Bitcoin Core 29.99.0
P2P Digital Currency
scalar_8x32_impl.h
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1/***********************************************************************
2 * Copyright (c) 2014 Pieter Wuille *
3 * Distributed under the MIT software license, see the accompanying *
4 * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
5 ***********************************************************************/
6
7#ifndef SECP256K1_SCALAR_REPR_IMPL_H
8#define SECP256K1_SCALAR_REPR_IMPL_H
9
10#include "checkmem.h"
11#include "modinv32_impl.h"
12#include "util.h"
13
14/* Limbs of the secp256k1 order. */
15#define SECP256K1_N_0 ((uint32_t)0xD0364141UL)
16#define SECP256K1_N_1 ((uint32_t)0xBFD25E8CUL)
17#define SECP256K1_N_2 ((uint32_t)0xAF48A03BUL)
18#define SECP256K1_N_3 ((uint32_t)0xBAAEDCE6UL)
19#define SECP256K1_N_4 ((uint32_t)0xFFFFFFFEUL)
20#define SECP256K1_N_5 ((uint32_t)0xFFFFFFFFUL)
21#define SECP256K1_N_6 ((uint32_t)0xFFFFFFFFUL)
22#define SECP256K1_N_7 ((uint32_t)0xFFFFFFFFUL)
23
24/* Limbs of 2^256 minus the secp256k1 order. */
25#define SECP256K1_N_C_0 (~SECP256K1_N_0 + 1)
26#define SECP256K1_N_C_1 (~SECP256K1_N_1)
27#define SECP256K1_N_C_2 (~SECP256K1_N_2)
28#define SECP256K1_N_C_3 (~SECP256K1_N_3)
29#define SECP256K1_N_C_4 (1)
30
31/* Limbs of half the secp256k1 order. */
32#define SECP256K1_N_H_0 ((uint32_t)0x681B20A0UL)
33#define SECP256K1_N_H_1 ((uint32_t)0xDFE92F46UL)
34#define SECP256K1_N_H_2 ((uint32_t)0x57A4501DUL)
35#define SECP256K1_N_H_3 ((uint32_t)0x5D576E73UL)
36#define SECP256K1_N_H_4 ((uint32_t)0xFFFFFFFFUL)
37#define SECP256K1_N_H_5 ((uint32_t)0xFFFFFFFFUL)
38#define SECP256K1_N_H_6 ((uint32_t)0xFFFFFFFFUL)
39#define SECP256K1_N_H_7 ((uint32_t)0x7FFFFFFFUL)
40
41SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
42 r->d[0] = v;
43 r->d[1] = 0;
44 r->d[2] = 0;
45 r->d[3] = 0;
46 r->d[4] = 0;
47 r->d[5] = 0;
48 r->d[6] = 0;
49 r->d[7] = 0;
50
51 SECP256K1_SCALAR_VERIFY(r);
52}
53
54SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_limb32(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
55 SECP256K1_SCALAR_VERIFY(a);
56 VERIFY_CHECK(count > 0 && count <= 32);
57 VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
58
59 return (a->d[offset >> 5] >> (offset & 0x1F)) & (0xFFFFFFFF >> (32 - count));
60}
61
62SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
63 SECP256K1_SCALAR_VERIFY(a);
64 VERIFY_CHECK(count > 0 && count <= 32);
65 VERIFY_CHECK(offset + count <= 256);
66
67 if ((offset + count - 1) >> 5 == offset >> 5) {
68 return secp256k1_scalar_get_bits_limb32(a, offset, count);
69 } else {
70 VERIFY_CHECK((offset >> 5) + 1 < 8);
71 return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & (0xFFFFFFFF >> (32 - count));
72 }
73}
74
75SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
76 int yes = 0;
77 int no = 0;
78 no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
79 no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
80 no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
81 no |= (a->d[4] < SECP256K1_N_4);
82 yes |= (a->d[4] > SECP256K1_N_4) & ~no;
83 no |= (a->d[3] < SECP256K1_N_3) & ~yes;
84 yes |= (a->d[3] > SECP256K1_N_3) & ~no;
85 no |= (a->d[2] < SECP256K1_N_2) & ~yes;
86 yes |= (a->d[2] > SECP256K1_N_2) & ~no;
87 no |= (a->d[1] < SECP256K1_N_1) & ~yes;
88 yes |= (a->d[1] > SECP256K1_N_1) & ~no;
89 yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
90 return yes;
91}
92
93SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
94 uint64_t t;
95 VERIFY_CHECK(overflow <= 1);
96
97 t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
98 r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
99 t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
100 r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
101 t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
102 r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
103 t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
104 r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
105 t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
106 r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
107 t += (uint64_t)r->d[5];
108 r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
109 t += (uint64_t)r->d[6];
110 r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
111 t += (uint64_t)r->d[7];
112 r->d[7] = t & 0xFFFFFFFFUL;
113
114 SECP256K1_SCALAR_VERIFY(r);
115 return overflow;
116}
117
118static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
119 int overflow;
120 uint64_t t = (uint64_t)a->d[0] + b->d[0];
121 SECP256K1_SCALAR_VERIFY(a);
122 SECP256K1_SCALAR_VERIFY(b);
123
124 r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
125 t += (uint64_t)a->d[1] + b->d[1];
126 r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
127 t += (uint64_t)a->d[2] + b->d[2];
128 r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
129 t += (uint64_t)a->d[3] + b->d[3];
130 r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
131 t += (uint64_t)a->d[4] + b->d[4];
132 r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
133 t += (uint64_t)a->d[5] + b->d[5];
134 r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
135 t += (uint64_t)a->d[6] + b->d[6];
136 r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
137 t += (uint64_t)a->d[7] + b->d[7];
138 r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
139 overflow = t + secp256k1_scalar_check_overflow(r);
140 VERIFY_CHECK(overflow == 0 || overflow == 1);
141 secp256k1_scalar_reduce(r, overflow);
142
143 SECP256K1_SCALAR_VERIFY(r);
144 return overflow;
145}
146
147static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
148 uint64_t t;
149 volatile int vflag = flag;
150 SECP256K1_SCALAR_VERIFY(r);
151 VERIFY_CHECK(bit < 256);
152
153 bit += ((uint32_t) vflag - 1) & 0x100; /* forcing (bit >> 5) > 7 makes this a noop */
154 t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
155 r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
156 t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
157 r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
158 t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
159 r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
160 t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
161 r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
162 t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
163 r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
164 t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
165 r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
166 t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
167 r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
168 t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
169 r->d[7] = t & 0xFFFFFFFFULL;
170
171 SECP256K1_SCALAR_VERIFY(r);
172 VERIFY_CHECK((t >> 32) == 0);
173}
174
175static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
176 int over;
177 r->d[0] = secp256k1_read_be32(&b32[28]);
178 r->d[1] = secp256k1_read_be32(&b32[24]);
179 r->d[2] = secp256k1_read_be32(&b32[20]);
180 r->d[3] = secp256k1_read_be32(&b32[16]);
181 r->d[4] = secp256k1_read_be32(&b32[12]);
182 r->d[5] = secp256k1_read_be32(&b32[8]);
183 r->d[6] = secp256k1_read_be32(&b32[4]);
184 r->d[7] = secp256k1_read_be32(&b32[0]);
185 over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
186 if (overflow) {
187 *overflow = over;
188 }
189
190 SECP256K1_SCALAR_VERIFY(r);
191}
192
193static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
194 SECP256K1_SCALAR_VERIFY(a);
195
196 secp256k1_write_be32(&bin[0], a->d[7]);
197 secp256k1_write_be32(&bin[4], a->d[6]);
198 secp256k1_write_be32(&bin[8], a->d[5]);
199 secp256k1_write_be32(&bin[12], a->d[4]);
200 secp256k1_write_be32(&bin[16], a->d[3]);
201 secp256k1_write_be32(&bin[20], a->d[2]);
202 secp256k1_write_be32(&bin[24], a->d[1]);
203 secp256k1_write_be32(&bin[28], a->d[0]);
204}
205
206SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
207 SECP256K1_SCALAR_VERIFY(a);
208
209 return (a->d[0] | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
210}
211
212static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
213 uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
214 uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
215 SECP256K1_SCALAR_VERIFY(a);
216
217 r->d[0] = t & nonzero; t >>= 32;
218 t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
219 r->d[1] = t & nonzero; t >>= 32;
220 t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
221 r->d[2] = t & nonzero; t >>= 32;
222 t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
223 r->d[3] = t & nonzero; t >>= 32;
224 t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
225 r->d[4] = t & nonzero; t >>= 32;
226 t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
227 r->d[5] = t & nonzero; t >>= 32;
228 t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
229 r->d[6] = t & nonzero; t >>= 32;
230 t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
231 r->d[7] = t & nonzero;
232
233 SECP256K1_SCALAR_VERIFY(r);
234}
235
236static void secp256k1_scalar_half(secp256k1_scalar *r, const secp256k1_scalar *a) {
237 /* Writing `/` for field division and `//` for integer division, we compute
238 *
239 * a/2 = (a - (a&1))/2 + (a&1)/2
240 * = (a >> 1) + (a&1 ? 1/2 : 0)
241 * = (a >> 1) + (a&1 ? n//2+1 : 0),
242 *
243 * where n is the group order and in the last equality we have used 1/2 = n//2+1 (mod n).
244 * For n//2, we have the constants SECP256K1_N_H_0, ...
245 *
246 * This sum does not overflow. The most extreme case is a = -2, the largest odd scalar. Here:
247 * - the left summand is: a >> 1 = (a - a&1)/2 = (n-2-1)//2 = (n-3)//2
248 * - the right summand is: a&1 ? n//2+1 : 0 = n//2+1 = (n-1)//2 + 2//2 = (n+1)//2
249 * Together they sum to (n-3)//2 + (n+1)//2 = (2n-2)//2 = n - 1, which is less than n.
250 */
251 uint32_t mask = -(uint32_t)(a->d[0] & 1U);
252 uint64_t t = (uint32_t)((a->d[0] >> 1) | (a->d[1] << 31));
253 SECP256K1_SCALAR_VERIFY(a);
254
255 t += (SECP256K1_N_H_0 + 1U) & mask;
256 r->d[0] = t; t >>= 32;
257 t += (uint32_t)((a->d[1] >> 1) | (a->d[2] << 31));
258 t += SECP256K1_N_H_1 & mask;
259 r->d[1] = t; t >>= 32;
260 t += (uint32_t)((a->d[2] >> 1) | (a->d[3] << 31));
261 t += SECP256K1_N_H_2 & mask;
262 r->d[2] = t; t >>= 32;
263 t += (uint32_t)((a->d[3] >> 1) | (a->d[4] << 31));
264 t += SECP256K1_N_H_3 & mask;
265 r->d[3] = t; t >>= 32;
266 t += (uint32_t)((a->d[4] >> 1) | (a->d[5] << 31));
267 t += SECP256K1_N_H_4 & mask;
268 r->d[4] = t; t >>= 32;
269 t += (uint32_t)((a->d[5] >> 1) | (a->d[6] << 31));
270 t += SECP256K1_N_H_5 & mask;
271 r->d[5] = t; t >>= 32;
272 t += (uint32_t)((a->d[6] >> 1) | (a->d[7] << 31));
273 t += SECP256K1_N_H_6 & mask;
274 r->d[6] = t; t >>= 32;
275 r->d[7] = (uint32_t)t + (uint32_t)(a->d[7] >> 1) + (SECP256K1_N_H_7 & mask);
276
277 /* The line above only computed the bottom 32 bits of r->d[7]. Redo the computation
278 * in full 64 bits to make sure the top 32 bits are indeed zero. */
279 VERIFY_CHECK((t + (a->d[7] >> 1) + (SECP256K1_N_H_7 & mask)) >> 32 == 0);
280
281 SECP256K1_SCALAR_VERIFY(r);
282}
283
284SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
285 SECP256K1_SCALAR_VERIFY(a);
286
287 return ((a->d[0] ^ 1) | a->d[1] | a->d[2] | a->d[3] | a->d[4] | a->d[5] | a->d[6] | a->d[7]) == 0;
288}
289
290static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
291 int yes = 0;
292 int no = 0;
293 SECP256K1_SCALAR_VERIFY(a);
294
295 no |= (a->d[7] < SECP256K1_N_H_7);
296 yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
297 no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
298 no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
299 no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
300 no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
301 yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
302 no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
303 yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
304 no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
305 yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
306 yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
307 return yes;
308}
309
310static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
311 /* If we are flag = 0, mask = 00...00 and this is a no-op;
312 * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
313 volatile int vflag = flag;
314 uint32_t mask = -vflag;
315 uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
316 uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
317 SECP256K1_SCALAR_VERIFY(r);
318
319 r->d[0] = t & nonzero; t >>= 32;
320 t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
321 r->d[1] = t & nonzero; t >>= 32;
322 t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
323 r->d[2] = t & nonzero; t >>= 32;
324 t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
325 r->d[3] = t & nonzero; t >>= 32;
326 t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
327 r->d[4] = t & nonzero; t >>= 32;
328 t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
329 r->d[5] = t & nonzero; t >>= 32;
330 t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
331 r->d[6] = t & nonzero; t >>= 32;
332 t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
333 r->d[7] = t & nonzero;
334
335 SECP256K1_SCALAR_VERIFY(r);
336 return 2 * (mask == 0) - 1;
337}
338
339
340/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
341
343#define muladd(a,b) { \
344 uint32_t tl, th; \
345 { \
346 uint64_t t = (uint64_t)a * b; \
347 th = t >> 32; /* at most 0xFFFFFFFE */ \
348 tl = t; \
349 } \
350 c0 += tl; /* overflow is handled on the next line */ \
351 th += (c0 < tl); /* at most 0xFFFFFFFF */ \
352 c1 += th; /* overflow is handled on the next line */ \
353 c2 += (c1 < th); /* never overflows by contract (verified in the next line) */ \
354 VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
355}
356
358#define muladd_fast(a,b) { \
359 uint32_t tl, th; \
360 { \
361 uint64_t t = (uint64_t)a * b; \
362 th = t >> 32; /* at most 0xFFFFFFFE */ \
363 tl = t; \
364 } \
365 c0 += tl; /* overflow is handled on the next line */ \
366 th += (c0 < tl); /* at most 0xFFFFFFFF */ \
367 c1 += th; /* never overflows by contract (verified in the next line) */ \
368 VERIFY_CHECK(c1 >= th); \
369}
370
372#define sumadd(a) { \
373 unsigned int over; \
374 c0 += (a); /* overflow is handled on the next line */ \
375 over = (c0 < (a)); \
376 c1 += over; /* overflow is handled on the next line */ \
377 c2 += (c1 < over); /* never overflows by contract */ \
378}
379
381#define sumadd_fast(a) { \
382 c0 += (a); /* overflow is handled on the next line */ \
383 c1 += (c0 < (a)); /* never overflows by contract (verified the next line) */ \
384 VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
385 VERIFY_CHECK(c2 == 0); \
386}
387
389#define extract(n) { \
390 (n) = c0; \
391 c0 = c1; \
392 c1 = c2; \
393 c2 = 0; \
394}
395
397#define extract_fast(n) { \
398 (n) = c0; \
399 c0 = c1; \
400 c1 = 0; \
401 VERIFY_CHECK(c2 == 0); \
402}
403
404static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
405 uint64_t c;
406 uint32_t n0 = l[8], n1 = l[9], n2 = l[10], n3 = l[11], n4 = l[12], n5 = l[13], n6 = l[14], n7 = l[15];
407 uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
408 uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
409
410 /* 96 bit accumulator. */
411 uint32_t c0, c1, c2;
412
413 /* Reduce 512 bits into 385. */
414 /* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
415 c0 = l[0]; c1 = 0; c2 = 0;
416 muladd_fast(n0, SECP256K1_N_C_0);
417 extract_fast(m0);
418 sumadd_fast(l[1]);
419 muladd(n1, SECP256K1_N_C_0);
420 muladd(n0, SECP256K1_N_C_1);
421 extract(m1);
422 sumadd(l[2]);
423 muladd(n2, SECP256K1_N_C_0);
424 muladd(n1, SECP256K1_N_C_1);
425 muladd(n0, SECP256K1_N_C_2);
426 extract(m2);
427 sumadd(l[3]);
428 muladd(n3, SECP256K1_N_C_0);
429 muladd(n2, SECP256K1_N_C_1);
430 muladd(n1, SECP256K1_N_C_2);
431 muladd(n0, SECP256K1_N_C_3);
432 extract(m3);
433 sumadd(l[4]);
434 muladd(n4, SECP256K1_N_C_0);
435 muladd(n3, SECP256K1_N_C_1);
436 muladd(n2, SECP256K1_N_C_2);
437 muladd(n1, SECP256K1_N_C_3);
438 sumadd(n0);
439 extract(m4);
440 sumadd(l[5]);
441 muladd(n5, SECP256K1_N_C_0);
442 muladd(n4, SECP256K1_N_C_1);
443 muladd(n3, SECP256K1_N_C_2);
444 muladd(n2, SECP256K1_N_C_3);
445 sumadd(n1);
446 extract(m5);
447 sumadd(l[6]);
448 muladd(n6, SECP256K1_N_C_0);
449 muladd(n5, SECP256K1_N_C_1);
450 muladd(n4, SECP256K1_N_C_2);
451 muladd(n3, SECP256K1_N_C_3);
452 sumadd(n2);
453 extract(m6);
454 sumadd(l[7]);
455 muladd(n7, SECP256K1_N_C_0);
456 muladd(n6, SECP256K1_N_C_1);
457 muladd(n5, SECP256K1_N_C_2);
458 muladd(n4, SECP256K1_N_C_3);
459 sumadd(n3);
460 extract(m7);
461 muladd(n7, SECP256K1_N_C_1);
462 muladd(n6, SECP256K1_N_C_2);
463 muladd(n5, SECP256K1_N_C_3);
464 sumadd(n4);
465 extract(m8);
466 muladd(n7, SECP256K1_N_C_2);
467 muladd(n6, SECP256K1_N_C_3);
468 sumadd(n5);
469 extract(m9);
470 muladd(n7, SECP256K1_N_C_3);
471 sumadd(n6);
472 extract(m10);
473 sumadd_fast(n7);
474 extract_fast(m11);
475 VERIFY_CHECK(c0 <= 1);
476 m12 = c0;
477
478 /* Reduce 385 bits into 258. */
479 /* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
480 c0 = m0; c1 = 0; c2 = 0;
481 muladd_fast(m8, SECP256K1_N_C_0);
482 extract_fast(p0);
483 sumadd_fast(m1);
484 muladd(m9, SECP256K1_N_C_0);
485 muladd(m8, SECP256K1_N_C_1);
486 extract(p1);
487 sumadd(m2);
488 muladd(m10, SECP256K1_N_C_0);
489 muladd(m9, SECP256K1_N_C_1);
490 muladd(m8, SECP256K1_N_C_2);
491 extract(p2);
492 sumadd(m3);
493 muladd(m11, SECP256K1_N_C_0);
494 muladd(m10, SECP256K1_N_C_1);
495 muladd(m9, SECP256K1_N_C_2);
496 muladd(m8, SECP256K1_N_C_3);
497 extract(p3);
498 sumadd(m4);
499 muladd(m12, SECP256K1_N_C_0);
500 muladd(m11, SECP256K1_N_C_1);
501 muladd(m10, SECP256K1_N_C_2);
502 muladd(m9, SECP256K1_N_C_3);
503 sumadd(m8);
504 extract(p4);
505 sumadd(m5);
506 muladd(m12, SECP256K1_N_C_1);
507 muladd(m11, SECP256K1_N_C_2);
508 muladd(m10, SECP256K1_N_C_3);
509 sumadd(m9);
510 extract(p5);
511 sumadd(m6);
512 muladd(m12, SECP256K1_N_C_2);
513 muladd(m11, SECP256K1_N_C_3);
514 sumadd(m10);
515 extract(p6);
516 sumadd_fast(m7);
517 muladd_fast(m12, SECP256K1_N_C_3);
518 sumadd_fast(m11);
519 extract_fast(p7);
520 p8 = c0 + m12;
521 VERIFY_CHECK(p8 <= 2);
522
523 /* Reduce 258 bits into 256. */
524 /* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
525 c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
526 r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
527 c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
528 r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
529 c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
530 r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
531 c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
532 r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
533 c += p4 + (uint64_t)p8;
534 r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
535 c += p5;
536 r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
537 c += p6;
538 r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
539 c += p7;
540 r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
541
542 /* Final reduction of r. */
543 secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
544}
545
546static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
547 /* 96 bit accumulator. */
548 uint32_t c0 = 0, c1 = 0, c2 = 0;
549
550 /* l[0..15] = a[0..7] * b[0..7]. */
551 muladd_fast(a->d[0], b->d[0]);
552 extract_fast(l[0]);
553 muladd(a->d[0], b->d[1]);
554 muladd(a->d[1], b->d[0]);
555 extract(l[1]);
556 muladd(a->d[0], b->d[2]);
557 muladd(a->d[1], b->d[1]);
558 muladd(a->d[2], b->d[0]);
559 extract(l[2]);
560 muladd(a->d[0], b->d[3]);
561 muladd(a->d[1], b->d[2]);
562 muladd(a->d[2], b->d[1]);
563 muladd(a->d[3], b->d[0]);
564 extract(l[3]);
565 muladd(a->d[0], b->d[4]);
566 muladd(a->d[1], b->d[3]);
567 muladd(a->d[2], b->d[2]);
568 muladd(a->d[3], b->d[1]);
569 muladd(a->d[4], b->d[0]);
570 extract(l[4]);
571 muladd(a->d[0], b->d[5]);
572 muladd(a->d[1], b->d[4]);
573 muladd(a->d[2], b->d[3]);
574 muladd(a->d[3], b->d[2]);
575 muladd(a->d[4], b->d[1]);
576 muladd(a->d[5], b->d[0]);
577 extract(l[5]);
578 muladd(a->d[0], b->d[6]);
579 muladd(a->d[1], b->d[5]);
580 muladd(a->d[2], b->d[4]);
581 muladd(a->d[3], b->d[3]);
582 muladd(a->d[4], b->d[2]);
583 muladd(a->d[5], b->d[1]);
584 muladd(a->d[6], b->d[0]);
585 extract(l[6]);
586 muladd(a->d[0], b->d[7]);
587 muladd(a->d[1], b->d[6]);
588 muladd(a->d[2], b->d[5]);
589 muladd(a->d[3], b->d[4]);
590 muladd(a->d[4], b->d[3]);
591 muladd(a->d[5], b->d[2]);
592 muladd(a->d[6], b->d[1]);
593 muladd(a->d[7], b->d[0]);
594 extract(l[7]);
595 muladd(a->d[1], b->d[7]);
596 muladd(a->d[2], b->d[6]);
597 muladd(a->d[3], b->d[5]);
598 muladd(a->d[4], b->d[4]);
599 muladd(a->d[5], b->d[3]);
600 muladd(a->d[6], b->d[2]);
601 muladd(a->d[7], b->d[1]);
602 extract(l[8]);
603 muladd(a->d[2], b->d[7]);
604 muladd(a->d[3], b->d[6]);
605 muladd(a->d[4], b->d[5]);
606 muladd(a->d[5], b->d[4]);
607 muladd(a->d[6], b->d[3]);
608 muladd(a->d[7], b->d[2]);
609 extract(l[9]);
610 muladd(a->d[3], b->d[7]);
611 muladd(a->d[4], b->d[6]);
612 muladd(a->d[5], b->d[5]);
613 muladd(a->d[6], b->d[4]);
614 muladd(a->d[7], b->d[3]);
615 extract(l[10]);
616 muladd(a->d[4], b->d[7]);
617 muladd(a->d[5], b->d[6]);
618 muladd(a->d[6], b->d[5]);
619 muladd(a->d[7], b->d[4]);
620 extract(l[11]);
621 muladd(a->d[5], b->d[7]);
622 muladd(a->d[6], b->d[6]);
623 muladd(a->d[7], b->d[5]);
624 extract(l[12]);
625 muladd(a->d[6], b->d[7]);
626 muladd(a->d[7], b->d[6]);
627 extract(l[13]);
628 muladd_fast(a->d[7], b->d[7]);
629 extract_fast(l[14]);
630 VERIFY_CHECK(c1 == 0);
631 l[15] = c0;
632}
633
634#undef sumadd
635#undef sumadd_fast
636#undef muladd
637#undef muladd_fast
638#undef extract
639#undef extract_fast
640
641static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
642 uint32_t l[16];
643 SECP256K1_SCALAR_VERIFY(a);
644 SECP256K1_SCALAR_VERIFY(b);
645
646 secp256k1_scalar_mul_512(l, a, b);
647 secp256k1_scalar_reduce_512(r, l);
648
649 SECP256K1_SCALAR_VERIFY(r);
650}
651
652static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) {
653 SECP256K1_SCALAR_VERIFY(k);
654
655 r1->d[0] = k->d[0];
656 r1->d[1] = k->d[1];
657 r1->d[2] = k->d[2];
658 r1->d[3] = k->d[3];
659 r1->d[4] = 0;
660 r1->d[5] = 0;
661 r1->d[6] = 0;
662 r1->d[7] = 0;
663 r2->d[0] = k->d[4];
664 r2->d[1] = k->d[5];
665 r2->d[2] = k->d[6];
666 r2->d[3] = k->d[7];
667 r2->d[4] = 0;
668 r2->d[5] = 0;
669 r2->d[6] = 0;
670 r2->d[7] = 0;
671
672 SECP256K1_SCALAR_VERIFY(r1);
673 SECP256K1_SCALAR_VERIFY(r2);
674}
675
676SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
677 SECP256K1_SCALAR_VERIFY(a);
678 SECP256K1_SCALAR_VERIFY(b);
679
680 return ((a->d[0] ^ b->d[0]) | (a->d[1] ^ b->d[1]) | (a->d[2] ^ b->d[2]) | (a->d[3] ^ b->d[3]) | (a->d[4] ^ b->d[4]) | (a->d[5] ^ b->d[5]) | (a->d[6] ^ b->d[6]) | (a->d[7] ^ b->d[7])) == 0;
681}
682
683SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
684 uint32_t l[16];
685 unsigned int shiftlimbs;
686 unsigned int shiftlow;
687 unsigned int shifthigh;
688 SECP256K1_SCALAR_VERIFY(a);
689 SECP256K1_SCALAR_VERIFY(b);
690 VERIFY_CHECK(shift >= 256);
691
692 secp256k1_scalar_mul_512(l, a, b);
693 shiftlimbs = shift >> 5;
694 shiftlow = shift & 0x1F;
695 shifthigh = 32 - shiftlow;
696 r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
697 r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
698 r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
699 r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
700 r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
701 r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
702 r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
703 r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow) : 0;
704 secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
705
706 SECP256K1_SCALAR_VERIFY(r);
707}
708
709static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) {
710 uint32_t mask0, mask1;
711 volatile int vflag = flag;
712 SECP256K1_SCALAR_VERIFY(a);
713 SECP256K1_CHECKMEM_CHECK_VERIFY(r->d, sizeof(r->d));
714
715 mask0 = vflag + ~((uint32_t)0);
716 mask1 = ~mask0;
717 r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1);
718 r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1);
719 r->d[2] = (r->d[2] & mask0) | (a->d[2] & mask1);
720 r->d[3] = (r->d[3] & mask0) | (a->d[3] & mask1);
721 r->d[4] = (r->d[4] & mask0) | (a->d[4] & mask1);
722 r->d[5] = (r->d[5] & mask0) | (a->d[5] & mask1);
723 r->d[6] = (r->d[6] & mask0) | (a->d[6] & mask1);
724 r->d[7] = (r->d[7] & mask0) | (a->d[7] & mask1);
725
726 SECP256K1_SCALAR_VERIFY(r);
727}
728
729static void secp256k1_scalar_from_signed30(secp256k1_scalar *r, const secp256k1_modinv32_signed30 *a) {
730 const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4],
731 a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8];
732
733 /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and
734 * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8).
735 */
736 VERIFY_CHECK(a0 >> 30 == 0);
737 VERIFY_CHECK(a1 >> 30 == 0);
738 VERIFY_CHECK(a2 >> 30 == 0);
739 VERIFY_CHECK(a3 >> 30 == 0);
740 VERIFY_CHECK(a4 >> 30 == 0);
741 VERIFY_CHECK(a5 >> 30 == 0);
742 VERIFY_CHECK(a6 >> 30 == 0);
743 VERIFY_CHECK(a7 >> 30 == 0);
744 VERIFY_CHECK(a8 >> 16 == 0);
745
746 r->d[0] = a0 | a1 << 30;
747 r->d[1] = a1 >> 2 | a2 << 28;
748 r->d[2] = a2 >> 4 | a3 << 26;
749 r->d[3] = a3 >> 6 | a4 << 24;
750 r->d[4] = a4 >> 8 | a5 << 22;
751 r->d[5] = a5 >> 10 | a6 << 20;
752 r->d[6] = a6 >> 12 | a7 << 18;
753 r->d[7] = a7 >> 14 | a8 << 16;
754
755 SECP256K1_SCALAR_VERIFY(r);
756}
757
758static void secp256k1_scalar_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_scalar *a) {
759 const uint32_t M30 = UINT32_MAX >> 2;
760 const uint32_t a0 = a->d[0], a1 = a->d[1], a2 = a->d[2], a3 = a->d[3],
761 a4 = a->d[4], a5 = a->d[5], a6 = a->d[6], a7 = a->d[7];
762 SECP256K1_SCALAR_VERIFY(a);
763
764 r->v[0] = a0 & M30;
765 r->v[1] = (a0 >> 30 | a1 << 2) & M30;
766 r->v[2] = (a1 >> 28 | a2 << 4) & M30;
767 r->v[3] = (a2 >> 26 | a3 << 6) & M30;
768 r->v[4] = (a3 >> 24 | a4 << 8) & M30;
769 r->v[5] = (a4 >> 22 | a5 << 10) & M30;
770 r->v[6] = (a5 >> 20 | a6 << 12) & M30;
771 r->v[7] = (a6 >> 18 | a7 << 14) & M30;
772 r->v[8] = a7 >> 16;
773}
774
775static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_scalar = {
776 {{0x10364141L, 0x3F497A33L, 0x348A03BBL, 0x2BB739ABL, -0x146L, 0, 0, 0, 65536}},
777 0x2A774EC1L
778};
779
780static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x) {
781 secp256k1_modinv32_signed30 s;
782#ifdef VERIFY
783 int zero_in = secp256k1_scalar_is_zero(x);
784#endif
785 SECP256K1_SCALAR_VERIFY(x);
786
787 secp256k1_scalar_to_signed30(&s, x);
788 secp256k1_modinv32(&s, &secp256k1_const_modinfo_scalar);
789 secp256k1_scalar_from_signed30(r, &s);
790
791 SECP256K1_SCALAR_VERIFY(r);
792 VERIFY_CHECK(secp256k1_scalar_is_zero(r) == zero_in);
793}
794
795static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x) {
796 secp256k1_modinv32_signed30 s;
797#ifdef VERIFY
798 int zero_in = secp256k1_scalar_is_zero(x);
799#endif
800 SECP256K1_SCALAR_VERIFY(x);
801
802 secp256k1_scalar_to_signed30(&s, x);
803 secp256k1_modinv32_var(&s, &secp256k1_const_modinfo_scalar);
804 secp256k1_scalar_from_signed30(r, &s);
805
806 SECP256K1_SCALAR_VERIFY(r);
807 VERIFY_CHECK(secp256k1_scalar_is_zero(r) == zero_in);
808}
809
810SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
811 SECP256K1_SCALAR_VERIFY(a);
812
813 return !(a->d[0] & 1);
814}
815
816#endif /* SECP256K1_SCALAR_REPR_IMPL_H */
SECP256K1_CHECKMEM_CHECK_VERIFY
#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len)
Definition: checkmem.h:99
secp256k1_modinv32_var
static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
secp256k1_modinv32
static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
modinv32_impl.h
test_vectors_musig2_generate.s
tuple s
Definition: test_vectors_musig2_generate.py:72
SECP256K1_SCALAR_VERIFY
#define SECP256K1_SCALAR_VERIFY(r)
Definition: scalar.h:103
secp256k1_scalar_is_even
static SECP256K1_INLINE int secp256k1_scalar_is_even(const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:810
secp256k1_scalar_check_overflow
static SECP256K1_INLINE int secp256k1_scalar_check_overflow(const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:75
secp256k1_scalar_mul_shift_var
static SECP256K1_INLINE void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift)
Definition: scalar_8x32_impl.h:683
SECP256K1_N_5
#define SECP256K1_N_5
Definition: scalar_8x32_impl.h:20
SECP256K1_N_C_4
#define SECP256K1_N_C_4
Definition: scalar_8x32_impl.h:29
secp256k1_scalar_half
static void secp256k1_scalar_half(secp256k1_scalar *r, const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:236
SECP256K1_N_3
#define SECP256K1_N_3
Definition: scalar_8x32_impl.h:18
secp256k1_scalar_split_128
static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k)
Definition: scalar_8x32_impl.h:652
extract
#define extract(n)
Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits.
Definition: scalar_8x32_impl.h:389
SECP256K1_N_6
#define SECP256K1_N_6
Definition: scalar_8x32_impl.h:21
SECP256K1_N_C_2
#define SECP256K1_N_C_2
Definition: scalar_8x32_impl.h:27
secp256k1_scalar_set_b32
static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow)
Definition: scalar_8x32_impl.h:175
SECP256K1_N_C_1
#define SECP256K1_N_C_1
Definition: scalar_8x32_impl.h:26
secp256k1_scalar_mul_512
static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b)
Definition: scalar_8x32_impl.h:546
secp256k1_scalar_get_bits_var
static SECP256K1_INLINE uint32_t secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count)
Definition: scalar_8x32_impl.h:62
secp256k1_scalar_inverse_var
static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x)
Definition: scalar_8x32_impl.h:795
sumadd_fast
#define sumadd_fast(a)
Add a to the number defined by (c0,c1).
Definition: scalar_8x32_impl.h:381
secp256k1_scalar_get_b32
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:193
SECP256K1_N_1
#define SECP256K1_N_1
Definition: scalar_8x32_impl.h:16
SECP256K1_N_2
#define SECP256K1_N_2
Definition: scalar_8x32_impl.h:17
SECP256K1_N_H_2
#define SECP256K1_N_H_2
Definition: scalar_8x32_impl.h:34
secp256k1_scalar_set_int
static SECP256K1_INLINE void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v)
Definition: scalar_8x32_impl.h:41
secp256k1_scalar_inverse
static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x)
Definition: scalar_8x32_impl.h:780
SECP256K1_N_C_0
#define SECP256K1_N_C_0
Definition: scalar_8x32_impl.h:25
secp256k1_scalar_cmov
static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag)
Definition: scalar_8x32_impl.h:709
extract_fast
#define extract_fast(n)
Extract the lowest 32 bits of (c0,c1,c2) into n, and left shift the number 32 bits.
Definition: scalar_8x32_impl.h:397
muladd
#define muladd(a, b)
Add a*b to the number defined by (c0,c1,c2).
Definition: scalar_8x32_impl.h:343
SECP256K1_N_H_5
#define SECP256K1_N_H_5
Definition: scalar_8x32_impl.h:37
secp256k1_scalar_reduce_512
static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l)
Definition: scalar_8x32_impl.h:404
SECP256K1_N_H_0
#define SECP256K1_N_H_0
Definition: scalar_8x32_impl.h:32
secp256k1_scalar_eq
static SECP256K1_INLINE int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b)
Definition: scalar_8x32_impl.h:676
SECP256K1_N_C_3
#define SECP256K1_N_C_3
Definition: scalar_8x32_impl.h:28
secp256k1_scalar_add
static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b)
Definition: scalar_8x32_impl.h:118
sumadd
#define sumadd(a)
Add a to the number defined by (c0,c1,c2).
Definition: scalar_8x32_impl.h:372
secp256k1_scalar_cond_negate
static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag)
Definition: scalar_8x32_impl.h:310
secp256k1_scalar_mul
static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b)
Definition: scalar_8x32_impl.h:641
secp256k1_const_modinfo_scalar
static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_scalar
Definition: scalar_8x32_impl.h:775
secp256k1_scalar_reduce
static SECP256K1_INLINE int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow)
Definition: scalar_8x32_impl.h:93
SECP256K1_N_H_1
#define SECP256K1_N_H_1
Definition: scalar_8x32_impl.h:33
SECP256K1_N_H_6
#define SECP256K1_N_H_6
Definition: scalar_8x32_impl.h:38
SECP256K1_N_0
#define SECP256K1_N_0
Definition: scalar_8x32_impl.h:15
secp256k1_scalar_negate
static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:212
secp256k1_scalar_is_zero
static SECP256K1_INLINE int secp256k1_scalar_is_zero(const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:206
SECP256K1_N_H_7
#define SECP256K1_N_H_7
Definition: scalar_8x32_impl.h:39
secp256k1_scalar_is_high
static int secp256k1_scalar_is_high(const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:290
SECP256K1_N_H_3
#define SECP256K1_N_H_3
Definition: scalar_8x32_impl.h:35
SECP256K1_N_H_4
#define SECP256K1_N_H_4
Definition: scalar_8x32_impl.h:36
secp256k1_scalar_from_signed30
static void secp256k1_scalar_from_signed30(secp256k1_scalar *r, const secp256k1_modinv32_signed30 *a)
Definition: scalar_8x32_impl.h:729
secp256k1_scalar_get_bits_limb32
static SECP256K1_INLINE uint32_t secp256k1_scalar_get_bits_limb32(const secp256k1_scalar *a, unsigned int offset, unsigned int count)
Definition: scalar_8x32_impl.h:54
secp256k1_scalar_cadd_bit
static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag)
Definition: scalar_8x32_impl.h:147
muladd_fast
#define muladd_fast(a, b)
Add a*b to the number defined by (c0,c1).
Definition: scalar_8x32_impl.h:358
secp256k1_scalar_is_one
static SECP256K1_INLINE int secp256k1_scalar_is_one(const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:284
SECP256K1_N_4
#define SECP256K1_N_4
Definition: scalar_8x32_impl.h:19
SECP256K1_N_7
#define SECP256K1_N_7
Definition: scalar_8x32_impl.h:22
secp256k1_scalar_to_signed30
static void secp256k1_scalar_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_scalar *a)
Definition: scalar_8x32_impl.h:758
secp256k1_read_be32
static SECP256K1_INLINE uint32_t secp256k1_read_be32(const unsigned char *p)
Definition: util.h:400
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition: util.h:54
secp256k1_write_be32
static SECP256K1_INLINE void secp256k1_write_be32(unsigned char *p, uint32_t x)
Definition: util.h:408
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition: util.h:159
secp256k1_modinv32_modinfo
Definition: modinv32.h:19
secp256k1_modinv32_signed30
Definition: modinv32.h:15
secp256k1_modinv32_signed30::v
int32_t v[9]
Definition: modinv32.h:16
secp256k1_scalar
A scalar modulo the group order of the secp256k1 curve.
Definition: scalar_4x64.h:13
secp256k1_scalar::d
uint64_t d[4]
Definition: scalar_4x64.h:14
count
static int count
Definition: tests_exhaustive.c:34
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