Bitcoin Core 28.0.0
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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_clear(secp256k1_scalar *r) {
42 r->d[0] = 0;
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
52SECP256K1_INLINE static void secp256k1_scalar_set_int(secp256k1_scalar *r, unsigned int v) {
53 r->d[0] = v;
54 r->d[1] = 0;
55 r->d[2] = 0;
56 r->d[3] = 0;
57 r->d[4] = 0;
58 r->d[5] = 0;
59 r->d[6] = 0;
60 r->d[7] = 0;
61
62 SECP256K1_SCALAR_VERIFY(r);
63}
64
65SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_limb32(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
66 SECP256K1_SCALAR_VERIFY(a);
67 VERIFY_CHECK(count > 0 && count <= 32);
68 VERIFY_CHECK((offset + count - 1) >> 5 == offset >> 5);
69
70 return (a->d[offset >> 5] >> (offset & 0x1F)) & (0xFFFFFFFF >> (32 - count));
71}
72
73SECP256K1_INLINE static uint32_t secp256k1_scalar_get_bits_var(const secp256k1_scalar *a, unsigned int offset, unsigned int count) {
74 SECP256K1_SCALAR_VERIFY(a);
75 VERIFY_CHECK(count > 0 && count <= 32);
76 VERIFY_CHECK(offset + count <= 256);
77
78 if ((offset + count - 1) >> 5 == offset >> 5) {
79 return secp256k1_scalar_get_bits_limb32(a, offset, count);
80 } else {
81 VERIFY_CHECK((offset >> 5) + 1 < 8);
82 return ((a->d[offset >> 5] >> (offset & 0x1F)) | (a->d[(offset >> 5) + 1] << (32 - (offset & 0x1F)))) & (0xFFFFFFFF >> (32 - count));
83 }
84}
85
86SECP256K1_INLINE static int secp256k1_scalar_check_overflow(const secp256k1_scalar *a) {
87 int yes = 0;
88 int no = 0;
89 no |= (a->d[7] < SECP256K1_N_7); /* No need for a > check. */
90 no |= (a->d[6] < SECP256K1_N_6); /* No need for a > check. */
91 no |= (a->d[5] < SECP256K1_N_5); /* No need for a > check. */
92 no |= (a->d[4] < SECP256K1_N_4);
93 yes |= (a->d[4] > SECP256K1_N_4) & ~no;
94 no |= (a->d[3] < SECP256K1_N_3) & ~yes;
95 yes |= (a->d[3] > SECP256K1_N_3) & ~no;
96 no |= (a->d[2] < SECP256K1_N_2) & ~yes;
97 yes |= (a->d[2] > SECP256K1_N_2) & ~no;
98 no |= (a->d[1] < SECP256K1_N_1) & ~yes;
99 yes |= (a->d[1] > SECP256K1_N_1) & ~no;
100 yes |= (a->d[0] >= SECP256K1_N_0) & ~no;
101 return yes;
102}
103
104SECP256K1_INLINE static int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow) {
105 uint64_t t;
106 VERIFY_CHECK(overflow <= 1);
107
108 t = (uint64_t)r->d[0] + overflow * SECP256K1_N_C_0;
109 r->d[0] = t & 0xFFFFFFFFUL; t >>= 32;
110 t += (uint64_t)r->d[1] + overflow * SECP256K1_N_C_1;
111 r->d[1] = t & 0xFFFFFFFFUL; t >>= 32;
112 t += (uint64_t)r->d[2] + overflow * SECP256K1_N_C_2;
113 r->d[2] = t & 0xFFFFFFFFUL; t >>= 32;
114 t += (uint64_t)r->d[3] + overflow * SECP256K1_N_C_3;
115 r->d[3] = t & 0xFFFFFFFFUL; t >>= 32;
116 t += (uint64_t)r->d[4] + overflow * SECP256K1_N_C_4;
117 r->d[4] = t & 0xFFFFFFFFUL; t >>= 32;
118 t += (uint64_t)r->d[5];
119 r->d[5] = t & 0xFFFFFFFFUL; t >>= 32;
120 t += (uint64_t)r->d[6];
121 r->d[6] = t & 0xFFFFFFFFUL; t >>= 32;
122 t += (uint64_t)r->d[7];
123 r->d[7] = t & 0xFFFFFFFFUL;
124
125 SECP256K1_SCALAR_VERIFY(r);
126 return overflow;
127}
128
129static int secp256k1_scalar_add(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
130 int overflow;
131 uint64_t t = (uint64_t)a->d[0] + b->d[0];
132 SECP256K1_SCALAR_VERIFY(a);
133 SECP256K1_SCALAR_VERIFY(b);
134
135 r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
136 t += (uint64_t)a->d[1] + b->d[1];
137 r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
138 t += (uint64_t)a->d[2] + b->d[2];
139 r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
140 t += (uint64_t)a->d[3] + b->d[3];
141 r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
142 t += (uint64_t)a->d[4] + b->d[4];
143 r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
144 t += (uint64_t)a->d[5] + b->d[5];
145 r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
146 t += (uint64_t)a->d[6] + b->d[6];
147 r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
148 t += (uint64_t)a->d[7] + b->d[7];
149 r->d[7] = t & 0xFFFFFFFFULL; t >>= 32;
150 overflow = t + secp256k1_scalar_check_overflow(r);
151 VERIFY_CHECK(overflow == 0 || overflow == 1);
152 secp256k1_scalar_reduce(r, overflow);
153
154 SECP256K1_SCALAR_VERIFY(r);
155 return overflow;
156}
157
158static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag) {
159 uint64_t t;
160 volatile int vflag = flag;
161 SECP256K1_SCALAR_VERIFY(r);
162 VERIFY_CHECK(bit < 256);
163
164 bit += ((uint32_t) vflag - 1) & 0x100; /* forcing (bit >> 5) > 7 makes this a noop */
165 t = (uint64_t)r->d[0] + (((uint32_t)((bit >> 5) == 0)) << (bit & 0x1F));
166 r->d[0] = t & 0xFFFFFFFFULL; t >>= 32;
167 t += (uint64_t)r->d[1] + (((uint32_t)((bit >> 5) == 1)) << (bit & 0x1F));
168 r->d[1] = t & 0xFFFFFFFFULL; t >>= 32;
169 t += (uint64_t)r->d[2] + (((uint32_t)((bit >> 5) == 2)) << (bit & 0x1F));
170 r->d[2] = t & 0xFFFFFFFFULL; t >>= 32;
171 t += (uint64_t)r->d[3] + (((uint32_t)((bit >> 5) == 3)) << (bit & 0x1F));
172 r->d[3] = t & 0xFFFFFFFFULL; t >>= 32;
173 t += (uint64_t)r->d[4] + (((uint32_t)((bit >> 5) == 4)) << (bit & 0x1F));
174 r->d[4] = t & 0xFFFFFFFFULL; t >>= 32;
175 t += (uint64_t)r->d[5] + (((uint32_t)((bit >> 5) == 5)) << (bit & 0x1F));
176 r->d[5] = t & 0xFFFFFFFFULL; t >>= 32;
177 t += (uint64_t)r->d[6] + (((uint32_t)((bit >> 5) == 6)) << (bit & 0x1F));
178 r->d[6] = t & 0xFFFFFFFFULL; t >>= 32;
179 t += (uint64_t)r->d[7] + (((uint32_t)((bit >> 5) == 7)) << (bit & 0x1F));
180 r->d[7] = t & 0xFFFFFFFFULL;
181
182 SECP256K1_SCALAR_VERIFY(r);
183 VERIFY_CHECK((t >> 32) == 0);
184}
185
186static void secp256k1_scalar_set_b32(secp256k1_scalar *r, const unsigned char *b32, int *overflow) {
187 int over;
188 r->d[0] = secp256k1_read_be32(&b32[28]);
189 r->d[1] = secp256k1_read_be32(&b32[24]);
190 r->d[2] = secp256k1_read_be32(&b32[20]);
191 r->d[3] = secp256k1_read_be32(&b32[16]);
192 r->d[4] = secp256k1_read_be32(&b32[12]);
193 r->d[5] = secp256k1_read_be32(&b32[8]);
194 r->d[6] = secp256k1_read_be32(&b32[4]);
195 r->d[7] = secp256k1_read_be32(&b32[0]);
196 over = secp256k1_scalar_reduce(r, secp256k1_scalar_check_overflow(r));
197 if (overflow) {
198 *overflow = over;
199 }
200
201 SECP256K1_SCALAR_VERIFY(r);
202}
203
204static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar* a) {
205 SECP256K1_SCALAR_VERIFY(a);
206
207 secp256k1_write_be32(&bin[0], a->d[7]);
208 secp256k1_write_be32(&bin[4], a->d[6]);
209 secp256k1_write_be32(&bin[8], a->d[5]);
210 secp256k1_write_be32(&bin[12], a->d[4]);
211 secp256k1_write_be32(&bin[16], a->d[3]);
212 secp256k1_write_be32(&bin[20], a->d[2]);
213 secp256k1_write_be32(&bin[24], a->d[1]);
214 secp256k1_write_be32(&bin[28], a->d[0]);
215}
216
217SECP256K1_INLINE static int secp256k1_scalar_is_zero(const secp256k1_scalar *a) {
218 SECP256K1_SCALAR_VERIFY(a);
219
220 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;
221}
222
223static void secp256k1_scalar_negate(secp256k1_scalar *r, const secp256k1_scalar *a) {
224 uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(a) == 0);
225 uint64_t t = (uint64_t)(~a->d[0]) + SECP256K1_N_0 + 1;
226 SECP256K1_SCALAR_VERIFY(a);
227
228 r->d[0] = t & nonzero; t >>= 32;
229 t += (uint64_t)(~a->d[1]) + SECP256K1_N_1;
230 r->d[1] = t & nonzero; t >>= 32;
231 t += (uint64_t)(~a->d[2]) + SECP256K1_N_2;
232 r->d[2] = t & nonzero; t >>= 32;
233 t += (uint64_t)(~a->d[3]) + SECP256K1_N_3;
234 r->d[3] = t & nonzero; t >>= 32;
235 t += (uint64_t)(~a->d[4]) + SECP256K1_N_4;
236 r->d[4] = t & nonzero; t >>= 32;
237 t += (uint64_t)(~a->d[5]) + SECP256K1_N_5;
238 r->d[5] = t & nonzero; t >>= 32;
239 t += (uint64_t)(~a->d[6]) + SECP256K1_N_6;
240 r->d[6] = t & nonzero; t >>= 32;
241 t += (uint64_t)(~a->d[7]) + SECP256K1_N_7;
242 r->d[7] = t & nonzero;
243
244 SECP256K1_SCALAR_VERIFY(r);
245}
246
247static void secp256k1_scalar_half(secp256k1_scalar *r, const secp256k1_scalar *a) {
248 /* Writing `/` for field division and `//` for integer division, we compute
249 *
250 * a/2 = (a - (a&1))/2 + (a&1)/2
251 * = (a >> 1) + (a&1 ? 1/2 : 0)
252 * = (a >> 1) + (a&1 ? n//2+1 : 0),
253 *
254 * where n is the group order and in the last equality we have used 1/2 = n//2+1 (mod n).
255 * For n//2, we have the constants SECP256K1_N_H_0, ...
256 *
257 * This sum does not overflow. The most extreme case is a = -2, the largest odd scalar. Here:
258 * - the left summand is: a >> 1 = (a - a&1)/2 = (n-2-1)//2 = (n-3)//2
259 * - the right summand is: a&1 ? n//2+1 : 0 = n//2+1 = (n-1)//2 + 2//2 = (n+1)//2
260 * Together they sum to (n-3)//2 + (n+1)//2 = (2n-2)//2 = n - 1, which is less than n.
261 */
262 uint32_t mask = -(uint32_t)(a->d[0] & 1U);
263 uint64_t t = (uint32_t)((a->d[0] >> 1) | (a->d[1] << 31));
264 SECP256K1_SCALAR_VERIFY(a);
265
266 t += (SECP256K1_N_H_0 + 1U) & mask;
267 r->d[0] = t; t >>= 32;
268 t += (uint32_t)((a->d[1] >> 1) | (a->d[2] << 31));
269 t += SECP256K1_N_H_1 & mask;
270 r->d[1] = t; t >>= 32;
271 t += (uint32_t)((a->d[2] >> 1) | (a->d[3] << 31));
272 t += SECP256K1_N_H_2 & mask;
273 r->d[2] = t; t >>= 32;
274 t += (uint32_t)((a->d[3] >> 1) | (a->d[4] << 31));
275 t += SECP256K1_N_H_3 & mask;
276 r->d[3] = t; t >>= 32;
277 t += (uint32_t)((a->d[4] >> 1) | (a->d[5] << 31));
278 t += SECP256K1_N_H_4 & mask;
279 r->d[4] = t; t >>= 32;
280 t += (uint32_t)((a->d[5] >> 1) | (a->d[6] << 31));
281 t += SECP256K1_N_H_5 & mask;
282 r->d[5] = t; t >>= 32;
283 t += (uint32_t)((a->d[6] >> 1) | (a->d[7] << 31));
284 t += SECP256K1_N_H_6 & mask;
285 r->d[6] = t; t >>= 32;
286 r->d[7] = (uint32_t)t + (uint32_t)(a->d[7] >> 1) + (SECP256K1_N_H_7 & mask);
287
288 /* The line above only computed the bottom 32 bits of r->d[7]. Redo the computation
289 * in full 64 bits to make sure the top 32 bits are indeed zero. */
290 VERIFY_CHECK((t + (a->d[7] >> 1) + (SECP256K1_N_H_7 & mask)) >> 32 == 0);
291
292 SECP256K1_SCALAR_VERIFY(r);
293}
294
295SECP256K1_INLINE static int secp256k1_scalar_is_one(const secp256k1_scalar *a) {
296 SECP256K1_SCALAR_VERIFY(a);
297
298 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;
299}
300
301static int secp256k1_scalar_is_high(const secp256k1_scalar *a) {
302 int yes = 0;
303 int no = 0;
304 SECP256K1_SCALAR_VERIFY(a);
305
306 no |= (a->d[7] < SECP256K1_N_H_7);
307 yes |= (a->d[7] > SECP256K1_N_H_7) & ~no;
308 no |= (a->d[6] < SECP256K1_N_H_6) & ~yes; /* No need for a > check. */
309 no |= (a->d[5] < SECP256K1_N_H_5) & ~yes; /* No need for a > check. */
310 no |= (a->d[4] < SECP256K1_N_H_4) & ~yes; /* No need for a > check. */
311 no |= (a->d[3] < SECP256K1_N_H_3) & ~yes;
312 yes |= (a->d[3] > SECP256K1_N_H_3) & ~no;
313 no |= (a->d[2] < SECP256K1_N_H_2) & ~yes;
314 yes |= (a->d[2] > SECP256K1_N_H_2) & ~no;
315 no |= (a->d[1] < SECP256K1_N_H_1) & ~yes;
316 yes |= (a->d[1] > SECP256K1_N_H_1) & ~no;
317 yes |= (a->d[0] > SECP256K1_N_H_0) & ~no;
318 return yes;
319}
320
321static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag) {
322 /* If we are flag = 0, mask = 00...00 and this is a no-op;
323 * if we are flag = 1, mask = 11...11 and this is identical to secp256k1_scalar_negate */
324 volatile int vflag = flag;
325 uint32_t mask = -vflag;
326 uint32_t nonzero = 0xFFFFFFFFUL * (secp256k1_scalar_is_zero(r) == 0);
327 uint64_t t = (uint64_t)(r->d[0] ^ mask) + ((SECP256K1_N_0 + 1) & mask);
328 SECP256K1_SCALAR_VERIFY(r);
329
330 r->d[0] = t & nonzero; t >>= 32;
331 t += (uint64_t)(r->d[1] ^ mask) + (SECP256K1_N_1 & mask);
332 r->d[1] = t & nonzero; t >>= 32;
333 t += (uint64_t)(r->d[2] ^ mask) + (SECP256K1_N_2 & mask);
334 r->d[2] = t & nonzero; t >>= 32;
335 t += (uint64_t)(r->d[3] ^ mask) + (SECP256K1_N_3 & mask);
336 r->d[3] = t & nonzero; t >>= 32;
337 t += (uint64_t)(r->d[4] ^ mask) + (SECP256K1_N_4 & mask);
338 r->d[4] = t & nonzero; t >>= 32;
339 t += (uint64_t)(r->d[5] ^ mask) + (SECP256K1_N_5 & mask);
340 r->d[5] = t & nonzero; t >>= 32;
341 t += (uint64_t)(r->d[6] ^ mask) + (SECP256K1_N_6 & mask);
342 r->d[6] = t & nonzero; t >>= 32;
343 t += (uint64_t)(r->d[7] ^ mask) + (SECP256K1_N_7 & mask);
344 r->d[7] = t & nonzero;
345
346 SECP256K1_SCALAR_VERIFY(r);
347 return 2 * (mask == 0) - 1;
348}
349
350
351/* Inspired by the macros in OpenSSL's crypto/bn/asm/x86_64-gcc.c. */
352
354#define muladd(a,b) { \
355 uint32_t tl, th; \
356 { \
357 uint64_t t = (uint64_t)a * b; \
358 th = t >> 32; /* at most 0xFFFFFFFE */ \
359 tl = t; \
360 } \
361 c0 += tl; /* overflow is handled on the next line */ \
362 th += (c0 < tl); /* at most 0xFFFFFFFF */ \
363 c1 += th; /* overflow is handled on the next line */ \
364 c2 += (c1 < th); /* never overflows by contract (verified in the next line) */ \
365 VERIFY_CHECK((c1 >= th) || (c2 != 0)); \
366}
367
369#define muladd_fast(a,b) { \
370 uint32_t tl, th; \
371 { \
372 uint64_t t = (uint64_t)a * b; \
373 th = t >> 32; /* at most 0xFFFFFFFE */ \
374 tl = t; \
375 } \
376 c0 += tl; /* overflow is handled on the next line */ \
377 th += (c0 < tl); /* at most 0xFFFFFFFF */ \
378 c1 += th; /* never overflows by contract (verified in the next line) */ \
379 VERIFY_CHECK(c1 >= th); \
380}
381
383#define sumadd(a) { \
384 unsigned int over; \
385 c0 += (a); /* overflow is handled on the next line */ \
386 over = (c0 < (a)); \
387 c1 += over; /* overflow is handled on the next line */ \
388 c2 += (c1 < over); /* never overflows by contract */ \
389}
390
392#define sumadd_fast(a) { \
393 c0 += (a); /* overflow is handled on the next line */ \
394 c1 += (c0 < (a)); /* never overflows by contract (verified the next line) */ \
395 VERIFY_CHECK((c1 != 0) | (c0 >= (a))); \
396 VERIFY_CHECK(c2 == 0); \
397}
398
400#define extract(n) { \
401 (n) = c0; \
402 c0 = c1; \
403 c1 = c2; \
404 c2 = 0; \
405}
406
408#define extract_fast(n) { \
409 (n) = c0; \
410 c0 = c1; \
411 c1 = 0; \
412 VERIFY_CHECK(c2 == 0); \
413}
414
415static void secp256k1_scalar_reduce_512(secp256k1_scalar *r, const uint32_t *l) {
416 uint64_t c;
417 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];
418 uint32_t m0, m1, m2, m3, m4, m5, m6, m7, m8, m9, m10, m11, m12;
419 uint32_t p0, p1, p2, p3, p4, p5, p6, p7, p8;
420
421 /* 96 bit accumulator. */
422 uint32_t c0, c1, c2;
423
424 /* Reduce 512 bits into 385. */
425 /* m[0..12] = l[0..7] + n[0..7] * SECP256K1_N_C. */
426 c0 = l[0]; c1 = 0; c2 = 0;
427 muladd_fast(n0, SECP256K1_N_C_0);
428 extract_fast(m0);
429 sumadd_fast(l[1]);
430 muladd(n1, SECP256K1_N_C_0);
431 muladd(n0, SECP256K1_N_C_1);
432 extract(m1);
433 sumadd(l[2]);
434 muladd(n2, SECP256K1_N_C_0);
435 muladd(n1, SECP256K1_N_C_1);
436 muladd(n0, SECP256K1_N_C_2);
437 extract(m2);
438 sumadd(l[3]);
439 muladd(n3, SECP256K1_N_C_0);
440 muladd(n2, SECP256K1_N_C_1);
441 muladd(n1, SECP256K1_N_C_2);
442 muladd(n0, SECP256K1_N_C_3);
443 extract(m3);
444 sumadd(l[4]);
445 muladd(n4, SECP256K1_N_C_0);
446 muladd(n3, SECP256K1_N_C_1);
447 muladd(n2, SECP256K1_N_C_2);
448 muladd(n1, SECP256K1_N_C_3);
449 sumadd(n0);
450 extract(m4);
451 sumadd(l[5]);
452 muladd(n5, SECP256K1_N_C_0);
453 muladd(n4, SECP256K1_N_C_1);
454 muladd(n3, SECP256K1_N_C_2);
455 muladd(n2, SECP256K1_N_C_3);
456 sumadd(n1);
457 extract(m5);
458 sumadd(l[6]);
459 muladd(n6, SECP256K1_N_C_0);
460 muladd(n5, SECP256K1_N_C_1);
461 muladd(n4, SECP256K1_N_C_2);
462 muladd(n3, SECP256K1_N_C_3);
463 sumadd(n2);
464 extract(m6);
465 sumadd(l[7]);
466 muladd(n7, SECP256K1_N_C_0);
467 muladd(n6, SECP256K1_N_C_1);
468 muladd(n5, SECP256K1_N_C_2);
469 muladd(n4, SECP256K1_N_C_3);
470 sumadd(n3);
471 extract(m7);
472 muladd(n7, SECP256K1_N_C_1);
473 muladd(n6, SECP256K1_N_C_2);
474 muladd(n5, SECP256K1_N_C_3);
475 sumadd(n4);
476 extract(m8);
477 muladd(n7, SECP256K1_N_C_2);
478 muladd(n6, SECP256K1_N_C_3);
479 sumadd(n5);
480 extract(m9);
481 muladd(n7, SECP256K1_N_C_3);
482 sumadd(n6);
483 extract(m10);
484 sumadd_fast(n7);
485 extract_fast(m11);
486 VERIFY_CHECK(c0 <= 1);
487 m12 = c0;
488
489 /* Reduce 385 bits into 258. */
490 /* p[0..8] = m[0..7] + m[8..12] * SECP256K1_N_C. */
491 c0 = m0; c1 = 0; c2 = 0;
492 muladd_fast(m8, SECP256K1_N_C_0);
493 extract_fast(p0);
494 sumadd_fast(m1);
495 muladd(m9, SECP256K1_N_C_0);
496 muladd(m8, SECP256K1_N_C_1);
497 extract(p1);
498 sumadd(m2);
499 muladd(m10, SECP256K1_N_C_0);
500 muladd(m9, SECP256K1_N_C_1);
501 muladd(m8, SECP256K1_N_C_2);
502 extract(p2);
503 sumadd(m3);
504 muladd(m11, SECP256K1_N_C_0);
505 muladd(m10, SECP256K1_N_C_1);
506 muladd(m9, SECP256K1_N_C_2);
507 muladd(m8, SECP256K1_N_C_3);
508 extract(p3);
509 sumadd(m4);
510 muladd(m12, SECP256K1_N_C_0);
511 muladd(m11, SECP256K1_N_C_1);
512 muladd(m10, SECP256K1_N_C_2);
513 muladd(m9, SECP256K1_N_C_3);
514 sumadd(m8);
515 extract(p4);
516 sumadd(m5);
517 muladd(m12, SECP256K1_N_C_1);
518 muladd(m11, SECP256K1_N_C_2);
519 muladd(m10, SECP256K1_N_C_3);
520 sumadd(m9);
521 extract(p5);
522 sumadd(m6);
523 muladd(m12, SECP256K1_N_C_2);
524 muladd(m11, SECP256K1_N_C_3);
525 sumadd(m10);
526 extract(p6);
527 sumadd_fast(m7);
528 muladd_fast(m12, SECP256K1_N_C_3);
529 sumadd_fast(m11);
530 extract_fast(p7);
531 p8 = c0 + m12;
532 VERIFY_CHECK(p8 <= 2);
533
534 /* Reduce 258 bits into 256. */
535 /* r[0..7] = p[0..7] + p[8] * SECP256K1_N_C. */
536 c = p0 + (uint64_t)SECP256K1_N_C_0 * p8;
537 r->d[0] = c & 0xFFFFFFFFUL; c >>= 32;
538 c += p1 + (uint64_t)SECP256K1_N_C_1 * p8;
539 r->d[1] = c & 0xFFFFFFFFUL; c >>= 32;
540 c += p2 + (uint64_t)SECP256K1_N_C_2 * p8;
541 r->d[2] = c & 0xFFFFFFFFUL; c >>= 32;
542 c += p3 + (uint64_t)SECP256K1_N_C_3 * p8;
543 r->d[3] = c & 0xFFFFFFFFUL; c >>= 32;
544 c += p4 + (uint64_t)p8;
545 r->d[4] = c & 0xFFFFFFFFUL; c >>= 32;
546 c += p5;
547 r->d[5] = c & 0xFFFFFFFFUL; c >>= 32;
548 c += p6;
549 r->d[6] = c & 0xFFFFFFFFUL; c >>= 32;
550 c += p7;
551 r->d[7] = c & 0xFFFFFFFFUL; c >>= 32;
552
553 /* Final reduction of r. */
554 secp256k1_scalar_reduce(r, c + secp256k1_scalar_check_overflow(r));
555}
556
557static void secp256k1_scalar_mul_512(uint32_t *l, const secp256k1_scalar *a, const secp256k1_scalar *b) {
558 /* 96 bit accumulator. */
559 uint32_t c0 = 0, c1 = 0, c2 = 0;
560
561 /* l[0..15] = a[0..7] * b[0..7]. */
562 muladd_fast(a->d[0], b->d[0]);
563 extract_fast(l[0]);
564 muladd(a->d[0], b->d[1]);
565 muladd(a->d[1], b->d[0]);
566 extract(l[1]);
567 muladd(a->d[0], b->d[2]);
568 muladd(a->d[1], b->d[1]);
569 muladd(a->d[2], b->d[0]);
570 extract(l[2]);
571 muladd(a->d[0], b->d[3]);
572 muladd(a->d[1], b->d[2]);
573 muladd(a->d[2], b->d[1]);
574 muladd(a->d[3], b->d[0]);
575 extract(l[3]);
576 muladd(a->d[0], b->d[4]);
577 muladd(a->d[1], b->d[3]);
578 muladd(a->d[2], b->d[2]);
579 muladd(a->d[3], b->d[1]);
580 muladd(a->d[4], b->d[0]);
581 extract(l[4]);
582 muladd(a->d[0], b->d[5]);
583 muladd(a->d[1], b->d[4]);
584 muladd(a->d[2], b->d[3]);
585 muladd(a->d[3], b->d[2]);
586 muladd(a->d[4], b->d[1]);
587 muladd(a->d[5], b->d[0]);
588 extract(l[5]);
589 muladd(a->d[0], b->d[6]);
590 muladd(a->d[1], b->d[5]);
591 muladd(a->d[2], b->d[4]);
592 muladd(a->d[3], b->d[3]);
593 muladd(a->d[4], b->d[2]);
594 muladd(a->d[5], b->d[1]);
595 muladd(a->d[6], b->d[0]);
596 extract(l[6]);
597 muladd(a->d[0], b->d[7]);
598 muladd(a->d[1], b->d[6]);
599 muladd(a->d[2], b->d[5]);
600 muladd(a->d[3], b->d[4]);
601 muladd(a->d[4], b->d[3]);
602 muladd(a->d[5], b->d[2]);
603 muladd(a->d[6], b->d[1]);
604 muladd(a->d[7], b->d[0]);
605 extract(l[7]);
606 muladd(a->d[1], b->d[7]);
607 muladd(a->d[2], b->d[6]);
608 muladd(a->d[3], b->d[5]);
609 muladd(a->d[4], b->d[4]);
610 muladd(a->d[5], b->d[3]);
611 muladd(a->d[6], b->d[2]);
612 muladd(a->d[7], b->d[1]);
613 extract(l[8]);
614 muladd(a->d[2], b->d[7]);
615 muladd(a->d[3], b->d[6]);
616 muladd(a->d[4], b->d[5]);
617 muladd(a->d[5], b->d[4]);
618 muladd(a->d[6], b->d[3]);
619 muladd(a->d[7], b->d[2]);
620 extract(l[9]);
621 muladd(a->d[3], b->d[7]);
622 muladd(a->d[4], b->d[6]);
623 muladd(a->d[5], b->d[5]);
624 muladd(a->d[6], b->d[4]);
625 muladd(a->d[7], b->d[3]);
626 extract(l[10]);
627 muladd(a->d[4], b->d[7]);
628 muladd(a->d[5], b->d[6]);
629 muladd(a->d[6], b->d[5]);
630 muladd(a->d[7], b->d[4]);
631 extract(l[11]);
632 muladd(a->d[5], b->d[7]);
633 muladd(a->d[6], b->d[6]);
634 muladd(a->d[7], b->d[5]);
635 extract(l[12]);
636 muladd(a->d[6], b->d[7]);
637 muladd(a->d[7], b->d[6]);
638 extract(l[13]);
639 muladd_fast(a->d[7], b->d[7]);
640 extract_fast(l[14]);
641 VERIFY_CHECK(c1 == 0);
642 l[15] = c0;
643}
644
645#undef sumadd
646#undef sumadd_fast
647#undef muladd
648#undef muladd_fast
649#undef extract
650#undef extract_fast
651
652static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b) {
653 uint32_t l[16];
654 SECP256K1_SCALAR_VERIFY(a);
655 SECP256K1_SCALAR_VERIFY(b);
656
657 secp256k1_scalar_mul_512(l, a, b);
658 secp256k1_scalar_reduce_512(r, l);
659
660 SECP256K1_SCALAR_VERIFY(r);
661}
662
663static void secp256k1_scalar_split_128(secp256k1_scalar *r1, secp256k1_scalar *r2, const secp256k1_scalar *k) {
664 SECP256K1_SCALAR_VERIFY(k);
665
666 r1->d[0] = k->d[0];
667 r1->d[1] = k->d[1];
668 r1->d[2] = k->d[2];
669 r1->d[3] = k->d[3];
670 r1->d[4] = 0;
671 r1->d[5] = 0;
672 r1->d[6] = 0;
673 r1->d[7] = 0;
674 r2->d[0] = k->d[4];
675 r2->d[1] = k->d[5];
676 r2->d[2] = k->d[6];
677 r2->d[3] = k->d[7];
678 r2->d[4] = 0;
679 r2->d[5] = 0;
680 r2->d[6] = 0;
681 r2->d[7] = 0;
682
683 SECP256K1_SCALAR_VERIFY(r1);
684 SECP256K1_SCALAR_VERIFY(r2);
685}
686
687SECP256K1_INLINE static int secp256k1_scalar_eq(const secp256k1_scalar *a, const secp256k1_scalar *b) {
688 SECP256K1_SCALAR_VERIFY(a);
689 SECP256K1_SCALAR_VERIFY(b);
690
691 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;
692}
693
694SECP256K1_INLINE static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift) {
695 uint32_t l[16];
696 unsigned int shiftlimbs;
697 unsigned int shiftlow;
698 unsigned int shifthigh;
699 SECP256K1_SCALAR_VERIFY(a);
700 SECP256K1_SCALAR_VERIFY(b);
701 VERIFY_CHECK(shift >= 256);
702
703 secp256k1_scalar_mul_512(l, a, b);
704 shiftlimbs = shift >> 5;
705 shiftlow = shift & 0x1F;
706 shifthigh = 32 - shiftlow;
707 r->d[0] = shift < 512 ? (l[0 + shiftlimbs] >> shiftlow | (shift < 480 && shiftlow ? (l[1 + shiftlimbs] << shifthigh) : 0)) : 0;
708 r->d[1] = shift < 480 ? (l[1 + shiftlimbs] >> shiftlow | (shift < 448 && shiftlow ? (l[2 + shiftlimbs] << shifthigh) : 0)) : 0;
709 r->d[2] = shift < 448 ? (l[2 + shiftlimbs] >> shiftlow | (shift < 416 && shiftlow ? (l[3 + shiftlimbs] << shifthigh) : 0)) : 0;
710 r->d[3] = shift < 416 ? (l[3 + shiftlimbs] >> shiftlow | (shift < 384 && shiftlow ? (l[4 + shiftlimbs] << shifthigh) : 0)) : 0;
711 r->d[4] = shift < 384 ? (l[4 + shiftlimbs] >> shiftlow | (shift < 352 && shiftlow ? (l[5 + shiftlimbs] << shifthigh) : 0)) : 0;
712 r->d[5] = shift < 352 ? (l[5 + shiftlimbs] >> shiftlow | (shift < 320 && shiftlow ? (l[6 + shiftlimbs] << shifthigh) : 0)) : 0;
713 r->d[6] = shift < 320 ? (l[6 + shiftlimbs] >> shiftlow | (shift < 288 && shiftlow ? (l[7 + shiftlimbs] << shifthigh) : 0)) : 0;
714 r->d[7] = shift < 288 ? (l[7 + shiftlimbs] >> shiftlow) : 0;
715 secp256k1_scalar_cadd_bit(r, 0, (l[(shift - 1) >> 5] >> ((shift - 1) & 0x1f)) & 1);
716
717 SECP256K1_SCALAR_VERIFY(r);
718}
719
720static SECP256K1_INLINE void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag) {
721 uint32_t mask0, mask1;
722 volatile int vflag = flag;
723 SECP256K1_SCALAR_VERIFY(a);
724 SECP256K1_CHECKMEM_CHECK_VERIFY(r->d, sizeof(r->d));
725
726 mask0 = vflag + ~((uint32_t)0);
727 mask1 = ~mask0;
728 r->d[0] = (r->d[0] & mask0) | (a->d[0] & mask1);
729 r->d[1] = (r->d[1] & mask0) | (a->d[1] & mask1);
730 r->d[2] = (r->d[2] & mask0) | (a->d[2] & mask1);
731 r->d[3] = (r->d[3] & mask0) | (a->d[3] & mask1);
732 r->d[4] = (r->d[4] & mask0) | (a->d[4] & mask1);
733 r->d[5] = (r->d[5] & mask0) | (a->d[5] & mask1);
734 r->d[6] = (r->d[6] & mask0) | (a->d[6] & mask1);
735 r->d[7] = (r->d[7] & mask0) | (a->d[7] & mask1);
736
737 SECP256K1_SCALAR_VERIFY(r);
738}
739
740static void secp256k1_scalar_from_signed30(secp256k1_scalar *r, const secp256k1_modinv32_signed30 *a) {
741 const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4],
742 a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8];
743
744 /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and
745 * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8).
746 */
747 VERIFY_CHECK(a0 >> 30 == 0);
748 VERIFY_CHECK(a1 >> 30 == 0);
749 VERIFY_CHECK(a2 >> 30 == 0);
750 VERIFY_CHECK(a3 >> 30 == 0);
751 VERIFY_CHECK(a4 >> 30 == 0);
752 VERIFY_CHECK(a5 >> 30 == 0);
753 VERIFY_CHECK(a6 >> 30 == 0);
754 VERIFY_CHECK(a7 >> 30 == 0);
755 VERIFY_CHECK(a8 >> 16 == 0);
756
757 r->d[0] = a0 | a1 << 30;
758 r->d[1] = a1 >> 2 | a2 << 28;
759 r->d[2] = a2 >> 4 | a3 << 26;
760 r->d[3] = a3 >> 6 | a4 << 24;
761 r->d[4] = a4 >> 8 | a5 << 22;
762 r->d[5] = a5 >> 10 | a6 << 20;
763 r->d[6] = a6 >> 12 | a7 << 18;
764 r->d[7] = a7 >> 14 | a8 << 16;
765
766 SECP256K1_SCALAR_VERIFY(r);
767}
768
769static void secp256k1_scalar_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_scalar *a) {
770 const uint32_t M30 = UINT32_MAX >> 2;
771 const uint32_t a0 = a->d[0], a1 = a->d[1], a2 = a->d[2], a3 = a->d[3],
772 a4 = a->d[4], a5 = a->d[5], a6 = a->d[6], a7 = a->d[7];
773 SECP256K1_SCALAR_VERIFY(a);
774
775 r->v[0] = a0 & M30;
776 r->v[1] = (a0 >> 30 | a1 << 2) & M30;
777 r->v[2] = (a1 >> 28 | a2 << 4) & M30;
778 r->v[3] = (a2 >> 26 | a3 << 6) & M30;
779 r->v[4] = (a3 >> 24 | a4 << 8) & M30;
780 r->v[5] = (a4 >> 22 | a5 << 10) & M30;
781 r->v[6] = (a5 >> 20 | a6 << 12) & M30;
782 r->v[7] = (a6 >> 18 | a7 << 14) & M30;
783 r->v[8] = a7 >> 16;
784}
785
786static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_scalar = {
787 {{0x10364141L, 0x3F497A33L, 0x348A03BBL, 0x2BB739ABL, -0x146L, 0, 0, 0, 65536}},
788 0x2A774EC1L
789};
790
805
820
821SECP256K1_INLINE static int secp256k1_scalar_is_even(const secp256k1_scalar *a) {
822 SECP256K1_SCALAR_VERIFY(a);
823
824 return !(a->d[0] & 1);
825}
826
827#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
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:821
secp256k1_scalar_check_overflow
static SECP256K1_INLINE int secp256k1_scalar_check_overflow(const secp256k1_scalar *a)
Definition scalar_8x32_impl.h:86
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:694
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:247
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:663
secp256k1_scalar_clear
static SECP256K1_INLINE void secp256k1_scalar_clear(secp256k1_scalar *r)
Definition scalar_8x32_impl.h:41
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:400
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:186
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:557
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:73
secp256k1_scalar_inverse_var
static void secp256k1_scalar_inverse_var(secp256k1_scalar *r, const secp256k1_scalar *x)
Definition scalar_8x32_impl.h:806
sumadd_fast
#define sumadd_fast(a)
Add a to the number defined by (c0,c1).
Definition scalar_8x32_impl.h:392
secp256k1_scalar_get_b32
static void secp256k1_scalar_get_b32(unsigned char *bin, const secp256k1_scalar *a)
Definition scalar_8x32_impl.h:204
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:52
secp256k1_scalar_inverse
static void secp256k1_scalar_inverse(secp256k1_scalar *r, const secp256k1_scalar *x)
Definition scalar_8x32_impl.h:791
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:720
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:408
muladd
#define muladd(a, b)
Add a*b to the number defined by (c0,c1,c2).
Definition scalar_8x32_impl.h:354
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:415
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:687
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:129
sumadd
#define sumadd(a)
Add a to the number defined by (c0,c1,c2).
Definition scalar_8x32_impl.h:383
secp256k1_scalar_cond_negate
static int secp256k1_scalar_cond_negate(secp256k1_scalar *r, int flag)
Definition scalar_8x32_impl.h:321
secp256k1_scalar_mul
static void secp256k1_scalar_mul(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b)
Definition scalar_8x32_impl.h:652
secp256k1_const_modinfo_scalar
static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_scalar
Definition scalar_8x32_impl.h:786
secp256k1_scalar_reduce
static SECP256K1_INLINE int secp256k1_scalar_reduce(secp256k1_scalar *r, uint32_t overflow)
Definition scalar_8x32_impl.h:104
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:223
secp256k1_scalar_is_zero
static SECP256K1_INLINE int secp256k1_scalar_is_zero(const secp256k1_scalar *a)
Definition scalar_8x32_impl.h:217
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:301
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:740
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:65
secp256k1_scalar_cadd_bit
static void secp256k1_scalar_cadd_bit(secp256k1_scalar *r, unsigned int bit, int flag)
Definition scalar_8x32_impl.h:158
muladd_fast
#define muladd_fast(a, b)
Add a*b to the number defined by (c0,c1).
Definition scalar_8x32_impl.h:369
secp256k1_scalar_is_one
static SECP256K1_INLINE int secp256k1_scalar_is_one(const secp256k1_scalar *a)
Definition scalar_8x32_impl.h:295
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:769
secp256k1_read_be32
static SECP256K1_INLINE uint32_t secp256k1_read_be32(const unsigned char *p)
Definition util.h:358
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition util.h:48
secp256k1_write_be32
static SECP256K1_INLINE void secp256k1_write_be32(unsigned char *p, uint32_t x)
Definition util.h:366
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition util.h:153
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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