * Preconditions: b in {0,1}. |
1516 | */ | |
1517 | static void fe_cmov(fe f, const fe g, unsigned b) | |
1518 | { | |
1519 | size_t i; | |
1520 | ||
1521 | b = 0-b; | |
1522 | for (i = 0; i < 10; i++) { | |
1523 | int32_t x = f[i] ^ g[i]; | |
1524 | x &= b; | |
1525 | f[i] ^= x; | |
1526 | } | |
a90def6b DSH |
1527 | } |
1528 | ||
3a17b9a4 DMSP |
1529 | /* |
1530 | * return 0 if f == 0 | |
06c6d05f DSH |
1531 | * return 1 if f != 0 |
1532 | * | |
1533 | * Preconditions: | |
3a17b9a4 DMSP |
1534 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
1535 | */ | |
1536 | static int fe_isnonzero(const fe f) | |
1537 | { | |
1538 | uint8_t s[32]; | |
1539 | static const uint8_t zero[32] = {0}; | |
06c6d05f | 1540 | |
3a17b9a4 DMSP |
1541 | fe_tobytes(s, f); |
1542 | ||
1543 | return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; | |
06c6d05f DSH |
1544 | } |
1545 | ||
3a17b9a4 DMSP |
1546 | /* |
1547 | * return 1 if f is in {1,3,5,...,q-2} | |
06c6d05f DSH |
1548 | * return 0 if f is in {0,2,4,...,q-1} |
1549 | * | |
1550 | * Preconditions: | |
3a17b9a4 DMSP |
1551 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. |
1552 | */ | |
1553 | static int fe_isnegative(const fe f) | |
1554 | { | |
1555 | uint8_t s[32]; | |
1556 | ||
1557 | fe_tobytes(s, f); | |
1558 | return s[0] & 1; | |
06c6d05f DSH |
1559 | } |
1560 | ||
3a17b9a4 DMSP |
1561 | /* |
1562 | * h = 2 * f * f | |
1563 | * | |
a90def6b DSH |
1564 | * Can overlap h with f. |
1565 | * | |
1566 | * Preconditions: | |
1567 | * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. | |
1568 | * | |
1569 | * Postconditions: | |
1570 | * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. | |
1571 | * | |
3a17b9a4 DMSP |
1572 | * See fe_mul.c for discussion of implementation strategy. |
1573 | */ | |
1574 | static void fe_sq2(fe h, const fe f) | |
1575 | { | |
1576 | int32_t f0 = f[0]; | |
1577 | int32_t f1 = f[1]; | |
1578 | int32_t f2 = f[2]; | |
1579 | int32_t f3 = f[3]; | |
1580 | int32_t f4 = f[4]; | |
1581 | int32_t f5 = f[5]; | |
1582 | int32_t f6 = f[6]; | |
1583 | int32_t f7 = f[7]; | |
1584 | int32_t f8 = f[8]; | |
1585 | int32_t f9 = f[9]; | |
1586 | int32_t f0_2 = 2 * f0; | |
1587 | int32_t f1_2 = 2 * f1; | |
1588 | int32_t f2_2 = 2 * f2; | |
1589 | int32_t f3_2 = 2 * f3; | |
1590 | int32_t f4_2 = 2 * f4; | |
1591 | int32_t f5_2 = 2 * f5; | |
1592 | int32_t f6_2 = 2 * f6; | |
1593 | int32_t f7_2 = 2 * f7; | |
1594 | int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ | |
1595 | int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ | |
1596 | int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ | |
1597 | int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ | |
1598 | int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ | |
1599 | int64_t f0f0 = f0 * (int64_t) f0; | |
1600 | int64_t f0f1_2 = f0_2 * (int64_t) f1; | |
1601 | int64_t f0f2_2 = f0_2 * (int64_t) f2; | |
1602 | int64_t f0f3_2 = f0_2 * (int64_t) f3; | |
1603 | int64_t f0f4_2 = f0_2 * (int64_t) f4; | |
1604 | int64_t f0f5_2 = f0_2 * (int64_t) f5; | |
1605 | int64_t f0f6_2 = f0_2 * (int64_t) f6; | |
1606 | int64_t f0f7_2 = f0_2 * (int64_t) f7; | |
1607 | int64_t f0f8_2 = f0_2 * (int64_t) f8; | |
1608 | int64_t f0f9_2 = f0_2 * (int64_t) f9; | |
1609 | int64_t f1f1_2 = f1_2 * (int64_t) f1; | |
1610 | int64_t f1f2_2 = f1_2 * (int64_t) f2; | |
1611 | int64_t f1f3_4 = f1_2 * (int64_t) f3_2; | |
1612 | int64_t f1f4_2 = f1_2 * (int64_t) f4; | |
1613 | int64_t f1f5_4 = f1_2 * (int64_t) f5_2; | |
1614 | int64_t f1f6_2 = f1_2 * (int64_t) f6; | |
1615 | int64_t f1f7_4 = f1_2 * (int64_t) f7_2; | |
1616 | int64_t f1f8_2 = f1_2 * (int64_t) f8; | |
1617 | int64_t f1f9_76 = f1_2 * (int64_t) f9_38; | |
1618 | int64_t f2f2 = f2 * (int64_t) f2; | |
1619 | int64_t f2f3_2 = f2_2 * (int64_t) f3; | |
1620 | int64_t f2f4_2 = f2_2 * (int64_t) f4; | |
1621 | int64_t f2f5_2 = f2_2 * (int64_t) f5; | |
1622 | int64_t f2f6_2 = f2_2 * (int64_t) f6; | |
1623 | int64_t f2f7_2 = f2_2 * (int64_t) f7; | |
1624 | int64_t f2f8_38 = f2_2 * (int64_t) f8_19; | |
1625 | int64_t f2f9_38 = f2 * (int64_t) f9_38; | |
1626 | int64_t f3f3_2 = f3_2 * (int64_t) f3; | |
1627 | int64_t f3f4_2 = f3_2 * (int64_t) f4; | |
1628 | int64_t f3f5_4 = f3_2 * (int64_t) f5_2; | |
1629 | int64_t f3f6_2 = f3_2 * (int64_t) f6; | |
1630 | int64_t f3f7_76 = f3_2 * (int64_t) f7_38; | |
1631 | int64_t f3f8_38 = f3_2 * (int64_t) f8_19; | |
1632 | int64_t f3f9_76 = f3_2 * (int64_t) f9_38; | |
1633 | int64_t f4f4 = f4 * (int64_t) f4; | |
1634 | int64_t f4f5_2 = f4_2 * (int64_t) f5; | |
1635 | int64_t f4f6_38 = f4_2 * (int64_t) f6_19; | |
1636 | int64_t f4f7_38 = f4 * (int64_t) f7_38; | |
1637 | int64_t f4f8_38 = f4_2 * (int64_t) f8_19; | |
1638 | int64_t f4f9_38 = f4 * (int64_t) f9_38; | |
1639 | int64_t f5f5_38 = f5 * (int64_t) f5_38; | |
1640 | int64_t f5f6_38 = f5_2 * (int64_t) f6_19; | |
1641 | int64_t f5f7_76 = f5_2 * (int64_t) f7_38; | |
1642 | int64_t f5f8_38 = f5_2 * (int64_t) f8_19; | |
1643 | int64_t f5f9_76 = f5_2 * (int64_t) f9_38; | |
1644 | int64_t f6f6_19 = f6 * (int64_t) f6_19; | |
1645 | int64_t f6f7_38 = f6 * (int64_t) f7_38; | |
1646 | int64_t f6f8_38 = f6_2 * (int64_t) f8_19; | |
1647 | int64_t f6f9_38 = f6 * (int64_t) f9_38; | |
1648 | int64_t f7f7_38 = f7 * (int64_t) f7_38; | |
1649 | int64_t f7f8_38 = f7_2 * (int64_t) f8_19; | |
1650 | int64_t f7f9_76 = f7_2 * (int64_t) f9_38; | |
1651 | int64_t f8f8_19 = f8 * (int64_t) f8_19; | |
1652 | int64_t f8f9_38 = f8 * (int64_t) f9_38; | |
1653 | int64_t f9f9_38 = f9 * (int64_t) f9_38; | |
425dde5d DMSP |
1654 | int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; |
1655 | int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; | |
1656 | int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; | |
1657 | int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; | |
1658 | int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; | |
1659 | int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; | |
1660 | int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; | |
1661 | int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; | |
1662 | int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; | |
1663 | int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; | |
3a17b9a4 DMSP |
1664 | int64_t carry0; |
1665 | int64_t carry1; | |
1666 | int64_t carry2; | |
1667 | int64_t carry3; | |
1668 | int64_t carry4; | |
1669 | int64_t carry5; | |
1670 | int64_t carry6; | |
1671 | int64_t carry7; | |
1672 | int64_t carry8; | |
1673 | int64_t carry9; | |
1674 | ||
1675 | h0 += h0; | |
1676 | h1 += h1; | |
1677 | h2 += h2; | |
1678 | h3 += h3; | |
1679 | h4 += h4; | |
1680 | h5 += h5; | |
1681 | h6 += h6; | |
1682 | h7 += h7; | |
1683 | h8 += h8; | |
1684 | h9 += h9; | |
1685 | ||
1686 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
1687 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
1688 | ||
1689 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; | |
1690 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
1691 | ||
1692 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; | |
1693 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
1694 | ||
1695 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; | |
1696 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
1697 | ||
1698 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
1699 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
1700 | ||
1701 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; | |
1702 | ||
1703 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
1704 | ||
1705 | h[0] = (int32_t)h0; | |
1706 | h[1] = (int32_t)h1; | |
1707 | h[2] = (int32_t)h2; | |
1708 | h[3] = (int32_t)h3; | |
1709 | h[4] = (int32_t)h4; | |
1710 | h[5] = (int32_t)h5; | |
1711 | h[6] = (int32_t)h6; | |
1712 | h[7] = (int32_t)h7; | |
1713 | h[8] = (int32_t)h8; | |
1714 | h[9] = (int32_t)h9; | |
a90def6b DSH |
1715 | } |
1716 | ||
3a17b9a4 DMSP |
1717 | static void fe_pow22523(fe out, const fe z) |
1718 | { | |
1719 | fe t0; | |
1720 | fe t1; | |
1721 | fe t2; | |
1722 | int i; | |
06c6d05f | 1723 | |
3a17b9a4 DMSP |
1724 | fe_sq(t0, z); |
1725 | fe_sq(t1, t0); | |
1726 | for (i = 1; i < 2; ++i) { | |
1727 | fe_sq(t1, t1); | |
1728 | } | |
1729 | fe_mul(t1, z, t1); | |
1730 | fe_mul(t0, t0, t1); | |
1731 | fe_sq(t0, t0); | |
1732 | fe_mul(t0, t1, t0); | |
1733 | fe_sq(t1, t0); | |
1734 | for (i = 1; i < 5; ++i) { | |
1735 | fe_sq(t1, t1); | |
1736 | } | |
1737 | fe_mul(t0, t1, t0); | |
1738 | fe_sq(t1, t0); | |
1739 | for (i = 1; i < 10; ++i) { | |
1740 | fe_sq(t1, t1); | |
1741 | } | |
1742 | fe_mul(t1, t1, t0); | |
1743 | fe_sq(t2, t1); | |
1744 | for (i = 1; i < 20; ++i) { | |
1745 | fe_sq(t2, t2); | |
1746 | } | |
1747 | fe_mul(t1, t2, t1); | |
06c6d05f | 1748 | fe_sq(t1, t1); |
3a17b9a4 DMSP |
1749 | for (i = 1; i < 10; ++i) { |
1750 | fe_sq(t1, t1); | |
1751 | } | |
1752 | fe_mul(t0, t1, t0); | |
1753 | fe_sq(t1, t0); | |
1754 | for (i = 1; i < 50; ++i) { | |
1755 | fe_sq(t1, t1); | |
1756 | } | |
1757 | fe_mul(t1, t1, t0); | |
1758 | fe_sq(t2, t1); | |
1759 | for (i = 1; i < 100; ++i) { | |
1760 | fe_sq(t2, t2); | |
1761 | } | |
1762 | fe_mul(t1, t2, t1); | |
06c6d05f | 1763 | fe_sq(t1, t1); |
3a17b9a4 DMSP |
1764 | for (i = 1; i < 50; ++i) { |
1765 | fe_sq(t1, t1); | |
1766 | } | |
1767 | fe_mul(t0, t1, t0); | |
06c6d05f | 1768 | fe_sq(t0, t0); |
3a17b9a4 DMSP |
1769 | for (i = 1; i < 2; ++i) { |
1770 | fe_sq(t0, t0); | |
1771 | } | |
1772 | fe_mul(out, t0, z); | |
06c6d05f DSH |
1773 | } |
1774 | ||
3a17b9a4 DMSP |
1775 | /* |
1776 | * ge means group element. | |
1777 | * | |
a90def6b DSH |
1778 | * Here the group is the set of pairs (x,y) of field elements (see fe.h) |
1779 | * satisfying -x^2 + y^2 = 1 + d x^2y^2 | |
1780 | * where d = -121665/121666. | |
1781 | * | |
1782 | * Representations: | |
1783 | * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z | |
1784 | * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT | |
1785 | * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T | |
3a17b9a4 DMSP |
1786 | * ge_precomp (Duif): (y+x,y-x,2dxy) |
1787 | */ | |
a90def6b | 1788 | typedef struct { |
3a17b9a4 DMSP |
1789 | fe X; |
1790 | fe Y; | |
1791 | fe Z; | |
a90def6b DSH |
1792 | } ge_p2; |
1793 | ||
1794 | typedef struct { | |
3a17b9a4 DMSP |
1795 | fe X; |
1796 | fe Y; | |
1797 | fe Z; | |
1798 | fe T; | |
a90def6b DSH |
1799 | } ge_p3; |
1800 | ||
1801 | typedef struct { | |
3a17b9a4 DMSP |
1802 | fe X; |
1803 | fe Y; | |
1804 | fe Z; | |
1805 | fe T; | |
a90def6b DSH |
1806 | } ge_p1p1; |
1807 | ||
1808 | typedef struct { | |
3a17b9a4 DMSP |
1809 | fe yplusx; |
1810 | fe yminusx; | |
1811 | fe xy2d; | |
a90def6b DSH |
1812 | } ge_precomp; |
1813 | ||
1814 | typedef struct { | |
3a17b9a4 DMSP |
1815 | fe YplusX; |
1816 | fe YminusX; | |
1817 | fe Z; | |
1818 | fe T2d; | |
a90def6b DSH |
1819 | } ge_cached; |
1820 | ||
3a17b9a4 DMSP |
1821 | static void ge_tobytes(uint8_t *s, const ge_p2 *h) |
1822 | { | |
1823 | fe recip; | |
1824 | fe x; | |
1825 | fe y; | |
1826 | ||
1827 | fe_invert(recip, h->Z); | |
1828 | fe_mul(x, h->X, recip); | |
1829 | fe_mul(y, h->Y, recip); | |
1830 | fe_tobytes(s, y); | |
1831 | s[31] ^= fe_isnegative(x) << 7; | |
1832 | } | |
06c6d05f | 1833 | |
3a17b9a4 DMSP |
1834 | static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) |
1835 | { | |
1836 | fe recip; | |
1837 | fe x; | |
1838 | fe y; | |
1839 | ||
1840 | fe_invert(recip, h->Z); | |
1841 | fe_mul(x, h->X, recip); | |
1842 | fe_mul(y, h->Y, recip); | |
1843 | fe_tobytes(s, y); | |
1844 | s[31] ^= fe_isnegative(x) << 7; | |
06c6d05f DSH |
1845 | } |
1846 | ||
3a17b9a4 DMSP |
1847 | static const fe d = { |
1848 | -10913610, 13857413, -15372611, 6949391, 114729, | |
1849 | -8787816, -6275908, -3247719, -18696448, -12055116 | |
1850 | }; | |
06c6d05f | 1851 | |
3a17b9a4 DMSP |
1852 | static const fe sqrtm1 = { |
1853 | -32595792, -7943725, 9377950, 3500415, 12389472, | |
1854 | -272473, -25146209, -2005654, 326686, 11406482 | |
1855 | }; | |
06c6d05f | 1856 | |
3a17b9a4 DMSP |
1857 | static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) |
1858 | { | |
1859 | fe u; | |
1860 | fe v; | |
1861 | fe v3; | |
1862 | fe vxx; | |
1863 | fe check; | |
1864 | ||
1865 | fe_frombytes(h->Y, s); | |
1866 | fe_1(h->Z); | |
1867 | fe_sq(u, h->Y); | |
1868 | fe_mul(v, u, d); | |
1869 | fe_sub(u, u, h->Z); /* u = y^2-1 */ | |
1870 | fe_add(v, v, h->Z); /* v = dy^2+1 */ | |
1871 | ||
1872 | fe_sq(v3, v); | |
1873 | fe_mul(v3, v3, v); /* v3 = v^3 */ | |
1874 | fe_sq(h->X, v3); | |
1875 | fe_mul(h->X, h->X, v); | |
1876 | fe_mul(h->X, h->X, u); /* x = uv^7 */ | |
1877 | ||
1878 | fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ | |
1879 | fe_mul(h->X, h->X, v3); | |
1880 | fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ | |
1881 | ||
1882 | fe_sq(vxx, h->X); | |
1883 | fe_mul(vxx, vxx, v); | |
1884 | fe_sub(check, vxx, u); /* vx^2-u */ | |
06c6d05f | 1885 | if (fe_isnonzero(check)) { |
3a17b9a4 DMSP |
1886 | fe_add(check, vxx, u); /* vx^2+u */ |
1887 | if (fe_isnonzero(check)) { | |
1888 | return -1; | |
1889 | } | |
1890 | fe_mul(h->X, h->X, sqrtm1); | |
06c6d05f | 1891 | } |
06c6d05f | 1892 | |
3a17b9a4 DMSP |
1893 | if (fe_isnegative(h->X) != (s[31] >> 7)) { |
1894 | fe_neg(h->X, h->X); | |
1895 | } | |
06c6d05f | 1896 | |
3a17b9a4 DMSP |
1897 | fe_mul(h->T, h->X, h->Y); |
1898 | return 0; | |
06c6d05f DSH |
1899 | } |
1900 | ||
3a17b9a4 DMSP |
1901 | static void ge_p2_0(ge_p2 *h) |
1902 | { | |
1903 | fe_0(h->X); | |
1904 | fe_1(h->Y); | |
1905 | fe_1(h->Z); | |
06c6d05f DSH |
1906 | } |
1907 | ||
3a17b9a4 DMSP |
1908 | static void ge_p3_0(ge_p3 *h) |
1909 | { | |
1910 | fe_0(h->X); | |
1911 | fe_1(h->Y); | |
1912 | fe_1(h->Z); | |
1913 | fe_0(h->T); | |
a90def6b DSH |
1914 | } |
1915 | ||
3a17b9a4 DMSP |
1916 | static void ge_precomp_0(ge_precomp *h) |
1917 | { | |
1918 | fe_1(h->yplusx); | |
1919 | fe_1(h->yminusx); | |
1920 | fe_0(h->xy2d); | |
a90def6b DSH |
1921 | } |
1922 | ||
1923 | /* r = p */ | |
3a17b9a4 DMSP |
1924 | static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) |
1925 | { | |
1926 | fe_copy(r->X, p->X); | |
1927 | fe_copy(r->Y, p->Y); | |
1928 | fe_copy(r->Z, p->Z); | |
a90def6b DSH |
1929 | } |
1930 | ||
3a17b9a4 DMSP |
1931 | static const fe d2 = { |
1932 | -21827239, -5839606, -30745221, 13898782, 229458, | |
1933 | 15978800, -12551817, -6495438, 29715968, 9444199 | |
1934 | }; | |
06c6d05f DSH |
1935 | |
1936 | /* r = p */ | |
3a17b9a4 DMSP |
1937 | static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) |
1938 | { | |
1939 | fe_add(r->YplusX, p->Y, p->X); | |
1940 | fe_sub(r->YminusX, p->Y, p->X); | |
1941 | fe_copy(r->Z, p->Z); | |
1942 | fe_mul(r->T2d, p->T, d2); | |
06c6d05f DSH |
1943 | } |
1944 | ||
a90def6b | 1945 | /* r = p */ |
3a17b9a4 DMSP |
1946 | static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) |
1947 | { | |
1948 | fe_mul(r->X, p->X, p->T); | |
1949 | fe_mul(r->Y, p->Y, p->Z); | |
1950 | fe_mul(r->Z, p->Z, p->T); | |
a90def6b DSH |
1951 | } |
1952 | ||
1953 | /* r = p */ | |
3a17b9a4 DMSP |
1954 | static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) |
1955 | { | |
1956 | fe_mul(r->X, p->X, p->T); | |
1957 | fe_mul(r->Y, p->Y, p->Z); | |
1958 | fe_mul(r->Z, p->Z, p->T); | |
1959 | fe_mul(r->T, p->X, p->Y); | |
a90def6b DSH |
1960 | } |
1961 | ||
1962 | /* r = 2 * p */ | |
3a17b9a4 DMSP |
1963 | static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) |
1964 | { | |
1965 | fe t0; | |
1966 | ||
1967 | fe_sq(r->X, p->X); | |
1968 | fe_sq(r->Z, p->Y); | |
1969 | fe_sq2(r->T, p->Z); | |
1970 | fe_add(r->Y, p->X, p->Y); | |
1971 | fe_sq(t0, r->Y); | |
1972 | fe_add(r->Y, r->Z, r->X); | |
1973 | fe_sub(r->Z, r->Z, r->X); | |
1974 | fe_sub(r->X, t0, r->Y); | |
1975 | fe_sub(r->T, r->T, r->Z); | |
a90def6b DSH |
1976 | } |
1977 | ||
1978 | /* r = 2 * p */ | |
3a17b9a4 DMSP |
1979 | static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) |
1980 | { | |
1981 | ge_p2 q; | |
1982 | ge_p3_to_p2(&q, p); | |
1983 | ge_p2_dbl(r, &q); | |
a90def6b DSH |
1984 | } |
1985 | ||
1986 | /* r = p + q */ | |
3a17b9a4 DMSP |
1987 | static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) |
1988 | { | |
1989 | fe t0; | |
1990 | ||
1991 | fe_add(r->X, p->Y, p->X); | |
1992 | fe_sub(r->Y, p->Y, p->X); | |
1993 | fe_mul(r->Z, r->X, q->yplusx); | |
1994 | fe_mul(r->Y, r->Y, q->yminusx); | |
1995 | fe_mul(r->T, q->xy2d, p->T); | |
1996 | fe_add(t0, p->Z, p->Z); | |
1997 | fe_sub(r->X, r->Z, r->Y); | |
1998 | fe_add(r->Y, r->Z, r->Y); | |
1999 | fe_add(r->Z, t0, r->T); | |
2000 | fe_sub(r->T, t0, r->T); | |
a90def6b DSH |
2001 | } |
2002 | ||
06c6d05f | 2003 | /* r = p - q */ |
3a17b9a4 DMSP |
2004 | static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) |
2005 | { | |
2006 | fe t0; | |
2007 | ||
2008 | fe_add(r->X, p->Y, p->X); | |
2009 | fe_sub(r->Y, p->Y, p->X); | |
2010 | fe_mul(r->Z, r->X, q->yminusx); | |
2011 | fe_mul(r->Y, r->Y, q->yplusx); | |
2012 | fe_mul(r->T, q->xy2d, p->T); | |
2013 | fe_add(t0, p->Z, p->Z); | |
2014 | fe_sub(r->X, r->Z, r->Y); | |
2015 | fe_add(r->Y, r->Z, r->Y); | |
2016 | fe_sub(r->Z, t0, r->T); | |
2017 | fe_add(r->T, t0, r->T); | |
06c6d05f DSH |
2018 | } |
2019 | ||
2020 | /* r = p + q */ | |
3a17b9a4 DMSP |
2021 | static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) |
2022 | { | |
2023 | fe t0; | |
2024 | ||
2025 | fe_add(r->X, p->Y, p->X); | |
2026 | fe_sub(r->Y, p->Y, p->X); | |
2027 | fe_mul(r->Z, r->X, q->YplusX); | |
2028 | fe_mul(r->Y, r->Y, q->YminusX); | |
2029 | fe_mul(r->T, q->T2d, p->T); | |
2030 | fe_mul(r->X, p->Z, q->Z); | |
2031 | fe_add(t0, r->X, r->X); | |
2032 | fe_sub(r->X, r->Z, r->Y); | |
2033 | fe_add(r->Y, r->Z, r->Y); | |
2034 | fe_add(r->Z, t0, r->T); | |
2035 | fe_sub(r->T, t0, r->T); | |
06c6d05f DSH |
2036 | } |
2037 | ||
2038 | /* r = p - q */ | |
3a17b9a4 DMSP |
2039 | static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) |
2040 | { | |
2041 | fe t0; | |
2042 | ||
2043 | fe_add(r->X, p->Y, p->X); | |
2044 | fe_sub(r->Y, p->Y, p->X); | |
2045 | fe_mul(r->Z, r->X, q->YminusX); | |
2046 | fe_mul(r->Y, r->Y, q->YplusX); | |
2047 | fe_mul(r->T, q->T2d, p->T); | |
2048 | fe_mul(r->X, p->Z, q->Z); | |
2049 | fe_add(t0, r->X, r->X); | |
2050 | fe_sub(r->X, r->Z, r->Y); | |
2051 | fe_add(r->Y, r->Z, r->Y); | |
2052 | fe_sub(r->Z, t0, r->T); | |
2053 | fe_add(r->T, t0, r->T); | |
06c6d05f DSH |
2054 | } |
2055 | ||
3a17b9a4 DMSP |
2056 | static uint8_t equal(signed char b, signed char c) |
2057 | { | |
2058 | uint8_t ub = b; | |
2059 | uint8_t uc = c; | |
2060 | uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ | |
2061 | uint32_t y = x; /* 0: yes; 1..255: no */ | |
2062 | y -= 1; /* 4294967295: yes; 0..254: no */ | |
2063 | y >>= 31; /* 1: yes; 0: no */ | |
2064 | return y; | |
a90def6b DSH |
2065 | } |
2066 | ||
3a17b9a4 DMSP |
2067 | static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) |
2068 | { | |
2069 | fe_cmov(t->yplusx, u->yplusx, b); | |
2070 | fe_cmov(t->yminusx, u->yminusx, b); | |
2071 | fe_cmov(t->xy2d, u->xy2d, b); | |
a90def6b DSH |
2072 | } |
2073 | ||
a90def6b | 2074 | /* k25519Precomp[i][j] = (j+1)*256^i*B */ |
dc22d6b3 | 2075 | static const ge_precomp k25519Precomp[32][8] = { |
a90def6b DSH |
2076 | { |
2077 | { | |
2078 | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, | |
2079 | 27544626, -11754271, -6079156, 2047605}, | |
2080 | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, | |
2081 | 5043384, 19500929, -15469378}, | |
2082 | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, | |
2083 | 29287919, 11864899, -24514362, -4438546}, | |
2084 | }, | |
2085 | { | |
2086 | {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, | |
2087 | -11717903, -3814571, -358445, -10211303}, | |
2088 | {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, | |
2089 | -15616551, 11189268, -26829678, -5319081}, | |
2090 | {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, | |
2091 | -3128826, -9541118, -15472047, -4166697}, | |
2092 | }, | |
2093 | { | |
2094 | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, | |
2095 | 27787600, -14772189, 28944400, -1550024}, | |
2096 | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, | |
2097 | 16354577, -11775962, 7689662, 11199574}, | |
2098 | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, | |
2099 | 7512774, 10017326, -17749093, -9920357}, | |
2100 | }, | |
2101 | { | |
2102 | {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, | |
2103 | -28926210, 15006023, 3284568, -6276540}, | |
2104 | {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, | |
2105 | 7464579, 9656445, 13059162, 10374397}, | |
2106 | {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, | |
2107 | -3839045, -641708, -101325}, | |
2108 | }, | |
2109 | { | |
2110 | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, | |
2111 | 32867885, 14515107, -15438304, 10819380}, | |
2112 | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, | |
2113 | 12483688, -12668491, 5581306}, | |
2114 | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, | |
2115 | 28542350, 13850243, -23678021, -15815942}, | |
2116 | }, | |
2117 | { | |
2118 | {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, | |
2119 | -19188627, -15224819, -9818940, -12085777}, | |
2120 | {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, | |
2121 | -15689887, 1762328, 14866737}, | |
2122 | {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, | |
2123 | -28236412, 3959421, 27914454, 4383652}, | |
2124 | }, | |
2125 | { | |
2126 | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, | |
2127 | 5230134, -23952439, -15175766}, | |
2128 | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, | |
2129 | 20654025, 16520125, 30598449, 7715701}, | |
2130 | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, | |
2131 | -31400660, 1370708, 29794553, -1409300}, | |
2132 | }, | |
2133 | { | |
2134 | {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, | |
2135 | 30290735, 10876454, -33154098, 2381726}, | |
2136 | {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, | |
2137 | -6236617, 3696005, -32300832, 15351955}, | |
2138 | {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, | |
2139 | -32961401, -2970515, 29551813, 10109425}, | |
2140 | }, | |
2141 | }, | |
2142 | { | |
2143 | { | |
2144 | {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, | |
2145 | -2378284, -1627556, 10092783, -4764171}, | |
2146 | {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, | |
2147 | -32508754, 12005538, -17810127, 12803510}, | |
2148 | {17228999, -15661624, -1233527, 300140, -1224870, -11714777, | |
2149 | 30364213, -9038194, 18016357, 4397660}, | |
2150 | }, | |
2151 | { | |
2152 | {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, | |
2153 | -26619106, 14544525, -17477504, 982639}, | |
2154 | {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, | |
2155 | -4120128, -21047696, 9934963}, | |
2156 | {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, | |
2157 | -14747930, 4559895, -30123922, -10897950}, | |
2158 | }, | |
2159 | { | |
2160 | {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, | |
2161 | 24191034, 4541697, -13338309, 5500568}, | |
2162 | {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, | |
2163 | -17430592, 12264343, 10874051, 13524335}, | |
2164 | {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, | |
2165 | 5080568, -22528059, 5376628}, | |
2166 | }, | |
2167 | { | |
2168 | {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, | |
2169 | -22321305, -9447443, 4535768, 1569007}, | |
2170 | {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, | |
2171 | -30494562, 3044290, 31848280, 12543772}, | |
2172 | {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, | |
2173 | -27377195, -2062731, 7718482, 14474653}, | |
2174 | }, | |
2175 | { | |
2176 | {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, | |
2177 | -7236665, 24316168, -5253567}, | |
2178 | {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, | |
2179 | 33040651, -13424532, -20729456, 8321686}, | |
2180 | {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, | |
2181 | 23845965, -11874838, -9984458, 608372}, | |
2182 | }, | |
2183 | { | |
2184 | {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, | |
2185 | 1123968, -6780577, 27229399, 23887}, | |
2186 | {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, | |
2187 | 12797024, -6440308, -1633405, 16678954}, | |
2188 | {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, | |
2189 | -1508144, -4795045, -17169265, 4904953}, | |
2190 | }, | |
2191 | { | |
2192 | {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, | |
2193 | 5169211, 16191880, 2128236, -4326833}, | |
2194 | {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, | |
2195 | -29806336, 916033, -6882542, -2986532}, | |
2196 | {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, | |
2197 | 285431, 2763829, 15736322, 4143876}, | |
2198 | }, | |
2199 | { | |
2200 | {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, | |
2201 | -14594663, 23527084, -16458268}, | |
2202 | {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, | |
2203 | -32625340, 4087881, -15188911, -14416214}, | |
2204 | {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, | |
2205 | 4357868, -4774191, -16323038}, | |
2206 | }, | |
2207 | }, | |
2208 | { | |
2209 | { | |
2210 | {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, | |
2211 | 23365147, -3949732, 7390890, 2759800}, | |
2212 | {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, | |
2213 | -4264057, 1244380, -12919645}, | |
2214 | {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, | |
2215 | 9208236, 15886429, 16489664}, | |
2216 | }, | |
2217 | { | |
2218 | {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, | |
2219 | -13693198, 398369, -30606455, -712933}, | |
2220 | {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, | |
2221 | 13348553, 12076947, -30836462, 5113182}, | |
2222 | {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, | |
2223 | -30341101, -7336386, 13847711, 5387222}, | |
2224 | }, | |
2225 | { | |
2226 | {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, | |
2227 | 8763061, 3617786, -19600662, 10370991}, | |
2228 | {20246567, -14369378, 22358229, -543712, 18507283, -10413996, | |
2229 | 14554437, -8746092, 32232924, 16763880}, | |
2230 | {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, | |
2231 | 11094161, 15689506, 3140038, -16510092}, | |
2232 | }, | |
2233 | { | |
2234 | {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, | |
2235 | -27224800, 9448613, -28774454, 366295}, | |
2236 | {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, | |
2237 | 28344573, 8041113, 719605, 11671788}, | |
2238 | {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, | |
2239 | -15266516, 27000813, -10195553}, | |
2240 | }, | |
2241 | { | |
2242 | {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, | |
2243 | 5336097, 6750977, -14521026}, | |
2244 | {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, | |
2245 | 1695823, -8819122, 8169720, 16220347}, | |
2246 | {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, | |
2247 | -11144307, -2627664, -5990708, -14166033}, | |
2248 | }, | |
2249 | { | |
2250 | {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, | |
2251 | 27884329, 2847284, 2655861, 1738395}, | |
2252 | {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, | |
2253 | 21651608, -3239336, -19087449, -11005278}, | |
2254 | {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, | |
2255 | 5821408, 10478196, 8544890}, | |
2256 | }, | |
2257 | { | |
2258 | {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, | |
2259 | 19270449, 12217473, 17789017, -3395995}, | |
2260 | {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, | |
2261 | 15479401, -3853233, 30460520, 1052596}, | |
2262 | {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, | |
2263 | 27491595, -4612359, 3179268, -9478891}, | |
2264 | }, | |
2265 | { | |
2266 | {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, | |
2267 | -14756777, -16411740, 19072640, -9511060}, | |
2268 | {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, | |
2269 | 5977896, -5215017, 473099, 5040608}, | |
2270 | {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, | |
2271 | 28326862, 1721092, -19558642, -3131606}, | |
2272 | }, | |
2273 | }, | |
2274 | { | |
2275 | { | |
2276 | {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, | |
2277 | 8076149, -27868496, 11538389}, | |
2278 | {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, | |
2279 | 8754525, 7446702, -5676054, 5797016}, | |
2280 | {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, | |
2281 | 2014099, -9050574, -2369172, -5877341}, | |
2282 | }, | |
2283 | { | |
2284 | {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, | |
2285 | 1192730, -3714199, 15123619, 10811505}, | |
2286 | {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, | |
2287 | 15776356, -28886779, -11974553}, | |
2288 | {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, | |
2289 | -20654173, -16484855, 4714547, -9600655}, | |
2290 | }, | |
2291 | { | |
2292 | {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, | |
2293 | 24611599, -4543832, -11745876, 12340220}, | |
2294 | {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, | |
2295 | 9613953, 8241152, 15370987, 9608631}, | |
2296 | {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, | |
2297 | 15866074, -28210621, -8814099}, | |
2298 | }, | |
2299 | { | |
2300 | {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, | |
2301 | 858697, 20571223, 8420556}, | |
2302 | {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, | |
2303 | 33531827, 12516406, -21574435, -12476749}, | |
2304 | {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, | |
2305 | 7256740, 8791136, 15069930}, | |
2306 | }, | |
2307 | { | |
2308 | {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, | |
2309 | 14711875, 4874229, -30663140, -2331391}, | |
2310 | {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, | |
2311 | -7912378, -33069337, 9234253}, | |
2312 | {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, | |
2313 | 31559055, -11609587, 18979186, 13396066}, | |
2314 | }, | |
2315 | { | |
2316 | {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, | |
2317 | -18816887, 13594782, 33514650, 7021958}, | |
2318 | {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, | |
2319 | -25948728, -3916677, -21480480, 12868082}, | |
2320 | {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, | |
2321 | -21446107, 2244500, -12455797, -8089383}, | |
2322 | }, | |
2323 | { | |
2324 | {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, | |
2325 | 33086546, 8957937, -15233648, 5540521}, | |
2326 | {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, | |
2327 | -23710744, -1568984, -16128528, -14962807}, | |
2328 | {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, | |
2329 | 892185, -11513277, -15205948}, | |
2330 | }, | |
2331 | { | |
2332 | {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, | |
2333 | 4763127, -19179614, 5867134}, | |
2334 | {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, | |
2335 | 27846559, 5931263, -29749703, -16108455}, | |
2336 | {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, | |
2337 | 7283490, -15148073, -19526700, 7734629}, | |
2338 | }, | |
2339 | }, | |
2340 | { | |
2341 | { | |
2342 | {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, | |
2343 | 7585295, -3176626, 18549497, 15302069}, | |
2344 | {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, | |
2345 | 10458790, -6418461, -8872242, 8424746}, | |
2346 | {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, | |
2347 | 19206234, 7134917, -11284482, -828919}, | |
2348 | }, | |
2349 | { | |
2350 | {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, | |
2351 | 10243738, -14685461, -5066034, 16498837}, | |
2352 | {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, | |
2353 | -14124238, 6536641, 10543906}, | |
2354 | {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, | |
2355 | -2669190, -16625574, -27235709, 8876771}, | |
2356 | }, | |
2357 | { | |
2358 | {-25742899, -12566864, -15649966, -846607, -33026686, -796288, | |
2359 | -33481822, 15824474, -604426, -9039817}, | |
2360 | {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, | |
2361 | -4890037, 1657394, 3084098}, | |
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4008 | {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, | |
4009 | 19797970, -12211255, 15192876, -2087490}, | |
4010 | {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, | |
4011 | 10609330, 12694420, 33473243, -13382104}, | |
4012 | {33184999, 11180355, 15832085, -11385430, -1633671, 225884, | |
4013 | 15089336, -11023903, -6135662, 14480053}, | |
4014 | }, | |
4015 | { | |
4016 | {31308717, -5619998, 31030840, -1897099, 15674547, -6582883, | |
4017 | 5496208, 13685227, 27595050, 8737275}, | |
4018 | {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, | |
4019 | -31008351, -12610604, 26498114, 66511}, | |
4020 | {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, | |
4021 | 30540766, -4286747, -13327787, -7515095}, | |
4022 | }, | |
4023 | { | |
4024 | {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, | |
4025 | 8205540, 13585437, -17127465, 15115439}, | |
4026 | {23711543, -672915, 31206561, -8362711, 6164647, -9709987, | |
4027 | -33535882, -1426096, 8236921, 16492939}, | |
4028 | {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, | |
4029 | 19574902, 10071562, 6708380, -6222424}, | |
4030 | }, | |
4031 | { | |
4032 | {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, | |
4033 | 9328700, 29955601, -11678310}, | |
4034 | {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, | |
4035 | -25892142, -12635595, -9917575, 6216608}, | |
4036 | {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, | |
4037 | 24822830, -6146567, -26767480, 7525079}, | |
4038 | }, | |
4039 | { | |
4040 | {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, | |
4041 | -910336, -2782495, -19386633, 11994101}, | |
4042 | {21691500, -13624626, -641331, -14367021, 3285881, -3483596, | |
4043 | -25064666, 9718258, -7477437, 13381418}, | |
4044 | {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, | |
4045 | 23111648, -6375247, 28535282, 15779576}, | |
4046 | }, | |
4047 | { | |
4048 | {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, | |
4049 | -14068454, 12021730, 9955285, -16303356}, | |
4050 | {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, | |
4051 | -18426029, 9924399, 20194861, 13380996}, | |
4052 | {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, | |
4053 | -1984914, 15707771, 26342023, 10146099}, | |
4054 | }, | |
4055 | }, | |
4056 | { | |
4057 | { | |
4058 | {-26016874, -219943, 21339191, -41388, 19745256, -2878700, | |
4059 | -29637280, 2227040, 21612326, -545728}, | |
4060 | {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, | |
4061 | 25764461, 12243797, -20856566, 11649658}, | |
4062 | {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, | |
4063 | 6114064, 33514190, 2333242}, | |
4064 | }, | |
4065 | { | |
4066 | {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, | |
4067 | -6679750, -12670638, 24350578, -13450001}, | |
4068 | {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, | |
4069 | -31536088, -10406836, 8317860, 12352766}, | |
4070 | {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, | |
4071 | -23552096, -2287550, 20712163, 6719373}, | |
4072 | }, | |
4073 | { | |
4074 | {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, | |
4075 | -3763210, 26224235, -3297458}, | |
4076 | {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, | |
4077 | 21728352, 9493610, 18620611, -16428628}, | |
4078 | {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, | |
4079 | -5269471, -9725556, -30701573, -16479657}, | |
4080 | }, | |
4081 | { | |
4082 | {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, | |
4083 | 12248509, -5240639, 13735342, 1934062}, | |
4084 | {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, | |
4085 | -15136294, -3765346, -21277997, 5473616}, | |
4086 | {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, | |
4087 | -7125085, 12469656, 29111212, -5451014}, | |
4088 | }, | |
4089 | { | |
4090 | {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, | |
4091 | 24367466, 6388839, -10295587, 452383}, | |
4092 | {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, | |
4093 | -24236251, -5915248, 15766062, 8407814}, | |
4094 | {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, | |
4095 | -8917023, -4388953, -8067909, 2276718}, | |
4096 | }, | |
4097 | { | |
4098 | {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, | |
4099 | -23827587, 5096219, 22740376, -7303417}, | |
4100 | {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, | |
4101 | 24051124, 13742383, -15637599, 13295222}, | |
4102 | {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, | |
4103 | -17720195, -4612972, -4451357, -14669444}, | |
4104 | }, | |
4105 | { | |
4106 | {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, | |
4107 | -2469266, -4141880, 7770569, 9620597}, | |
4108 | {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, | |
4109 | -1694323, -33502340, -14767970}, | |
4110 | {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, | |
4111 | 1220118, 30494170, -11440799}, | |
4112 | }, | |
4113 | { | |
4114 | {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, | |
4115 | -26739026, 926050, -1684339, -13333647}, | |
4116 | {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, | |
4117 | 9021034, 9078865, 3353509, 4033511}, | |
4118 | {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, | |
4119 | 23161163, 8839127, 27485041, 7356032}, | |
4120 | }, | |
4121 | }, | |
4122 | { | |
4123 | { | |
4124 | {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, | |
4125 | 2625015, 28431036, -16771834}, | |
4126 | {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, | |
4127 | -22545972, 14150565, 15970762, 4099461}, | |
4128 | {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, | |
4129 | 13617293, -9937143, 11465739, 8317062}, | |
4130 | }, | |
4131 | { | |
4132 | {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, | |
4133 | 14898637, 3848455, 20969334, -5157516}, | |
4134 | {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, | |
4135 | -21610826, -3649888, 11177095, 14989547}, | |
4136 | {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, | |
4137 | 13515641, 2581286, -28487508, 9930240}, | |
4138 | }, | |
4139 | { | |
4140 | {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, | |
4141 | 18345767, -13403753, 16291481, -5314038}, | |
4142 | {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, | |
4143 | 6957617, 4368891, 9788741}, | |
4144 | {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, | |
4145 | -21722536, -8613148, 16250552, -11111103}, | |
4146 | }, | |
4147 | { | |
4148 | {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, | |
4149 | 10604807, -30190403, 4782747}, | |
4150 | {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, | |
4151 | -9981571, 4383045, 22546403, 437323}, | |
4152 | {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, | |
4153 | 27343084, 2786261, -30633590, -14097016}, | |
4154 | }, | |
4155 | { | |
4156 | {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, | |
4157 | -19690631, 2355319, -19284671, -6114373}, | |
4158 | {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, | |
4159 | 18952177, 15496498, -29380133, 11754228}, | |
4160 | {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, | |
4161 | 7141596, 11724556, 22761615, -10134141}, | |
4162 | }, | |
4163 | { | |
4164 | {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, | |
4165 | -28741185, -12227393, 32851222, 11717399}, | |
4166 | {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, | |
4167 | 31474879, 3483633, -1193175, -4030831}, | |
4168 | {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, | |
4169 | 33142652, 6546660, -19985279, -3948376}, | |
4170 | }, | |
4171 | { | |
4172 | {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, | |
4173 | -8537131, -12833048, -30772034, -15486313}, | |
4174 | {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, | |
4175 | -31135347, -16049879, 10928917, 3011958}, | |
4176 | {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, | |
4177 | -30831056, -12805180, 18008031, 10258577}, | |
4178 | }, | |
4179 | { | |
4180 | {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, | |
4181 | -1853465, 1367120, 25127874, 6671743}, | |
4182 | {29701166, -14373934, -10878120, 9279288, -17568, 13127210, | |
4183 | 21382910, 11042292, 25838796, 4642684}, | |
4184 | {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, | |
4185 | 30468147, -13900640, 18423289, 4177476}, | |
4186 | }, | |
4187 | }, | |
4188 | }; | |
4189 | ||
3a17b9a4 DMSP |
4190 | static uint8_t negative(signed char b) |
4191 | { | |
4192 | uint32_t x = b; | |
4193 | ||
4194 | x >>= 31; /* 1: yes; 0: no */ | |
4195 | return x; | |
a90def6b DSH |
4196 | } |
4197 | ||
3a17b9a4 DMSP |
4198 | static void table_select(ge_precomp *t, int pos, signed char b) |
4199 | { | |
4200 | ge_precomp minust; | |
4201 | uint8_t bnegative = negative(b); | |
4202 | uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); | |
4203 | ||
4204 | ge_precomp_0(t); | |
4205 | cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); | |
4206 | cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); | |
4207 | cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); | |
4208 | cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); | |
4209 | cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); | |
4210 | cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); | |
4211 | cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); | |
4212 | cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); | |
4213 | fe_copy(minust.yplusx, t->yminusx); | |
4214 | fe_copy(minust.yminusx, t->yplusx); | |
4215 | fe_neg(minust.xy2d, t->xy2d); | |
4216 | cmov(t, &minust, bnegative); | |
a90def6b DSH |
4217 | } |
4218 | ||
3a17b9a4 DMSP |
4219 | /* |
4220 | * h = a * B | |
4221 | * | |
a90def6b DSH |
4222 | * where a = a[0]+256*a[1]+...+256^31 a[31] |
4223 | * B is the Ed25519 base point (x,4/5) with x positive. | |
4224 | * | |
4225 | * Preconditions: | |
3a17b9a4 DMSP |
4226 | * a[31] <= 127 |
4227 | */ | |
4228 | static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) | |
4229 | { | |
4230 | signed char e[64]; | |
4231 | signed char carry; | |
4232 | ge_p1p1 r; | |
4233 | ge_p2 s; | |
4234 | ge_precomp t; | |
4235 | int i; | |
4236 | ||
4237 | for (i = 0; i < 32; ++i) { | |
4238 | e[2 * i + 0] = (a[i] >> 0) & 15; | |
4239 | e[2 * i + 1] = (a[i] >> 4) & 15; | |
4240 | } | |
4241 | /* each e[i] is between 0 and 15 */ | |
4242 | /* e[63] is between 0 and 7 */ | |
4243 | ||
4244 | carry = 0; | |
4245 | for (i = 0; i < 63; ++i) { | |
4246 | e[i] += carry; | |
4247 | carry = e[i] + 8; | |
4248 | carry >>= 4; | |
4249 | e[i] -= carry << 4; | |
4250 | } | |
4251 | e[63] += carry; | |
4252 | /* each e[i] is between -8 and 8 */ | |
4253 | ||
4254 | ge_p3_0(h); | |
4255 | for (i = 1; i < 64; i += 2) { | |
4256 | table_select(&t, i / 2, e[i]); | |
4257 | ge_madd(&r, h, &t); | |
4258 | ge_p1p1_to_p3(h, &r); | |
4259 | } | |
4260 | ||
4261 | ge_p3_dbl(&r, h); | |
4262 | ge_p1p1_to_p2(&s, &r); | |
4263 | ge_p2_dbl(&r, &s); | |
4264 | ge_p1p1_to_p2(&s, &r); | |
4265 | ge_p2_dbl(&r, &s); | |
4266 | ge_p1p1_to_p2(&s, &r); | |
4267 | ge_p2_dbl(&r, &s); | |
a90def6b | 4268 | ge_p1p1_to_p3(h, &r); |
78f1e4d0 | 4269 | |
3a17b9a4 DMSP |
4270 | for (i = 0; i < 64; i += 2) { |
4271 | table_select(&t, i / 2, e[i]); | |
4272 | ge_madd(&r, h, &t); | |
4273 | ge_p1p1_to_p3(h, &r); | |
4274 | } | |
4275 | ||
4276 | OPENSSL_cleanse(e, sizeof(e)); | |
a90def6b DSH |
4277 | } |
4278 | ||
cfc32a1e | 4279 | #if !defined(BASE_2_51_IMPLEMENTED) |
3a17b9a4 DMSP |
4280 | /* |
4281 | * Replace (f,g) with (g,f) if b == 1; | |
a90def6b DSH |
4282 | * replace (f,g) with (f,g) if b == 0. |
4283 | * | |
3a17b9a4 DMSP |
4284 | * Preconditions: b in {0,1}. |
4285 | */ | |
4286 | static void fe_cswap(fe f, fe g, unsigned int b) | |
4287 | { | |
4288 | size_t i; | |
4289 | ||
4290 | b = 0-b; | |
4291 | for (i = 0; i < 10; i++) { | |
4292 | int32_t x = f[i] ^ g[i]; | |
4293 | x &= b; | |
4294 | f[i] ^= x; | |
4295 | g[i] ^= x; | |
4296 | } | |
a90def6b DSH |
4297 | } |
4298 | ||
3a17b9a4 DMSP |
4299 | /* |
4300 | * h = f * 121666 | |
4301 | * | |
a90def6b DSH |
4302 | * Can overlap h with f. |
4303 | * | |
4304 | * Preconditions: | |
4305 | * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. | |
4306 | * | |
4307 | * Postconditions: | |
3a17b9a4 DMSP |
4308 | * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |
4309 | */ | |
4310 | static void fe_mul121666(fe h, fe f) | |
4311 | { | |
4312 | int32_t f0 = f[0]; | |
4313 | int32_t f1 = f[1]; | |
4314 | int32_t f2 = f[2]; | |
4315 | int32_t f3 = f[3]; | |
4316 | int32_t f4 = f[4]; | |
4317 | int32_t f5 = f[5]; | |
4318 | int32_t f6 = f[6]; | |
4319 | int32_t f7 = f[7]; | |
4320 | int32_t f8 = f[8]; | |
4321 | int32_t f9 = f[9]; | |
4322 | int64_t h0 = f0 * (int64_t) 121666; | |
4323 | int64_t h1 = f1 * (int64_t) 121666; | |
4324 | int64_t h2 = f2 * (int64_t) 121666; | |
4325 | int64_t h3 = f3 * (int64_t) 121666; | |
4326 | int64_t h4 = f4 * (int64_t) 121666; | |
4327 | int64_t h5 = f5 * (int64_t) 121666; | |
4328 | int64_t h6 = f6 * (int64_t) 121666; | |
4329 | int64_t h7 = f7 * (int64_t) 121666; | |
4330 | int64_t h8 = f8 * (int64_t) 121666; | |
4331 | int64_t h9 = f9 * (int64_t) 121666; | |
4332 | int64_t carry0; | |
4333 | int64_t carry1; | |
4334 | int64_t carry2; | |
4335 | int64_t carry3; | |
4336 | int64_t carry4; | |
4337 | int64_t carry5; | |
4338 | int64_t carry6; | |
4339 | int64_t carry7; | |
4340 | int64_t carry8; | |
4341 | int64_t carry9; | |
4342 | ||
4343 | carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; | |
4344 | carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; | |
4345 | carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; | |
4346 | carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; | |
4347 | carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; | |
4348 | ||
4349 | carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; | |
4350 | carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; | |
4351 | carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; | |
4352 | carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; | |
4353 | carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; | |
4354 | ||
4355 | h[0] = (int32_t)h0; | |
4356 | h[1] = (int32_t)h1; | |
4357 | h[2] = (int32_t)h2; | |
4358 | h[3] = (int32_t)h3; | |
4359 | h[4] = (int32_t)h4; | |
4360 | h[5] = (int32_t)h5; | |
4361 | h[6] = (int32_t)h6; | |
4362 | h[7] = (int32_t)h7; | |
4363 | h[8] = (int32_t)h8; | |
4364 | h[9] = (int32_t)h9; | |
a90def6b DSH |
4365 | } |
4366 | ||
4367 | static void x25519_scalar_mult_generic(uint8_t out[32], | |
4368 | const uint8_t scalar[32], | |
4369 | const uint8_t point[32]) { | |
3a17b9a4 DMSP |
4370 | fe x1, x2, z2, x3, z3, tmp0, tmp1; |
4371 | uint8_t e[32]; | |
4372 | unsigned swap = 0; | |
4373 | int pos; | |
4374 | ||
4375 | memcpy(e, scalar, 32); | |
4376 | e[0] &= 248; | |
4377 | e[31] &= 127; | |
4378 | e[31] |= 64; | |
4379 | fe_frombytes(x1, point); | |
4380 | fe_1(x2); | |
4381 | fe_0(z2); | |
4382 | fe_copy(x3, x1); | |
4383 | fe_1(z3); | |
4384 | ||
4385 | for (pos = 254; pos >= 0; --pos) { | |
4386 | unsigned b = 1 & (e[pos / 8] >> (pos & 7)); | |
4387 | swap ^= b; | |
4388 | fe_cswap(x2, x3, swap); | |
4389 | fe_cswap(z2, z3, swap); | |
4390 | swap = b; | |
4391 | fe_sub(tmp0, x3, z3); | |
4392 | fe_sub(tmp1, x2, z2); | |
4393 | fe_add(x2, x2, z2); | |
4394 | fe_add(z2, x3, z3); | |
4395 | fe_mul(z3, tmp0, x2); | |
4396 | fe_mul(z2, z2, tmp1); | |
4397 | fe_sq(tmp0, tmp1); | |
4398 | fe_sq(tmp1, x2); | |
4399 | fe_add(x3, z3, z2); | |
4400 | fe_sub(z2, z3, z2); | |
4401 | fe_mul(x2, tmp1, tmp0); | |
4402 | fe_sub(tmp1, tmp1, tmp0); | |
4403 | fe_sq(z2, z2); | |
4404 | fe_mul121666(z3, tmp1); | |
4405 | fe_sq(x3, x3); | |
4406 | fe_add(tmp0, tmp0, z3); | |
4407 | fe_mul(z3, x1, z2); | |
4408 | fe_mul(z2, tmp1, tmp0); | |
4409 | } | |
4410 | ||
4411 | fe_invert(z2, z2); | |
4412 | fe_mul(x2, x2, z2); | |
4413 | fe_tobytes(out, x2); | |
4414 | ||
4415 | OPENSSL_cleanse(e, sizeof(e)); | |
a90def6b DSH |
4416 | } |
4417 | ||
4418 | static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], | |
4419 | const uint8_t point[32]) { | |
3a17b9a4 | 4420 | x25519_scalar_mult_generic(out, scalar, point); |
a90def6b | 4421 | } |
cfc32a1e | 4422 | #endif |
a90def6b | 4423 | |
3a17b9a4 DMSP |
4424 | static void slide(signed char *r, const uint8_t *a) |
4425 | { | |
4426 | int i; | |
4427 | int b; | |
4428 | int k; | |
4429 | ||
4430 | for (i = 0; i < 256; ++i) { | |
4431 | r[i] = 1 & (a[i >> 3] >> (i & 7)); | |
4432 | } | |
4433 | ||
4434 | for (i = 0; i < 256; ++i) { | |
4435 | if (r[i]) { | |
4436 | for (b = 1; b <= 6 && i + b < 256; ++b) { | |
4437 | if (r[i + b]) { | |
4438 | if (r[i] + (r[i + b] << b) <= 15) { | |
4439 | r[i] += r[i + b] << b; | |
4440 | r[i + b] = 0; | |
4441 | } else if (r[i] - (r[i + b] << b) >= -15) { | |
4442 | r[i] -= r[i + b] << b; | |
4443 | for (k = i + b; k < 256; ++k) { | |
4444 | if (!r[k]) { | |
4445 | r[k] = 1; | |
4446 | break; | |
4447 | } | |
4448 | r[k] = 0; | |
4449 | } | |
4450 | } else { | |
4451 | break; | |
4452 | } | |
4453 | } | |
06c6d05f | 4454 | } |
06c6d05f | 4455 | } |
06c6d05f | 4456 | } |
06c6d05f DSH |
4457 | } |
4458 | ||
4459 | static const ge_precomp Bi[8] = { | |
4460 | { | |
4461 | {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, | |
4462 | -11754271, -6079156, 2047605}, | |
4463 | {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, | |
4464 | 5043384, 19500929, -15469378}, | |
4465 | {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, | |
4466 | 11864899, -24514362, -4438546}, | |
4467 | }, | |
4468 | { | |
4469 | {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, | |
4470 | -14772189, 28944400, -1550024}, | |
4471 | {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, | |
4472 | -11775962, 7689662, 11199574}, | |
4473 | {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, | |
4474 | 10017326, -17749093, -9920357}, | |
4475 | }, | |
4476 | { | |
4477 | {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, | |
4478 | 14515107, -15438304, 10819380}, | |
4479 | {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, | |
4480 | 12483688, -12668491, 5581306}, | |
4481 | {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, | |
4482 | 13850243, -23678021, -15815942}, | |
4483 | }, | |
4484 | { | |
4485 | {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, | |
4486 | 5230134, -23952439, -15175766}, | |
4487 | {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, | |
4488 | 16520125, 30598449, 7715701}, | |
4489 | {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, | |
4490 | 1370708, 29794553, -1409300}, | |
4491 | }, | |
4492 | { | |
4493 | {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, | |
4494 | -1361450, -13062696, 13821877}, | |
4495 | {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, | |
4496 | -7212327, 18853322, -14220951}, | |
4497 | {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, | |
4498 | -10431137, 2207753, -3209784}, | |
4499 | }, | |
4500 | { | |
4501 | {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, | |
4502 | -663000, -31111463, -16132436}, | |
4503 | {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, | |
4504 | 15725684, 171356, 6466918}, | |
4505 | {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, | |
4506 | -14088058, -30714912, 16193877}, | |
4507 | }, | |
4508 | { | |
4509 | {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, | |
4510 | 4729455, -18074513, 9256800}, | |
4511 | {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, | |
4512 | 9761698, -19827198, 630305}, | |
4513 | {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, | |
4514 | -15960994, -2449256, -14291300}, | |
4515 | }, | |
4516 | { | |
4517 | {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, | |
4518 | 15033784, 25105118, -7894876}, | |
4519 | {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, | |
4520 | 1573892, -2625887, 2198790, -15804619}, | |
4521 | {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, | |
4522 | -16236442, -32461234, -12290683}, | |
4523 | }, | |
4524 | }; | |
4525 | ||
3a17b9a4 DMSP |
4526 | /* |
4527 | * r = a * A + b * B | |
4528 | * | |
06c6d05f DSH |
4529 | * where a = a[0]+256*a[1]+...+256^31 a[31]. |
4530 | * and b = b[0]+256*b[1]+...+256^31 b[31]. | |
3a17b9a4 DMSP |
4531 | * B is the Ed25519 base point (x,4/5) with x positive. |
4532 | */ | |
06c6d05f | 4533 | static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, |
3a17b9a4 DMSP |
4534 | const ge_p3 *A, const uint8_t *b) |
4535 | { | |
4536 | signed char aslide[256]; | |
4537 | signed char bslide[256]; | |
4538 | ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ | |
4539 | ge_p1p1 t; | |
4540 | ge_p3 u; | |
4541 | ge_p3 A2; | |
4542 | int i; | |
4543 | ||
4544 | slide(aslide, a); | |
4545 | slide(bslide, b); | |
4546 | ||
4547 | ge_p3_to_cached(&Ai[0], A); | |
4548 | ge_p3_dbl(&t, A); | |
4549 | ge_p1p1_to_p3(&A2, &t); | |
4550 | ge_add(&t, &A2, &Ai[0]); | |
4551 | ge_p1p1_to_p3(&u, &t); | |
4552 | ge_p3_to_cached(&Ai[1], &u); | |
4553 | ge_add(&t, &A2, &Ai[1]); | |
4554 | ge_p1p1_to_p3(&u, &t); | |
4555 | ge_p3_to_cached(&Ai[2], &u); | |
4556 | ge_add(&t, &A2, &Ai[2]); | |
4557 | ge_p1p1_to_p3(&u, &t); | |
4558 | ge_p3_to_cached(&Ai[3], &u); | |
4559 | ge_add(&t, &A2, &Ai[3]); | |
4560 | ge_p1p1_to_p3(&u, &t); | |
4561 | ge_p3_to_cached(&Ai[4], &u); | |
4562 | ge_add(&t, &A2, &Ai[4]); | |
4563 | ge_p1p1_to_p3(&u, &t); | |
4564 | ge_p3_to_cached(&Ai[5], &u); | |
4565 | ge_add(&t, &A2, &Ai[5]); | |
4566 | ge_p1p1_to_p3(&u, &t); | |
4567 | ge_p3_to_cached(&Ai[6], &u); | |
4568 | ge_add(&t, &A2, &Ai[6]); | |
4569 | ge_p1p1_to_p3(&u, &t); | |
4570 | ge_p3_to_cached(&Ai[7], &u); | |
4571 | ||
4572 | ge_p2_0(r); | |
4573 | ||
4574 | for (i = 255; i >= 0; --i) { | |
4575 | if (aslide[i] || bslide[i]) { | |
4576 | break; | |
4577 | } | |
06c6d05f | 4578 | } |
06c6d05f | 4579 | |
3a17b9a4 DMSP |
4580 | for (; i >= 0; --i) { |
4581 | ge_p2_dbl(&t, r); | |
06c6d05f | 4582 | |
3a17b9a4 DMSP |
4583 | if (aslide[i] > 0) { |
4584 | ge_p1p1_to_p3(&u, &t); | |
4585 | ge_add(&t, &u, &Ai[aslide[i] / 2]); | |
4586 | } else if (aslide[i] < 0) { | |
4587 | ge_p1p1_to_p3(&u, &t); | |
4588 | ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); | |
4589 | } | |
06c6d05f | 4590 | |
3a17b9a4 DMSP |
4591 | if (bslide[i] > 0) { |
4592 | ge_p1p1_to_p3(&u, &t); | |
4593 | ge_madd(&t, &u, &Bi[bslide[i] / 2]); | |
4594 | } else if (bslide[i] < 0) { | |
4595 | ge_p1p1_to_p3(&u, &t); | |
4596 | ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); | |
4597 | } | |
06c6d05f | 4598 | |
3a17b9a4 DMSP |
4599 | ge_p1p1_to_p2(r, &t); |
4600 | } | |
06c6d05f DSH |
4601 | } |
4602 | ||
3a17b9a4 DMSP |
4603 | /* |
4604 | * The set of scalars is \Z/l | |
4605 | * where l = 2^252 + 27742317777372353535851937790883648493. | |
4606 | * | |
4607 | * Input: | |
06c6d05f DSH |
4608 | * s[0]+256*s[1]+...+256^63*s[63] = s |
4609 | * | |
4610 | * Output: | |
4611 | * s[0]+256*s[1]+...+256^31*s[31] = s mod l | |
4612 | * where l = 2^252 + 27742317777372353535851937790883648493. | |
3a17b9a4 DMSP |
4613 | * Overwrites s in place. |
4614 | */ | |
4615 | static void x25519_sc_reduce(uint8_t *s) | |
4616 | { | |
425dde5d DMSP |
4617 | int64_t s0 = kBottom21Bits & load_3(s); |
4618 | int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5); | |
4619 | int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2); | |
4620 | int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7); | |
4621 | int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4); | |
4622 | int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1); | |
4623 | int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6); | |
4624 | int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3); | |
4625 | int64_t s8 = kBottom21Bits & load_3(s + 21); | |
4626 | int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5); | |
4627 | int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2); | |
4628 | int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7); | |
4629 | int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4); | |
4630 | int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1); | |
4631 | int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6); | |
4632 | int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3); | |
4633 | int64_t s16 = kBottom21Bits & load_3(s + 42); | |
4634 | int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5); | |
4635 | int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2); | |
4636 | int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7); | |
4637 | int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4); | |
4638 | int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1); | |
4639 | int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6); | |
4640 | int64_t s23 = (load_4(s + 60) >> 3); | |
3a17b9a4 DMSP |
4641 | int64_t carry0; |
4642 | int64_t carry1; | |
4643 | int64_t carry2; | |
4644 | int64_t carry3; | |
4645 | int64_t carry4; | |
4646 | int64_t carry5; | |
4647 | int64_t carry6; | |
4648 | int64_t carry7; | |
4649 | int64_t carry8; | |
4650 | int64_t carry9; | |
4651 | int64_t carry10; | |
4652 | int64_t carry11; | |
4653 | int64_t carry12; | |
4654 | int64_t carry13; | |
4655 | int64_t carry14; | |
4656 | int64_t carry15; | |
4657 | int64_t carry16; | |
4658 | ||
4659 | s11 += s23 * 666643; | |
4660 | s12 += s23 * 470296; | |
4661 | s13 += s23 * 654183; | |
4662 | s14 -= s23 * 997805; | |
4663 | s15 += s23 * 136657; | |
4664 | s16 -= s23 * 683901; | |
425dde5d | 4665 | s23 = 0; |
3a17b9a4 DMSP |
4666 | |
4667 | s10 += s22 * 666643; | |
4668 | s11 += s22 * 470296; | |
4669 | s12 += s22 * 654183; | |
4670 | s13 -= s22 * 997805; | |
4671 | s14 += s22 * 136657; | |
4672 | s15 -= s22 * 683901; | |
425dde5d | 4673 | s22 = 0; |
3a17b9a4 | 4674 | |
425dde5d | 4675 | s9 += s21 * 666643; |
3a17b9a4 DMSP |
4676 | s10 += s21 * 470296; |
4677 | s11 += s21 * 654183; | |
4678 | s12 -= s21 * 997805; | |
4679 | s13 += s21 * 136657; | |
4680 | s14 -= s21 * 683901; | |
425dde5d | 4681 | s21 = 0; |
3a17b9a4 | 4682 | |
425dde5d DMSP |
4683 | s8 += s20 * 666643; |
4684 | s9 += s20 * 470296; | |
3a17b9a4 DMSP |
4685 | s10 += s20 * 654183; |
4686 | s11 -= s20 * 997805; | |
4687 | s12 += s20 * 136657; | |
4688 | s13 -= s20 * 683901; | |
425dde5d | 4689 | s20 = 0; |
3a17b9a4 | 4690 | |
425dde5d DMSP |
4691 | s7 += s19 * 666643; |
4692 | s8 += s19 * 470296; | |
4693 | s9 += s19 * 654183; | |
3a17b9a4 DMSP |
4694 | s10 -= s19 * 997805; |
4695 | s11 += s19 * 136657; | |
4696 | s12 -= s19 * 683901; | |
425dde5d | 4697 | s19 = 0; |
3a17b9a4 | 4698 | |
425dde5d DMSP |
4699 | s6 += s18 * 666643; |
4700 | s7 += s18 * 470296; | |
4701 | s8 += s18 * 654183; | |
4702 | s9 -= s18 * 997805; | |
3a17b9a4 DMSP |
4703 | s10 += s18 * 136657; |
4704 | s11 -= s18 * 683901; | |
425dde5d | 4705 | s18 = 0; |
3a17b9a4 DMSP |
4706 | |
4707 | carry6 = (s6 + (1 << 20)) >> 21; | |
425dde5d DMSP |
4708 | s7 += carry6; |
4709 | s6 -= carry6 * (1 << 21); | |
3a17b9a4 | 4710 | carry8 = (s8 + (1 << 20)) >> 21; |
425dde5d DMSP |
4711 | s9 += carry8; |
4712 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
4713 | carry10 = (s10 + (1 << 20)) >> 21; |
4714 | s11 += carry10; | |
4715 | s10 -= carry10 * (1 << 21); | |
4716 | carry12 = (s12 + (1 << 20)) >> 21; | |
4717 | s13 += carry12; | |
4718 | s12 -= carry12 * (1 << 21); | |
4719 | carry14 = (s14 + (1 << 20)) >> 21; | |
4720 | s15 += carry14; | |
4721 | s14 -= carry14 * (1 << 21); | |
4722 | carry16 = (s16 + (1 << 20)) >> 21; | |
4723 | s17 += carry16; | |
4724 | s16 -= carry16 * (1 << 21); | |
4725 | ||
4726 | carry7 = (s7 + (1 << 20)) >> 21; | |
425dde5d DMSP |
4727 | s8 += carry7; |
4728 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 DMSP |
4729 | carry9 = (s9 + (1 << 20)) >> 21; |
4730 | s10 += carry9; | |
425dde5d | 4731 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
4732 | carry11 = (s11 + (1 << 20)) >> 21; |
4733 | s12 += carry11; | |
4734 | s11 -= carry11 * (1 << 21); | |
4735 | carry13 = (s13 + (1 << 20)) >> 21; | |
4736 | s14 += carry13; | |
4737 | s13 -= carry13 * (1 << 21); | |
4738 | carry15 = (s15 + (1 << 20)) >> 21; | |
4739 | s16 += carry15; | |
4740 | s15 -= carry15 * (1 << 21); | |
4741 | ||
425dde5d DMSP |
4742 | s5 += s17 * 666643; |
4743 | s6 += s17 * 470296; | |
4744 | s7 += s17 * 654183; | |
4745 | s8 -= s17 * 997805; | |
4746 | s9 += s17 * 136657; | |
3a17b9a4 | 4747 | s10 -= s17 * 683901; |
425dde5d DMSP |
4748 | s17 = 0; |
4749 | ||
4750 | s4 += s16 * 666643; | |
4751 | s5 += s16 * 470296; | |
4752 | s6 += s16 * 654183; | |
4753 | s7 -= s16 * 997805; | |
4754 | s8 += s16 * 136657; | |
4755 | s9 -= s16 * 683901; | |
4756 | s16 = 0; | |
4757 | ||
4758 | s3 += s15 * 666643; | |
4759 | s4 += s15 * 470296; | |
4760 | s5 += s15 * 654183; | |
4761 | s6 -= s15 * 997805; | |
4762 | s7 += s15 * 136657; | |
4763 | s8 -= s15 * 683901; | |
4764 | s15 = 0; | |
4765 | ||
4766 | s2 += s14 * 666643; | |
4767 | s3 += s14 * 470296; | |
4768 | s4 += s14 * 654183; | |
4769 | s5 -= s14 * 997805; | |
4770 | s6 += s14 * 136657; | |
4771 | s7 -= s14 * 683901; | |
4772 | s14 = 0; | |
4773 | ||
4774 | s1 += s13 * 666643; | |
4775 | s2 += s13 * 470296; | |
4776 | s3 += s13 * 654183; | |
4777 | s4 -= s13 * 997805; | |
4778 | s5 += s13 * 136657; | |
4779 | s6 -= s13 * 683901; | |
4780 | s13 = 0; | |
4781 | ||
4782 | s0 += s12 * 666643; | |
4783 | s1 += s12 * 470296; | |
4784 | s2 += s12 * 654183; | |
4785 | s3 -= s12 * 997805; | |
4786 | s4 += s12 * 136657; | |
4787 | s5 -= s12 * 683901; | |
4788 | s12 = 0; | |
3a17b9a4 DMSP |
4789 | |
4790 | carry0 = (s0 + (1 << 20)) >> 21; | |
425dde5d DMSP |
4791 | s1 += carry0; |
4792 | s0 -= carry0 * (1 << 21); | |
3a17b9a4 | 4793 | carry2 = (s2 + (1 << 20)) >> 21; |
425dde5d DMSP |
4794 | s3 += carry2; |
4795 | s2 -= carry2 * (1 << 21); | |
3a17b9a4 | 4796 | carry4 = (s4 + (1 << 20)) >> 21; |
425dde5d DMSP |
4797 | s5 += carry4; |
4798 | s4 -= carry4 * (1 << 21); | |
3a17b9a4 DMSP |
4799 | carry6 = (s6 + (1 << 20)) >> 21; |
4800 | s7 += carry6; | |
4801 | s6 -= carry6 * (1 << 21); | |
4802 | carry8 = (s8 + (1 << 20)) >> 21; | |
425dde5d DMSP |
4803 | s9 += carry8; |
4804 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
4805 | carry10 = (s10 + (1 << 20)) >> 21; |
4806 | s11 += carry10; | |
4807 | s10 -= carry10 * (1 << 21); | |
4808 | ||
4809 | carry1 = (s1 + (1 << 20)) >> 21; | |
425dde5d DMSP |
4810 | s2 += carry1; |
4811 | s1 -= carry1 * (1 << 21); | |
3a17b9a4 | 4812 | carry3 = (s3 + (1 << 20)) >> 21; |
425dde5d DMSP |
4813 | s4 += carry3; |
4814 | s3 -= carry3 * (1 << 21); | |
3a17b9a4 | 4815 | carry5 = (s5 + (1 << 20)) >> 21; |
425dde5d DMSP |
4816 | s6 += carry5; |
4817 | s5 -= carry5 * (1 << 21); | |
3a17b9a4 | 4818 | carry7 = (s7 + (1 << 20)) >> 21; |
425dde5d DMSP |
4819 | s8 += carry7; |
4820 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 DMSP |
4821 | carry9 = (s9 + (1 << 20)) >> 21; |
4822 | s10 += carry9; | |
425dde5d | 4823 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
4824 | carry11 = (s11 + (1 << 20)) >> 21; |
4825 | s12 += carry11; | |
4826 | s11 -= carry11 * (1 << 21); | |
4827 | ||
425dde5d DMSP |
4828 | s0 += s12 * 666643; |
4829 | s1 += s12 * 470296; | |
4830 | s2 += s12 * 654183; | |
4831 | s3 -= s12 * 997805; | |
4832 | s4 += s12 * 136657; | |
4833 | s5 -= s12 * 683901; | |
4834 | s12 = 0; | |
3a17b9a4 DMSP |
4835 | |
4836 | carry0 = s0 >> 21; | |
425dde5d DMSP |
4837 | s1 += carry0; |
4838 | s0 -= carry0 * (1 << 21); | |
3a17b9a4 | 4839 | carry1 = s1 >> 21; |
425dde5d DMSP |
4840 | s2 += carry1; |
4841 | s1 -= carry1 * (1 << 21); | |
3a17b9a4 | 4842 | carry2 = s2 >> 21; |
425dde5d DMSP |
4843 | s3 += carry2; |
4844 | s2 -= carry2 * (1 << 21); | |
3a17b9a4 | 4845 | carry3 = s3 >> 21; |
425dde5d DMSP |
4846 | s4 += carry3; |
4847 | s3 -= carry3 * (1 << 21); | |
3a17b9a4 | 4848 | carry4 = s4 >> 21; |
425dde5d DMSP |
4849 | s5 += carry4; |
4850 | s4 -= carry4 * (1 << 21); | |
3a17b9a4 | 4851 | carry5 = s5 >> 21; |
425dde5d DMSP |
4852 | s6 += carry5; |
4853 | s5 -= carry5 * (1 << 21); | |
3a17b9a4 | 4854 | carry6 = s6 >> 21; |
425dde5d DMSP |
4855 | s7 += carry6; |
4856 | s6 -= carry6 * (1 << 21); | |
3a17b9a4 | 4857 | carry7 = s7 >> 21; |
425dde5d DMSP |
4858 | s8 += carry7; |
4859 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 | 4860 | carry8 = s8 >> 21; |
425dde5d DMSP |
4861 | s9 += carry8; |
4862 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
4863 | carry9 = s9 >> 21; |
4864 | s10 += carry9; | |
425dde5d | 4865 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
4866 | carry10 = s10 >> 21; |
4867 | s11 += carry10; | |
4868 | s10 -= carry10 * (1 << 21); | |
4869 | carry11 = s11 >> 21; | |
4870 | s12 += carry11; | |
4871 | s11 -= carry11 * (1 << 21); | |
4872 | ||
425dde5d DMSP |
4873 | s0 += s12 * 666643; |
4874 | s1 += s12 * 470296; | |
4875 | s2 += s12 * 654183; | |
4876 | s3 -= s12 * 997805; | |
4877 | s4 += s12 * 136657; | |
4878 | s5 -= s12 * 683901; | |
4879 | s12 = 0; | |
3a17b9a4 DMSP |
4880 | |
4881 | carry0 = s0 >> 21; | |
425dde5d DMSP |
4882 | s1 += carry0; |
4883 | s0 -= carry0 * (1 << 21); | |
3a17b9a4 | 4884 | carry1 = s1 >> 21; |
425dde5d DMSP |
4885 | s2 += carry1; |
4886 | s1 -= carry1 * (1 << 21); | |
3a17b9a4 | 4887 | carry2 = s2 >> 21; |
425dde5d DMSP |
4888 | s3 += carry2; |
4889 | s2 -= carry2 * (1 << 21); | |
3a17b9a4 | 4890 | carry3 = s3 >> 21; |
425dde5d DMSP |
4891 | s4 += carry3; |
4892 | s3 -= carry3 * (1 << 21); | |
3a17b9a4 | 4893 | carry4 = s4 >> 21; |
425dde5d DMSP |
4894 | s5 += carry4; |
4895 | s4 -= carry4 * (1 << 21); | |
3a17b9a4 | 4896 | carry5 = s5 >> 21; |
425dde5d DMSP |
4897 | s6 += carry5; |
4898 | s5 -= carry5 * (1 << 21); | |
3a17b9a4 | 4899 | carry6 = s6 >> 21; |
425dde5d DMSP |
4900 | s7 += carry6; |
4901 | s6 -= carry6 * (1 << 21); | |
3a17b9a4 | 4902 | carry7 = s7 >> 21; |
425dde5d DMSP |
4903 | s8 += carry7; |
4904 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 | 4905 | carry8 = s8 >> 21; |
425dde5d DMSP |
4906 | s9 += carry8; |
4907 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
4908 | carry9 = s9 >> 21; |
4909 | s10 += carry9; | |
425dde5d | 4910 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
4911 | carry10 = s10 >> 21; |
4912 | s11 += carry10; | |
4913 | s10 -= carry10 * (1 << 21); | |
4914 | ||
425dde5d DMSP |
4915 | s[ 0] = (uint8_t) (s0 >> 0); |
4916 | s[ 1] = (uint8_t) (s0 >> 8); | |
4917 | s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5)); | |
4918 | s[ 3] = (uint8_t) (s1 >> 3); | |
4919 | s[ 4] = (uint8_t) (s1 >> 11); | |
4920 | s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2)); | |
4921 | s[ 6] = (uint8_t) (s2 >> 6); | |
4922 | s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7)); | |
4923 | s[ 8] = (uint8_t) (s3 >> 1); | |
4924 | s[ 9] = (uint8_t) (s3 >> 9); | |
4925 | s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); | |
4926 | s[11] = (uint8_t) (s4 >> 4); | |
4927 | s[12] = (uint8_t) (s4 >> 12); | |
4928 | s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); | |
4929 | s[14] = (uint8_t) (s5 >> 7); | |
4930 | s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); | |
4931 | s[16] = (uint8_t) (s6 >> 2); | |
4932 | s[17] = (uint8_t) (s6 >> 10); | |
4933 | s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); | |
4934 | s[19] = (uint8_t) (s7 >> 5); | |
4935 | s[20] = (uint8_t) (s7 >> 13); | |
4936 | s[21] = (uint8_t) (s8 >> 0); | |
4937 | s[22] = (uint8_t) (s8 >> 8); | |
4938 | s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); | |
4939 | s[24] = (uint8_t) (s9 >> 3); | |
4940 | s[25] = (uint8_t) (s9 >> 11); | |
4941 | s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); | |
4942 | s[27] = (uint8_t) (s10 >> 6); | |
4943 | s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); | |
4944 | s[29] = (uint8_t) (s11 >> 1); | |
4945 | s[30] = (uint8_t) (s11 >> 9); | |
4946 | s[31] = (uint8_t) (s11 >> 17); | |
06c6d05f DSH |
4947 | } |
4948 | ||
3a17b9a4 DMSP |
4949 | /* |
4950 | * Input: | |
06c6d05f DSH |
4951 | * a[0]+256*a[1]+...+256^31*a[31] = a |
4952 | * b[0]+256*b[1]+...+256^31*b[31] = b | |
4953 | * c[0]+256*c[1]+...+256^31*c[31] = c | |
4954 | * | |
4955 | * Output: | |
4956 | * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l | |
3a17b9a4 DMSP |
4957 | * where l = 2^252 + 27742317777372353535851937790883648493. |
4958 | */ | |
06c6d05f | 4959 | static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, |
3a17b9a4 DMSP |
4960 | const uint8_t *c) |
4961 | { | |
425dde5d DMSP |
4962 | int64_t a0 = kBottom21Bits & load_3(a); |
4963 | int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5); | |
4964 | int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2); | |
4965 | int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7); | |
4966 | int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4); | |
4967 | int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1); | |
4968 | int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6); | |
4969 | int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3); | |
4970 | int64_t a8 = kBottom21Bits & load_3(a + 21); | |
4971 | int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5); | |
4972 | int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2); | |
4973 | int64_t a11 = (load_4(a + 28) >> 7); | |
4974 | int64_t b0 = kBottom21Bits & load_3(b); | |
4975 | int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5); | |
4976 | int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2); | |
4977 | int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7); | |
4978 | int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4); | |
4979 | int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1); | |
4980 | int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6); | |
4981 | int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3); | |
4982 | int64_t b8 = kBottom21Bits & load_3(b + 21); | |
4983 | int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5); | |
4984 | int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2); | |
4985 | int64_t b11 = (load_4(b + 28) >> 7); | |
4986 | int64_t c0 = kBottom21Bits & load_3(c); | |
4987 | int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5); | |
4988 | int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2); | |
4989 | int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7); | |
4990 | int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4); | |
4991 | int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1); | |
4992 | int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6); | |
4993 | int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3); | |
4994 | int64_t c8 = kBottom21Bits & load_3(c + 21); | |
4995 | int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5); | |
4996 | int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2); | |
4997 | int64_t c11 = (load_4(c + 28) >> 7); | |
3a17b9a4 DMSP |
4998 | int64_t s0; |
4999 | int64_t s1; | |
5000 | int64_t s2; | |
5001 | int64_t s3; | |
5002 | int64_t s4; | |
5003 | int64_t s5; | |
5004 | int64_t s6; | |
5005 | int64_t s7; | |
5006 | int64_t s8; | |
5007 | int64_t s9; | |
5008 | int64_t s10; | |
5009 | int64_t s11; | |
5010 | int64_t s12; | |
5011 | int64_t s13; | |
5012 | int64_t s14; | |
5013 | int64_t s15; | |
5014 | int64_t s16; | |
5015 | int64_t s17; | |
5016 | int64_t s18; | |
5017 | int64_t s19; | |
5018 | int64_t s20; | |
5019 | int64_t s21; | |
5020 | int64_t s22; | |
5021 | int64_t s23; | |
5022 | int64_t carry0; | |
5023 | int64_t carry1; | |
5024 | int64_t carry2; | |
5025 | int64_t carry3; | |
5026 | int64_t carry4; | |
5027 | int64_t carry5; | |
5028 | int64_t carry6; | |
5029 | int64_t carry7; | |
5030 | int64_t carry8; | |
5031 | int64_t carry9; | |
5032 | int64_t carry10; | |
5033 | int64_t carry11; | |
5034 | int64_t carry12; | |
5035 | int64_t carry13; | |
5036 | int64_t carry14; | |
5037 | int64_t carry15; | |
5038 | int64_t carry16; | |
5039 | int64_t carry17; | |
5040 | int64_t carry18; | |
5041 | int64_t carry19; | |
5042 | int64_t carry20; | |
5043 | int64_t carry21; | |
5044 | int64_t carry22; | |
5045 | ||
425dde5d DMSP |
5046 | s0 = c0 + a0 * b0; |
5047 | s1 = c1 + a0 * b1 + a1 * b0; | |
5048 | s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; | |
5049 | s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; | |
5050 | s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; | |
5051 | s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; | |
5052 | s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; | |
5053 | s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0; | |
5054 | s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0; | |
5055 | s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; | |
5056 | s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; | |
5057 | s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; | |
5058 | s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; | |
5059 | s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; | |
5060 | s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3; | |
5061 | s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4; | |
5062 | s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; | |
5063 | s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; | |
5064 | s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; | |
5065 | s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; | |
5066 | s20 = a9 * b11 + a10 * b10 + a11 * b9; | |
5067 | s21 = a10 * b11 + a11 * b10; | |
5068 | s22 = a11 * b11; | |
5069 | s23 = 0; | |
3a17b9a4 DMSP |
5070 | |
5071 | carry0 = (s0 + (1 << 20)) >> 21; | |
425dde5d DMSP |
5072 | s1 += carry0; |
5073 | s0 -= carry0 * (1 << 21); | |
3a17b9a4 | 5074 | carry2 = (s2 + (1 << 20)) >> 21; |
425dde5d DMSP |
5075 | s3 += carry2; |
5076 | s2 -= carry2 * (1 << 21); | |
3a17b9a4 | 5077 | carry4 = (s4 + (1 << 20)) >> 21; |
425dde5d DMSP |
5078 | s5 += carry4; |
5079 | s4 -= carry4 * (1 << 21); | |
3a17b9a4 | 5080 | carry6 = (s6 + (1 << 20)) >> 21; |
425dde5d DMSP |
5081 | s7 += carry6; |
5082 | s6 -= carry6 * (1 << 21); | |
3a17b9a4 | 5083 | carry8 = (s8 + (1 << 20)) >> 21; |
425dde5d DMSP |
5084 | s9 += carry8; |
5085 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
5086 | carry10 = (s10 + (1 << 20)) >> 21; |
5087 | s11 += carry10; | |
5088 | s10 -= carry10 * (1 << 21); | |
5089 | carry12 = (s12 + (1 << 20)) >> 21; | |
5090 | s13 += carry12; | |
5091 | s12 -= carry12 * (1 << 21); | |
5092 | carry14 = (s14 + (1 << 20)) >> 21; | |
5093 | s15 += carry14; | |
5094 | s14 -= carry14 * (1 << 21); | |
5095 | carry16 = (s16 + (1 << 20)) >> 21; | |
5096 | s17 += carry16; | |
5097 | s16 -= carry16 * (1 << 21); | |
5098 | carry18 = (s18 + (1 << 20)) >> 21; | |
5099 | s19 += carry18; | |
5100 | s18 -= carry18 * (1 << 21); | |
5101 | carry20 = (s20 + (1 << 20)) >> 21; | |
5102 | s21 += carry20; | |
5103 | s20 -= carry20 * (1 << 21); | |
5104 | carry22 = (s22 + (1 << 20)) >> 21; | |
5105 | s23 += carry22; | |
5106 | s22 -= carry22 * (1 << 21); | |
5107 | ||
5108 | carry1 = (s1 + (1 << 20)) >> 21; | |
425dde5d DMSP |
5109 | s2 += carry1; |
5110 | s1 -= carry1 * (1 << 21); | |
3a17b9a4 | 5111 | carry3 = (s3 + (1 << 20)) >> 21; |
425dde5d DMSP |
5112 | s4 += carry3; |
5113 | s3 -= carry3 * (1 << 21); | |
3a17b9a4 | 5114 | carry5 = (s5 + (1 << 20)) >> 21; |
425dde5d DMSP |
5115 | s6 += carry5; |
5116 | s5 -= carry5 * (1 << 21); | |
3a17b9a4 | 5117 | carry7 = (s7 + (1 << 20)) >> 21; |
425dde5d DMSP |
5118 | s8 += carry7; |
5119 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 DMSP |
5120 | carry9 = (s9 + (1 << 20)) >> 21; |
5121 | s10 += carry9; | |
425dde5d | 5122 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
5123 | carry11 = (s11 + (1 << 20)) >> 21; |
5124 | s12 += carry11; | |
5125 | s11 -= carry11 * (1 << 21); | |
5126 | carry13 = (s13 + (1 << 20)) >> 21; | |
5127 | s14 += carry13; | |
5128 | s13 -= carry13 * (1 << 21); | |
5129 | carry15 = (s15 + (1 << 20)) >> 21; | |
5130 | s16 += carry15; | |
5131 | s15 -= carry15 * (1 << 21); | |
5132 | carry17 = (s17 + (1 << 20)) >> 21; | |
5133 | s18 += carry17; | |
5134 | s17 -= carry17 * (1 << 21); | |
5135 | carry19 = (s19 + (1 << 20)) >> 21; | |
5136 | s20 += carry19; | |
5137 | s19 -= carry19 * (1 << 21); | |
5138 | carry21 = (s21 + (1 << 20)) >> 21; | |
5139 | s22 += carry21; | |
5140 | s21 -= carry21 * (1 << 21); | |
5141 | ||
5142 | s11 += s23 * 666643; | |
5143 | s12 += s23 * 470296; | |
5144 | s13 += s23 * 654183; | |
5145 | s14 -= s23 * 997805; | |
5146 | s15 += s23 * 136657; | |
5147 | s16 -= s23 * 683901; | |
425dde5d | 5148 | s23 = 0; |
3a17b9a4 DMSP |
5149 | |
5150 | s10 += s22 * 666643; | |
5151 | s11 += s22 * 470296; | |
5152 | s12 += s22 * 654183; | |
5153 | s13 -= s22 * 997805; | |
5154 | s14 += s22 * 136657; | |
5155 | s15 -= s22 * 683901; | |
425dde5d | 5156 | s22 = 0; |
3a17b9a4 | 5157 | |
425dde5d | 5158 | s9 += s21 * 666643; |
3a17b9a4 DMSP |
5159 | s10 += s21 * 470296; |
5160 | s11 += s21 * 654183; | |
5161 | s12 -= s21 * 997805; | |
5162 | s13 += s21 * 136657; | |
5163 | s14 -= s21 * 683901; | |
425dde5d | 5164 | s21 = 0; |
3a17b9a4 | 5165 | |
425dde5d DMSP |
5166 | s8 += s20 * 666643; |
5167 | s9 += s20 * 470296; | |
3a17b9a4 DMSP |
5168 | s10 += s20 * 654183; |
5169 | s11 -= s20 * 997805; | |
5170 | s12 += s20 * 136657; | |
5171 | s13 -= s20 * 683901; | |
425dde5d | 5172 | s20 = 0; |
3a17b9a4 | 5173 | |
425dde5d DMSP |
5174 | s7 += s19 * 666643; |
5175 | s8 += s19 * 470296; | |
5176 | s9 += s19 * 654183; | |
3a17b9a4 DMSP |
5177 | s10 -= s19 * 997805; |
5178 | s11 += s19 * 136657; | |
5179 | s12 -= s19 * 683901; | |
425dde5d | 5180 | s19 = 0; |
3a17b9a4 | 5181 | |
425dde5d DMSP |
5182 | s6 += s18 * 666643; |
5183 | s7 += s18 * 470296; | |
5184 | s8 += s18 * 654183; | |
5185 | s9 -= s18 * 997805; | |
3a17b9a4 DMSP |
5186 | s10 += s18 * 136657; |
5187 | s11 -= s18 * 683901; | |
425dde5d | 5188 | s18 = 0; |
3a17b9a4 DMSP |
5189 | |
5190 | carry6 = (s6 + (1 << 20)) >> 21; | |
425dde5d DMSP |
5191 | s7 += carry6; |
5192 | s6 -= carry6 * (1 << 21); | |
3a17b9a4 | 5193 | carry8 = (s8 + (1 << 20)) >> 21; |
425dde5d DMSP |
5194 | s9 += carry8; |
5195 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
5196 | carry10 = (s10 + (1 << 20)) >> 21; |
5197 | s11 += carry10; | |
5198 | s10 -= carry10 * (1 << 21); | |
5199 | carry12 = (s12 + (1 << 20)) >> 21; | |
5200 | s13 += carry12; | |
5201 | s12 -= carry12 * (1 << 21); | |
5202 | carry14 = (s14 + (1 << 20)) >> 21; | |
5203 | s15 += carry14; | |
5204 | s14 -= carry14 * (1 << 21); | |
5205 | carry16 = (s16 + (1 << 20)) >> 21; | |
5206 | s17 += carry16; | |
5207 | s16 -= carry16 * (1 << 21); | |
5208 | ||
5209 | carry7 = (s7 + (1 << 20)) >> 21; | |
425dde5d DMSP |
5210 | s8 += carry7; |
5211 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 DMSP |
5212 | carry9 = (s9 + (1 << 20)) >> 21; |
5213 | s10 += carry9; | |
425dde5d | 5214 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
5215 | carry11 = (s11 + (1 << 20)) >> 21; |
5216 | s12 += carry11; | |
5217 | s11 -= carry11 * (1 << 21); | |
5218 | carry13 = (s13 + (1 << 20)) >> 21; | |
5219 | s14 += carry13; | |
5220 | s13 -= carry13 * (1 << 21); | |
5221 | carry15 = (s15 + (1 << 20)) >> 21; | |
5222 | s16 += carry15; | |
5223 | s15 -= carry15 * (1 << 21); | |
5224 | ||
425dde5d DMSP |
5225 | s5 += s17 * 666643; |
5226 | s6 += s17 * 470296; | |
5227 | s7 += s17 * 654183; | |
5228 | s8 -= s17 * 997805; | |
5229 | s9 += s17 * 136657; | |
3a17b9a4 | 5230 | s10 -= s17 * 683901; |
425dde5d DMSP |
5231 | s17 = 0; |
5232 | ||
5233 | s4 += s16 * 666643; | |
5234 | s5 += s16 * 470296; | |
5235 | s6 += s16 * 654183; | |
5236 | s7 -= s16 * 997805; | |
5237 | s8 += s16 * 136657; | |
5238 | s9 -= s16 * 683901; | |
5239 | s16 = 0; | |
5240 | ||
5241 | s3 += s15 * 666643; | |
5242 | s4 += s15 * 470296; | |
5243 | s5 += s15 * 654183; | |
5244 | s6 -= s15 * 997805; | |
5245 | s7 += s15 * 136657; | |
5246 | s8 -= s15 * 683901; | |
5247 | s15 = 0; | |
5248 | ||
5249 | s2 += s14 * 666643; | |
5250 | s3 += s14 * 470296; | |
5251 | s4 += s14 * 654183; | |
5252 | s5 -= s14 * 997805; | |
5253 | s6 += s14 * 136657; | |
5254 | s7 -= s14 * 683901; | |
5255 | s14 = 0; | |
5256 | ||
5257 | s1 += s13 * 666643; | |
5258 | s2 += s13 * 470296; | |
5259 | s3 += s13 * 654183; | |
5260 | s4 -= s13 * 997805; | |
5261 | s5 += s13 * 136657; | |
5262 | s6 -= s13 * 683901; | |
5263 | s13 = 0; | |
5264 | ||
5265 | s0 += s12 * 666643; | |
5266 | s1 += s12 * 470296; | |
5267 | s2 += s12 * 654183; | |
5268 | s3 -= s12 * 997805; | |
5269 | s4 += s12 * 136657; | |
5270 | s5 -= s12 * 683901; | |
3a17b9a4 DMSP |
5271 | s12 = 0; |
5272 | ||
5273 | carry0 = (s0 + (1 << 20)) >> 21; | |
425dde5d DMSP |
5274 | s1 += carry0; |
5275 | s0 -= carry0 * (1 << 21); | |
3a17b9a4 | 5276 | carry2 = (s2 + (1 << 20)) >> 21; |
425dde5d DMSP |
5277 | s3 += carry2; |
5278 | s2 -= carry2 * (1 << 21); | |
3a17b9a4 | 5279 | carry4 = (s4 + (1 << 20)) >> 21; |
425dde5d DMSP |
5280 | s5 += carry4; |
5281 | s4 -= carry4 * (1 << 21); | |
3a17b9a4 | 5282 | carry6 = (s6 + (1 << 20)) >> 21; |
425dde5d DMSP |
5283 | s7 += carry6; |
5284 | s6 -= carry6 * (1 << 21); | |
3a17b9a4 | 5285 | carry8 = (s8 + (1 << 20)) >> 21; |
425dde5d DMSP |
5286 | s9 += carry8; |
5287 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
5288 | carry10 = (s10 + (1 << 20)) >> 21; |
5289 | s11 += carry10; | |
5290 | s10 -= carry10 * (1 << 21); | |
5291 | ||
5292 | carry1 = (s1 + (1 << 20)) >> 21; | |
425dde5d DMSP |
5293 | s2 += carry1; |
5294 | s1 -= carry1 * (1 << 21); | |
3a17b9a4 | 5295 | carry3 = (s3 + (1 << 20)) >> 21; |
425dde5d DMSP |
5296 | s4 += carry3; |
5297 | s3 -= carry3 * (1 << 21); | |
3a17b9a4 | 5298 | carry5 = (s5 + (1 << 20)) >> 21; |
425dde5d DMSP |
5299 | s6 += carry5; |
5300 | s5 -= carry5 * (1 << 21); | |
3a17b9a4 | 5301 | carry7 = (s7 + (1 << 20)) >> 21; |
425dde5d DMSP |
5302 | s8 += carry7; |
5303 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 DMSP |
5304 | carry9 = (s9 + (1 << 20)) >> 21; |
5305 | s10 += carry9; | |
425dde5d | 5306 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
5307 | carry11 = (s11 + (1 << 20)) >> 21; |
5308 | s12 += carry11; | |
5309 | s11 -= carry11 * (1 << 21); | |
5310 | ||
425dde5d DMSP |
5311 | s0 += s12 * 666643; |
5312 | s1 += s12 * 470296; | |
5313 | s2 += s12 * 654183; | |
5314 | s3 -= s12 * 997805; | |
5315 | s4 += s12 * 136657; | |
5316 | s5 -= s12 * 683901; | |
5317 | s12 = 0; | |
3a17b9a4 DMSP |
5318 | |
5319 | carry0 = s0 >> 21; | |
425dde5d DMSP |
5320 | s1 += carry0; |
5321 | s0 -= carry0 * (1 << 21); | |
3a17b9a4 | 5322 | carry1 = s1 >> 21; |
425dde5d DMSP |
5323 | s2 += carry1; |
5324 | s1 -= carry1 * (1 << 21); | |
3a17b9a4 | 5325 | carry2 = s2 >> 21; |
425dde5d DMSP |
5326 | s3 += carry2; |
5327 | s2 -= carry2 * (1 << 21); | |
3a17b9a4 | 5328 | carry3 = s3 >> 21; |
425dde5d DMSP |
5329 | s4 += carry3; |
5330 | s3 -= carry3 * (1 << 21); | |
3a17b9a4 | 5331 | carry4 = s4 >> 21; |
425dde5d DMSP |
5332 | s5 += carry4; |
5333 | s4 -= carry4 * (1 << 21); | |
3a17b9a4 | 5334 | carry5 = s5 >> 21; |
425dde5d DMSP |
5335 | s6 += carry5; |
5336 | s5 -= carry5 * (1 << 21); | |
3a17b9a4 | 5337 | carry6 = s6 >> 21; |
425dde5d DMSP |
5338 | s7 += carry6; |
5339 | s6 -= carry6 * (1 << 21); | |
3a17b9a4 | 5340 | carry7 = s7 >> 21; |
425dde5d DMSP |
5341 | s8 += carry7; |
5342 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 | 5343 | carry8 = s8 >> 21; |
425dde5d DMSP |
5344 | s9 += carry8; |
5345 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
5346 | carry9 = s9 >> 21; |
5347 | s10 += carry9; | |
425dde5d | 5348 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
5349 | carry10 = s10 >> 21; |
5350 | s11 += carry10; | |
5351 | s10 -= carry10 * (1 << 21); | |
5352 | carry11 = s11 >> 21; | |
5353 | s12 += carry11; | |
5354 | s11 -= carry11 * (1 << 21); | |
5355 | ||
425dde5d DMSP |
5356 | s0 += s12 * 666643; |
5357 | s1 += s12 * 470296; | |
5358 | s2 += s12 * 654183; | |
5359 | s3 -= s12 * 997805; | |
5360 | s4 += s12 * 136657; | |
5361 | s5 -= s12 * 683901; | |
5362 | s12 = 0; | |
3a17b9a4 DMSP |
5363 | |
5364 | carry0 = s0 >> 21; | |
425dde5d DMSP |
5365 | s1 += carry0; |
5366 | s0 -= carry0 * (1 << 21); | |
3a17b9a4 | 5367 | carry1 = s1 >> 21; |
425dde5d DMSP |
5368 | s2 += carry1; |
5369 | s1 -= carry1 * (1 << 21); | |
3a17b9a4 | 5370 | carry2 = s2 >> 21; |
425dde5d DMSP |
5371 | s3 += carry2; |
5372 | s2 -= carry2 * (1 << 21); | |
3a17b9a4 | 5373 | carry3 = s3 >> 21; |
425dde5d DMSP |
5374 | s4 += carry3; |
5375 | s3 -= carry3 * (1 << 21); | |
3a17b9a4 | 5376 | carry4 = s4 >> 21; |
425dde5d DMSP |
5377 | s5 += carry4; |
5378 | s4 -= carry4 * (1 << 21); | |
3a17b9a4 | 5379 | carry5 = s5 >> 21; |
425dde5d DMSP |
5380 | s6 += carry5; |
5381 | s5 -= carry5 * (1 << 21); | |
3a17b9a4 | 5382 | carry6 = s6 >> 21; |
425dde5d DMSP |
5383 | s7 += carry6; |
5384 | s6 -= carry6 * (1 << 21); | |
3a17b9a4 | 5385 | carry7 = s7 >> 21; |
425dde5d DMSP |
5386 | s8 += carry7; |
5387 | s7 -= carry7 * (1 << 21); | |
3a17b9a4 | 5388 | carry8 = s8 >> 21; |
425dde5d DMSP |
5389 | s9 += carry8; |
5390 | s8 -= carry8 * (1 << 21); | |
3a17b9a4 DMSP |
5391 | carry9 = s9 >> 21; |
5392 | s10 += carry9; | |
425dde5d | 5393 | s9 -= carry9 * (1 << 21); |
3a17b9a4 DMSP |
5394 | carry10 = s10 >> 21; |
5395 | s11 += carry10; | |
5396 | s10 -= carry10 * (1 << 21); | |
5397 | ||
425dde5d DMSP |
5398 | s[ 0] = (uint8_t) (s0 >> 0); |
5399 | s[ 1] = (uint8_t) (s0 >> 8); | |
5400 | s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5)); | |
5401 | s[ 3] = (uint8_t) (s1 >> 3); | |
5402 | s[ 4] = (uint8_t) (s1 >> 11); | |
5403 | s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2)); | |
5404 | s[ 6] = (uint8_t) (s2 >> 6); | |
5405 | s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7)); | |
5406 | s[ 8] = (uint8_t) (s3 >> 1); | |
5407 | s[ 9] = (uint8_t) (s3 >> 9); | |
5408 | s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); | |
5409 | s[11] = (uint8_t) (s4 >> 4); | |
5410 | s[12] = (uint8_t) (s4 >> 12); | |
5411 | s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); | |
5412 | s[14] = (uint8_t) (s5 >> 7); | |
5413 | s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); | |
5414 | s[16] = (uint8_t) (s6 >> 2); | |
5415 | s[17] = (uint8_t) (s6 >> 10); | |
5416 | s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); | |
5417 | s[19] = (uint8_t) (s7 >> 5); | |
5418 | s[20] = (uint8_t) (s7 >> 13); | |
5419 | s[21] = (uint8_t) (s8 >> 0); | |
5420 | s[22] = (uint8_t) (s8 >> 8); | |
5421 | s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); | |
5422 | s[24] = (uint8_t) (s9 >> 3); | |
5423 | s[25] = (uint8_t) (s9 >> 11); | |
5424 | s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); | |
5425 | s[27] = (uint8_t) (s10 >> 6); | |
3a17b9a4 | 5426 | s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); |
425dde5d DMSP |
5427 | s[29] = (uint8_t) (s11 >> 1); |
5428 | s[30] = (uint8_t) (s11 >> 9); | |
5429 | s[31] = (uint8_t) (s11 >> 17); | |
06c6d05f | 5430 | } |
d4d001df | 5431 | |
06c6d05f | 5432 | int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, |
3a17b9a4 DMSP |
5433 | const uint8_t public_key[32], const uint8_t private_key[32]) |
5434 | { | |
5435 | uint8_t az[SHA512_DIGEST_LENGTH]; | |
5436 | uint8_t nonce[SHA512_DIGEST_LENGTH]; | |
5437 | ge_p3 R; | |
5438 | uint8_t hram[SHA512_DIGEST_LENGTH]; | |
5439 | SHA512_CTX hash_ctx; | |
5440 | ||
5441 | SHA512_Init(&hash_ctx); | |
5442 | SHA512_Update(&hash_ctx, private_key, 32); | |
5443 | SHA512_Final(az, &hash_ctx); | |
5444 | ||
5445 | az[0] &= 248; | |
5446 | az[31] &= 63; | |
5447 | az[31] |= 64; | |
5448 | ||
5449 | SHA512_Init(&hash_ctx); | |
5450 | SHA512_Update(&hash_ctx, az + 32, 32); | |
5451 | SHA512_Update(&hash_ctx, message, message_len); | |
5452 | SHA512_Final(nonce, &hash_ctx); | |
5453 | ||
5454 | x25519_sc_reduce(nonce); | |
5455 | ge_scalarmult_base(&R, nonce); | |
5456 | ge_p3_tobytes(out_sig, &R); | |
5457 | ||
5458 | SHA512_Init(&hash_ctx); | |
5459 | SHA512_Update(&hash_ctx, out_sig, 32); | |
5460 | SHA512_Update(&hash_ctx, public_key, 32); | |
5461 | SHA512_Update(&hash_ctx, message, message_len); | |
5462 | SHA512_Final(hram, &hash_ctx); | |
5463 | ||
5464 | x25519_sc_reduce(hram); | |
5465 | sc_muladd(out_sig + 32, hram, az, nonce); | |
5466 | ||
5467 | OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx)); | |
5468 | OPENSSL_cleanse(nonce, sizeof(nonce)); | |
5469 | OPENSSL_cleanse(az, sizeof(az)); | |
5470 | ||
5471 | return 1; | |
06c6d05f DSH |
5472 | } |
5473 | ||
0ac8f35c MC |
5474 | static const char allzeroes[15]; |
5475 | ||
06c6d05f | 5476 | int ED25519_verify(const uint8_t *message, size_t message_len, |
3a17b9a4 DMSP |
5477 | const uint8_t signature[64], const uint8_t public_key[32]) |
5478 | { | |
5479 | int i; | |
5480 | ge_p3 A; | |
5481 | const uint8_t *r, *s; | |
5482 | SHA512_CTX hash_ctx; | |
5483 | ge_p2 R; | |
5484 | uint8_t rcheck[32]; | |
5485 | uint8_t h[SHA512_DIGEST_LENGTH]; | |
5486 | /* 27742317777372353535851937790883648493 in little endian format */ | |
5487 | const uint8_t l_low[16] = { | |
5488 | 0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2, | |
5489 | 0xDE, 0xF9, 0xDE, 0x14 | |
5490 | }; | |
5491 | ||
5492 | r = signature; | |
5493 | s = signature + 32; | |
5494 | ||
5495 | /* | |
5496 | * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493 | |
5497 | * | |
5498 | * If not the signature is publicly invalid. Since it's public we can do the | |
5499 | * check in variable time. | |
5500 | * | |
5501 | * First check the most significant byte | |
5502 | */ | |
5503 | if (s[31] > 0x10) | |
0ac8f35c | 5504 | return 0; |
3a17b9a4 DMSP |
5505 | if (s[31] == 0x10) { |
5506 | /* | |
5507 | * Most significant byte indicates a value close to 2^252 so check the | |
5508 | * rest | |
5509 | */ | |
5510 | if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0) | |
0ac8f35c | 5511 | return 0; |
3a17b9a4 DMSP |
5512 | for (i = 15; i >= 0; i--) { |
5513 | if (s[i] < l_low[i]) | |
5514 | break; | |
5515 | if (s[i] > l_low[i]) | |
5516 | return 0; | |
5517 | } | |
5518 | if (i < 0) | |
5519 | return 0; | |
5520 | } | |
0ac8f35c | 5521 | |
3a17b9a4 DMSP |
5522 | if (ge_frombytes_vartime(&A, public_key) != 0) { |
5523 | return 0; | |
5524 | } | |
06c6d05f | 5525 | |
3a17b9a4 DMSP |
5526 | fe_neg(A.X, A.X); |
5527 | fe_neg(A.T, A.T); | |
06c6d05f | 5528 | |
3a17b9a4 DMSP |
5529 | SHA512_Init(&hash_ctx); |
5530 | SHA512_Update(&hash_ctx, r, 32); | |
5531 | SHA512_Update(&hash_ctx, public_key, 32); | |
5532 | SHA512_Update(&hash_ctx, message, message_len); | |
5533 | SHA512_Final(h, &hash_ctx); | |
06c6d05f | 5534 | |
3a17b9a4 | 5535 | x25519_sc_reduce(h); |
06c6d05f | 5536 | |
3a17b9a4 | 5537 | ge_double_scalarmult_vartime(&R, h, &A, s); |
06c6d05f | 5538 | |
3a17b9a4 | 5539 | ge_tobytes(rcheck, &R); |
06c6d05f | 5540 | |
3a17b9a4 | 5541 | return CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0; |
06c6d05f DSH |
5542 | } |
5543 | ||
d4d001df | 5544 | void ED25519_public_from_private(uint8_t out_public_key[32], |
3a17b9a4 DMSP |
5545 | const uint8_t private_key[32]) |
5546 | { | |
5547 | uint8_t az[SHA512_DIGEST_LENGTH]; | |
5548 | ge_p3 A; | |
06c6d05f | 5549 | |
3a17b9a4 | 5550 | SHA512(private_key, 32, az); |
06c6d05f | 5551 | |
3a17b9a4 DMSP |
5552 | az[0] &= 248; |
5553 | az[31] &= 63; | |
5554 | az[31] |= 64; | |
06c6d05f | 5555 | |
3a17b9a4 DMSP |
5556 | ge_scalarmult_base(&A, az); |
5557 | ge_p3_tobytes(out_public_key, &A); | |
3790a2f6 | 5558 | |
3a17b9a4 | 5559 | OPENSSL_cleanse(az, sizeof(az)); |
06c6d05f DSH |
5560 | } |
5561 | ||
a90def6b | 5562 | int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], |
3a17b9a4 DMSP |
5563 | const uint8_t peer_public_value[32]) |
5564 | { | |
5565 | static const uint8_t kZeros[32] = {0}; | |
5566 | x25519_scalar_mult(out_shared_key, private_key, peer_public_value); | |
5567 | /* The all-zero output results when the input is a point of small order. */ | |
5568 | return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0; | |
a90def6b DSH |
5569 | } |
5570 | ||
a90def6b | 5571 | void X25519_public_from_private(uint8_t out_public_value[32], |
3a17b9a4 DMSP |
5572 | const uint8_t private_key[32]) |
5573 | { | |
5574 | uint8_t e[32]; | |
5575 | ge_p3 A; | |
5576 | fe zplusy, zminusy, zminusy_inv; | |
5577 | ||
5578 | memcpy(e, private_key, 32); | |
5579 | e[0] &= 248; | |
5580 | e[31] &= 127; | |
5581 | e[31] |= 64; | |
5582 | ||
5583 | ge_scalarmult_base(&A, e); | |
5584 | ||
5585 | /* | |
5586 | * We only need the u-coordinate of the curve25519 point. | |
5587 | * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives | |
5588 | * u=(Z+Y)/(Z-Y). | |
5589 | */ | |
5590 | fe_add(zplusy, A.Z, A.Y); | |
5591 | fe_sub(zminusy, A.Z, A.Y); | |
5592 | fe_invert(zminusy_inv, zminusy); | |
5593 | fe_mul(zplusy, zplusy, zminusy_inv); | |
5594 | fe_tobytes(out_public_value, zplusy); | |
5595 | ||
5596 | OPENSSL_cleanse(e, sizeof(e)); | |
a90def6b | 5597 | } |