7 #ifndef SECP256K1_FIELD_REPR_IMPL_H
8 #define SECP256K1_FIELD_REPR_IMPL_H
10 #if defined HAVE_CONFIG_H
18 #if defined(USE_ASM_X86_64)
34 const uint64_t *d = a->
n;
35 int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
37 r &= (d[0] <= 0xFFFFFFFFFFFFFULL *
m);
38 r &= (d[1] <= 0xFFFFFFFFFFFFFULL *
m);
39 r &= (d[2] <= 0xFFFFFFFFFFFFFULL *
m);
40 r &= (d[3] <= 0xFFFFFFFFFFFFFULL *
m);
41 r &= (d[4] <= 0x0FFFFFFFFFFFFULL *
m);
42 r &= (a->magnitude >= 0);
43 r &= (a->magnitude <= 2048);
45 r &= (a->magnitude <= 1);
46 if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
47 r &= (d[0] < 0xFFFFEFFFFFC2FULL);
55 uint64_t t0 = r->
n[0], t1 = r->
n[1], t2 = r->
n[2], t3 = r->
n[3], t4 = r->
n[4];
59 uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
62 t0 += x * 0x1000003D1ULL;
63 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
64 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
m = t1;
65 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
m &= t2;
66 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
m &= t3;
72 x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (
m == 0xFFFFFFFFFFFFFULL)
73 & (t0 >= 0xFFFFEFFFFFC2FULL));
76 t0 += x * 0x1000003D1ULL;
77 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
78 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
79 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
80 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
86 t4 &= 0x0FFFFFFFFFFFFULL;
88 r->
n[0] = t0; r->
n[1] = t1; r->
n[2] = t2; r->
n[3] = t3; r->
n[4] = t4;
93 secp256k1_fe_verify(r);
98 uint64_t t0 = r->
n[0], t1 = r->
n[1], t2 = r->
n[2], t3 = r->
n[3], t4 = r->
n[4];
101 uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
104 t0 += x * 0x1000003D1ULL;
105 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
106 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
107 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
108 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
113 r->
n[0] = t0; r->
n[1] = t1; r->
n[2] = t2; r->
n[3] = t3; r->
n[4] = t4;
117 secp256k1_fe_verify(r);
122 uint64_t t0 = r->
n[0], t1 = r->
n[1], t2 = r->
n[2], t3 = r->
n[3], t4 = r->
n[4];
126 uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
129 t0 += x * 0x1000003D1ULL;
130 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
131 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
m = t1;
132 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
m &= t2;
133 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
m &= t3;
139 x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (
m == 0xFFFFFFFFFFFFFULL)
140 & (t0 >= 0xFFFFEFFFFFC2FULL));
143 t0 += 0x1000003D1ULL;
144 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
145 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
146 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
147 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
153 t4 &= 0x0FFFFFFFFFFFFULL;
156 r->
n[0] = t0; r->
n[1] = t1; r->
n[2] = t2; r->
n[3] = t3; r->
n[4] = t4;
161 secp256k1_fe_verify(r);
166 uint64_t t0 = r->
n[0], t1 = r->
n[1], t2 = r->
n[2], t3 = r->
n[3], t4 = r->
n[4];
172 uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
175 t0 += x * 0x1000003D1ULL;
176 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL;
177 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
178 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
179 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
180 z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
185 return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
189 uint64_t t0, t1, t2, t3, t4;
200 t0 += x * 0x1000003D1ULL;
203 z0 = t0 & 0xFFFFFFFFFFFFFULL;
204 z1 = z0 ^ 0x1000003D0ULL;
207 if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) {
215 t4 &= 0x0FFFFFFFFFFFFULL;
218 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
219 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
220 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
221 z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
226 return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
232 r->
n[1] = r->
n[2] = r->
n[3] = r->
n[4] = 0;
234 r->magnitude = (a != 0);
236 secp256k1_fe_verify(r);
241 const uint64_t *
t = a->
n;
244 secp256k1_fe_verify(a);
246 return (
t[0] |
t[1] |
t[2] |
t[3] |
t[4]) == 0;
252 secp256k1_fe_verify(a);
263 for (i=0; i<5; i++) {
273 secp256k1_fe_verify(a);
274 secp256k1_fe_verify(b);
276 for (i = 4; i >= 0; i--) {
277 if (a->
n[i] > b->
n[i]) {
280 if (a->
n[i] < b->
n[i]) {
289 r->
n[0] = (uint64_t)a[31]
290 | ((uint64_t)a[30] << 8)
291 | ((uint64_t)a[29] << 16)
292 | ((uint64_t)a[28] << 24)
293 | ((uint64_t)a[27] << 32)
294 | ((uint64_t)a[26] << 40)
295 | ((uint64_t)(a[25] & 0xF) << 48);
296 r->
n[1] = (uint64_t)((a[25] >> 4) & 0xF)
297 | ((uint64_t)a[24] << 4)
298 | ((uint64_t)a[23] << 12)
299 | ((uint64_t)a[22] << 20)
300 | ((uint64_t)a[21] << 28)
301 | ((uint64_t)a[20] << 36)
302 | ((uint64_t)a[19] << 44);
303 r->
n[2] = (uint64_t)a[18]
304 | ((uint64_t)a[17] << 8)
305 | ((uint64_t)a[16] << 16)
306 | ((uint64_t)a[15] << 24)
307 | ((uint64_t)a[14] << 32)
308 | ((uint64_t)a[13] << 40)
309 | ((uint64_t)(a[12] & 0xF) << 48);
310 r->
n[3] = (uint64_t)((a[12] >> 4) & 0xF)
311 | ((uint64_t)a[11] << 4)
312 | ((uint64_t)a[10] << 12)
313 | ((uint64_t)a[9] << 20)
314 | ((uint64_t)a[8] << 28)
315 | ((uint64_t)a[7] << 36)
316 | ((uint64_t)a[6] << 44);
317 r->
n[4] = (uint64_t)a[5]
318 | ((uint64_t)a[4] << 8)
319 | ((uint64_t)a[3] << 16)
320 | ((uint64_t)a[2] << 24)
321 | ((uint64_t)a[1] << 32)
322 | ((uint64_t)a[0] << 40);
323 ret = !((r->
n[4] == 0x0FFFFFFFFFFFFULL) & ((r->
n[3] & r->
n[2] & r->
n[1]) == 0xFFFFFFFFFFFFFULL) & (r->
n[0] >= 0xFFFFEFFFFFC2FULL));
328 secp256k1_fe_verify(r);
340 secp256k1_fe_verify(a);
342 r[0] = (a->
n[4] >> 40) & 0xFF;
343 r[1] = (a->
n[4] >> 32) & 0xFF;
344 r[2] = (a->
n[4] >> 24) & 0xFF;
345 r[3] = (a->
n[4] >> 16) & 0xFF;
346 r[4] = (a->
n[4] >> 8) & 0xFF;
347 r[5] = a->
n[4] & 0xFF;
348 r[6] = (a->
n[3] >> 44) & 0xFF;
349 r[7] = (a->
n[3] >> 36) & 0xFF;
350 r[8] = (a->
n[3] >> 28) & 0xFF;
351 r[9] = (a->
n[3] >> 20) & 0xFF;
352 r[10] = (a->
n[3] >> 12) & 0xFF;
353 r[11] = (a->
n[3] >> 4) & 0xFF;
354 r[12] = ((a->
n[2] >> 48) & 0xF) | ((a->
n[3] & 0xF) << 4);
355 r[13] = (a->
n[2] >> 40) & 0xFF;
356 r[14] = (a->
n[2] >> 32) & 0xFF;
357 r[15] = (a->
n[2] >> 24) & 0xFF;
358 r[16] = (a->
n[2] >> 16) & 0xFF;
359 r[17] = (a->
n[2] >> 8) & 0xFF;
360 r[18] = a->
n[2] & 0xFF;
361 r[19] = (a->
n[1] >> 44) & 0xFF;
362 r[20] = (a->
n[1] >> 36) & 0xFF;
363 r[21] = (a->
n[1] >> 28) & 0xFF;
364 r[22] = (a->
n[1] >> 20) & 0xFF;
365 r[23] = (a->
n[1] >> 12) & 0xFF;
366 r[24] = (a->
n[1] >> 4) & 0xFF;
367 r[25] = ((a->
n[0] >> 48) & 0xF) | ((a->
n[1] & 0xF) << 4);
368 r[26] = (a->
n[0] >> 40) & 0xFF;
369 r[27] = (a->
n[0] >> 32) & 0xFF;
370 r[28] = (a->
n[0] >> 24) & 0xFF;
371 r[29] = (a->
n[0] >> 16) & 0xFF;
372 r[30] = (a->
n[0] >> 8) & 0xFF;
373 r[31] = a->
n[0] & 0xFF;
379 secp256k1_fe_verify(a);
381 r->
n[0] = 0xFFFFEFFFFFC2FULL * 2 * (
m + 1) - a->
n[0];
382 r->
n[1] = 0xFFFFFFFFFFFFFULL * 2 * (
m + 1) - a->
n[1];
383 r->
n[2] = 0xFFFFFFFFFFFFFULL * 2 * (
m + 1) - a->
n[2];
384 r->
n[3] = 0xFFFFFFFFFFFFFULL * 2 * (
m + 1) - a->
n[3];
385 r->
n[4] = 0x0FFFFFFFFFFFFULL * 2 * (
m + 1) - a->
n[4];
387 r->magnitude =
m + 1;
389 secp256k1_fe_verify(r);
402 secp256k1_fe_verify(r);
408 secp256k1_fe_verify(a);
416 r->magnitude += a->magnitude;
418 secp256k1_fe_verify(r);
426 secp256k1_fe_verify(a);
427 secp256k1_fe_verify(b);
435 secp256k1_fe_verify(r);
442 secp256k1_fe_verify(a);
448 secp256k1_fe_verify(r);
453 uint64_t mask0, mask1;
455 mask0 = flag + ~((uint64_t)0);
457 r->
n[0] = (r->
n[0] & mask0) | (a->
n[0] & mask1);
458 r->
n[1] = (r->
n[1] & mask0) | (a->
n[1] & mask1);
459 r->
n[2] = (r->
n[2] & mask0) | (a->
n[2] & mask1);
460 r->
n[3] = (r->
n[3] & mask0) | (a->
n[3] & mask1);
461 r->
n[4] = (r->
n[4] & mask0) | (a->
n[4] & mask1);
464 r->magnitude = a->magnitude;
465 r->normalized = a->normalized;
471 uint64_t mask0, mask1;
473 mask0 = flag + ~((uint64_t)0);
475 r->
n[0] = (r->
n[0] & mask0) | (a->
n[0] & mask1);
476 r->
n[1] = (r->
n[1] & mask0) | (a->
n[1] & mask1);
477 r->
n[2] = (r->
n[2] & mask0) | (a->
n[2] & mask1);
478 r->
n[3] = (r->
n[3] & mask0) | (a->
n[3] & mask1);
485 r->
n[0] = a->
n[0] | a->
n[1] << 52;
486 r->
n[1] = a->
n[1] >> 12 | a->
n[2] << 40;
487 r->
n[2] = a->
n[2] >> 24 | a->
n[3] << 28;
488 r->
n[3] = a->
n[3] >> 36 | a->
n[4] << 16;
492 r->
n[0] = a->
n[0] & 0xFFFFFFFFFFFFFULL;
493 r->
n[1] = a->
n[0] >> 52 | ((a->
n[1] << 12) & 0xFFFFFFFFFFFFFULL);
494 r->
n[2] = a->
n[1] >> 40 | ((a->
n[2] << 24) & 0xFFFFFFFFFFFFFULL);
495 r->
n[3] = a->
n[2] >> 28 | ((a->
n[3] << 36) & 0xFFFFFFFFFFFFFULL);
496 r->
n[4] = a->
n[3] >> 16;
500 secp256k1_fe_verify(r);
505 const uint64_t M52 = UINT64_MAX >> 12;
506 const uint64_t a0 = a->
v[0], a1 = a->
v[1], a2 = a->
v[2], a3 = a->
v[3], a4 = a->
v[4];
518 r->
n[1] = (a0 >> 52 | a1 << 10) & M52;
519 r->
n[2] = (a1 >> 42 | a2 << 20) & M52;
520 r->
n[3] = (a2 >> 32 | a3 << 30) & M52;
521 r->
n[4] = (a3 >> 22 | a4 << 40);
526 secp256k1_fe_verify(r);
531 const uint64_t M62 = UINT64_MAX >> 2;
532 const uint64_t a0 = a->
n[0], a1 = a->
n[1], a2 = a->
n[2], a3 = a->
n[3], a4 = a->
n[4];
538 r->
v[0] = (a0 | a1 << 52) & M62;
539 r->
v[1] = (a1 >> 10 | a2 << 42) & M62;
540 r->
v[2] = (a2 >> 20 | a3 << 32) & M62;
541 r->
v[3] = (a3 >> 30 | a4 << 22) & M62;
546 {{-0x1000003D1LL, 0, 0, 0, 256}},