Bitcoin Core 31.0.0
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field_10x26_impl.h
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1/***********************************************************************
2 * Copyright (c) 2013, 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_FIELD_REPR_IMPL_H
8#define SECP256K1_FIELD_REPR_IMPL_H
9
10#include "checkmem.h"
11#include "util.h"
12#include "field.h"
13#include "modinv32_impl.h"
14
15#ifdef VERIFY
16static void secp256k1_fe_impl_verify(const secp256k1_fe *a) {
17 const uint32_t *d = a->n;
18 int m = a->normalized ? 1 : 2 * a->magnitude;
19 VERIFY_CHECK(d[0] <= 0x3FFFFFFUL * m);
20 VERIFY_CHECK(d[1] <= 0x3FFFFFFUL * m);
21 VERIFY_CHECK(d[2] <= 0x3FFFFFFUL * m);
22 VERIFY_CHECK(d[3] <= 0x3FFFFFFUL * m);
23 VERIFY_CHECK(d[4] <= 0x3FFFFFFUL * m);
24 VERIFY_CHECK(d[5] <= 0x3FFFFFFUL * m);
25 VERIFY_CHECK(d[6] <= 0x3FFFFFFUL * m);
26 VERIFY_CHECK(d[7] <= 0x3FFFFFFUL * m);
27 VERIFY_CHECK(d[8] <= 0x3FFFFFFUL * m);
28 VERIFY_CHECK(d[9] <= 0x03FFFFFUL * m);
29 if (a->normalized) {
30 if (d[9] == 0x03FFFFFUL) {
31 uint32_t mid = d[8] & d[7] & d[6] & d[5] & d[4] & d[3] & d[2];
32 if (mid == 0x3FFFFFFUL) {
33 VERIFY_CHECK((d[1] + 0x40UL + ((d[0] + 0x3D1UL) >> 26)) <= 0x3FFFFFFUL);
34 }
35 }
36 }
37}
38#endif
39
40static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m) {
41 r->n[0] = 0x3FFFFFFUL * 2 * m;
42 r->n[1] = 0x3FFFFFFUL * 2 * m;
43 r->n[2] = 0x3FFFFFFUL * 2 * m;
44 r->n[3] = 0x3FFFFFFUL * 2 * m;
45 r->n[4] = 0x3FFFFFFUL * 2 * m;
46 r->n[5] = 0x3FFFFFFUL * 2 * m;
47 r->n[6] = 0x3FFFFFFUL * 2 * m;
48 r->n[7] = 0x3FFFFFFUL * 2 * m;
49 r->n[8] = 0x3FFFFFFUL * 2 * m;
50 r->n[9] = 0x03FFFFFUL * 2 * m;
51}
52
53static void secp256k1_fe_impl_normalize(secp256k1_fe *r) {
54 uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
55 t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
56
57 /* Reduce t9 at the start so there will be at most a single carry from the first pass */
58 uint32_t m;
59 uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
60
61 /* The first pass ensures the magnitude is 1, ... */
62 t0 += x * 0x3D1UL; t1 += (x << 6);
63 t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
64 t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
65 t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
66 t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
67 t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
68 t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
69 t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
70 t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
71 t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
72
73 /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
74 VERIFY_CHECK(t9 >> 23 == 0);
75
76 /* At most a single final reduction is needed; check if the value is >= the field characteristic */
77 x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
78 & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
79
80 /* Apply the final reduction (for constant-time behaviour, we do it always) */
81 t0 += x * 0x3D1UL; t1 += (x << 6);
82 t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
83 t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
84 t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
85 t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
86 t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
87 t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
88 t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
89 t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
90 t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
91
92 /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
93 VERIFY_CHECK(t9 >> 22 == x);
94
95 /* Mask off the possible multiple of 2^256 from the final reduction */
96 t9 &= 0x03FFFFFUL;
97
98 r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
99 r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
100}
101
102static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r) {
103 uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
104 t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
105
106 /* Reduce t9 at the start so there will be at most a single carry from the first pass */
107 uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
108
109 /* The first pass ensures the magnitude is 1, ... */
110 t0 += x * 0x3D1UL; t1 += (x << 6);
111 t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
112 t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
113 t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
114 t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
115 t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
116 t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
117 t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
118 t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
119 t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
120
121 /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
122 VERIFY_CHECK(t9 >> 23 == 0);
123
124 r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
125 r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
126}
127
128static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r) {
129 uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
130 t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
131
132 /* Reduce t9 at the start so there will be at most a single carry from the first pass */
133 uint32_t m;
134 uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
135
136 /* The first pass ensures the magnitude is 1, ... */
137 t0 += x * 0x3D1UL; t1 += (x << 6);
138 t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
139 t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
140 t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; m = t2;
141 t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; m &= t3;
142 t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; m &= t4;
143 t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; m &= t5;
144 t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; m &= t6;
145 t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; m &= t7;
146 t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; m &= t8;
147
148 /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
149 VERIFY_CHECK(t9 >> 23 == 0);
150
151 /* At most a single final reduction is needed; check if the value is >= the field characteristic */
152 x = (t9 >> 22) | ((t9 == 0x03FFFFFUL) & (m == 0x3FFFFFFUL)
153 & ((t1 + 0x40UL + ((t0 + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
154
155 if (x) {
156 t0 += 0x3D1UL; t1 += (x << 6);
157 t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL;
158 t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL;
159 t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL;
160 t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL;
161 t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL;
162 t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL;
163 t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL;
164 t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL;
165 t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL;
166
167 /* If t9 didn't carry to bit 22 already, then it should have after any final reduction */
168 VERIFY_CHECK(t9 >> 22 == x);
169
170 /* Mask off the possible multiple of 2^256 from the final reduction */
171 t9 &= 0x03FFFFFUL;
172 }
173
174 r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
175 r->n[5] = t5; r->n[6] = t6; r->n[7] = t7; r->n[8] = t8; r->n[9] = t9;
176}
177
178static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r) {
179 uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
180 t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
181
182 /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
183 uint32_t z0, z1;
184
185 /* Reduce t9 at the start so there will be at most a single carry from the first pass */
186 uint32_t x = t9 >> 22; t9 &= 0x03FFFFFUL;
187
188 /* The first pass ensures the magnitude is 1, ... */
189 t0 += x * 0x3D1UL; t1 += (x << 6);
190 t1 += (t0 >> 26); t0 &= 0x3FFFFFFUL; z0 = t0; z1 = t0 ^ 0x3D0UL;
191 t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
192 t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
193 t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
194 t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
195 t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
196 t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
197 t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
198 t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
199 z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
200
201 /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
202 VERIFY_CHECK(t9 >> 23 == 0);
203
204 return (z0 == 0) | (z1 == 0x3FFFFFFUL);
205}
206
207static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r) {
208 uint32_t t0, t1, t2, t3, t4, t5, t6, t7, t8, t9;
209 uint32_t z0, z1;
210 uint32_t x;
211
212 t0 = r->n[0];
213 t9 = r->n[9];
214
215 /* Reduce t9 at the start so there will be at most a single carry from the first pass */
216 x = t9 >> 22;
217
218 /* The first pass ensures the magnitude is 1, ... */
219 t0 += x * 0x3D1UL;
220
221 /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
222 z0 = t0 & 0x3FFFFFFUL;
223 z1 = z0 ^ 0x3D0UL;
224
225 /* Fast return path should catch the majority of cases */
226 if ((z0 != 0UL) & (z1 != 0x3FFFFFFUL)) {
227 return 0;
228 }
229
230 t1 = r->n[1];
231 t2 = r->n[2];
232 t3 = r->n[3];
233 t4 = r->n[4];
234 t5 = r->n[5];
235 t6 = r->n[6];
236 t7 = r->n[7];
237 t8 = r->n[8];
238
239 t9 &= 0x03FFFFFUL;
240 t1 += (x << 6);
241
242 t1 += (t0 >> 26);
243 t2 += (t1 >> 26); t1 &= 0x3FFFFFFUL; z0 |= t1; z1 &= t1 ^ 0x40UL;
244 t3 += (t2 >> 26); t2 &= 0x3FFFFFFUL; z0 |= t2; z1 &= t2;
245 t4 += (t3 >> 26); t3 &= 0x3FFFFFFUL; z0 |= t3; z1 &= t3;
246 t5 += (t4 >> 26); t4 &= 0x3FFFFFFUL; z0 |= t4; z1 &= t4;
247 t6 += (t5 >> 26); t5 &= 0x3FFFFFFUL; z0 |= t5; z1 &= t5;
248 t7 += (t6 >> 26); t6 &= 0x3FFFFFFUL; z0 |= t6; z1 &= t6;
249 t8 += (t7 >> 26); t7 &= 0x3FFFFFFUL; z0 |= t7; z1 &= t7;
250 t9 += (t8 >> 26); t8 &= 0x3FFFFFFUL; z0 |= t8; z1 &= t8;
251 z0 |= t9; z1 &= t9 ^ 0x3C00000UL;
252
253 /* ... except for a possible carry at bit 22 of t9 (i.e. bit 256 of the field element) */
254 VERIFY_CHECK(t9 >> 23 == 0);
255
256 return (z0 == 0) | (z1 == 0x3FFFFFFUL);
257}
258
259SECP256K1_INLINE static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a) {
260 r->n[0] = a;
261 r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
262}
263
264SECP256K1_INLINE static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a) {
265 const uint32_t *t = a->n;
266 return (t[0] | t[1] | t[2] | t[3] | t[4] | t[5] | t[6] | t[7] | t[8] | t[9]) == 0;
267}
268
269SECP256K1_INLINE static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a) {
270 return a->n[0] & 1;
271}
272
273static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
274 int i;
275 for (i = 9; i >= 0; i--) {
276 if (a->n[i] > b->n[i]) {
277 return 1;
278 }
279 if (a->n[i] < b->n[i]) {
280 return -1;
281 }
282 }
283 return 0;
284}
285
286static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
287 r->n[0] = (uint32_t)a[31] | ((uint32_t)a[30] << 8) | ((uint32_t)a[29] << 16) | ((uint32_t)(a[28] & 0x3) << 24);
288 r->n[1] = (uint32_t)((a[28] >> 2) & 0x3f) | ((uint32_t)a[27] << 6) | ((uint32_t)a[26] << 14) | ((uint32_t)(a[25] & 0xf) << 22);
289 r->n[2] = (uint32_t)((a[25] >> 4) & 0xf) | ((uint32_t)a[24] << 4) | ((uint32_t)a[23] << 12) | ((uint32_t)(a[22] & 0x3f) << 20);
290 r->n[3] = (uint32_t)((a[22] >> 6) & 0x3) | ((uint32_t)a[21] << 2) | ((uint32_t)a[20] << 10) | ((uint32_t)a[19] << 18);
291 r->n[4] = (uint32_t)a[18] | ((uint32_t)a[17] << 8) | ((uint32_t)a[16] << 16) | ((uint32_t)(a[15] & 0x3) << 24);
292 r->n[5] = (uint32_t)((a[15] >> 2) & 0x3f) | ((uint32_t)a[14] << 6) | ((uint32_t)a[13] << 14) | ((uint32_t)(a[12] & 0xf) << 22);
293 r->n[6] = (uint32_t)((a[12] >> 4) & 0xf) | ((uint32_t)a[11] << 4) | ((uint32_t)a[10] << 12) | ((uint32_t)(a[9] & 0x3f) << 20);
294 r->n[7] = (uint32_t)((a[9] >> 6) & 0x3) | ((uint32_t)a[8] << 2) | ((uint32_t)a[7] << 10) | ((uint32_t)a[6] << 18);
295 r->n[8] = (uint32_t)a[5] | ((uint32_t)a[4] << 8) | ((uint32_t)a[3] << 16) | ((uint32_t)(a[2] & 0x3) << 24);
296 r->n[9] = (uint32_t)((a[2] >> 2) & 0x3f) | ((uint32_t)a[1] << 6) | ((uint32_t)a[0] << 14);
297}
298
299static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
300 secp256k1_fe_impl_set_b32_mod(r, a);
301 return !((r->n[9] == 0x3FFFFFUL) & ((r->n[8] & r->n[7] & r->n[6] & r->n[5] & r->n[4] & r->n[3] & r->n[2]) == 0x3FFFFFFUL) & ((r->n[1] + 0x40UL + ((r->n[0] + 0x3D1UL) >> 26)) > 0x3FFFFFFUL));
302}
303
305static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a) {
306 r[0] = (a->n[9] >> 14) & 0xff;
307 r[1] = (a->n[9] >> 6) & 0xff;
308 r[2] = ((a->n[9] & 0x3F) << 2) | ((a->n[8] >> 24) & 0x3);
309 r[3] = (a->n[8] >> 16) & 0xff;
310 r[4] = (a->n[8] >> 8) & 0xff;
311 r[5] = a->n[8] & 0xff;
312 r[6] = (a->n[7] >> 18) & 0xff;
313 r[7] = (a->n[7] >> 10) & 0xff;
314 r[8] = (a->n[7] >> 2) & 0xff;
315 r[9] = ((a->n[7] & 0x3) << 6) | ((a->n[6] >> 20) & 0x3f);
316 r[10] = (a->n[6] >> 12) & 0xff;
317 r[11] = (a->n[6] >> 4) & 0xff;
318 r[12] = ((a->n[6] & 0xf) << 4) | ((a->n[5] >> 22) & 0xf);
319 r[13] = (a->n[5] >> 14) & 0xff;
320 r[14] = (a->n[5] >> 6) & 0xff;
321 r[15] = ((a->n[5] & 0x3f) << 2) | ((a->n[4] >> 24) & 0x3);
322 r[16] = (a->n[4] >> 16) & 0xff;
323 r[17] = (a->n[4] >> 8) & 0xff;
324 r[18] = a->n[4] & 0xff;
325 r[19] = (a->n[3] >> 18) & 0xff;
326 r[20] = (a->n[3] >> 10) & 0xff;
327 r[21] = (a->n[3] >> 2) & 0xff;
328 r[22] = ((a->n[3] & 0x3) << 6) | ((a->n[2] >> 20) & 0x3f);
329 r[23] = (a->n[2] >> 12) & 0xff;
330 r[24] = (a->n[2] >> 4) & 0xff;
331 r[25] = ((a->n[2] & 0xf) << 4) | ((a->n[1] >> 22) & 0xf);
332 r[26] = (a->n[1] >> 14) & 0xff;
333 r[27] = (a->n[1] >> 6) & 0xff;
334 r[28] = ((a->n[1] & 0x3f) << 2) | ((a->n[0] >> 24) & 0x3);
335 r[29] = (a->n[0] >> 16) & 0xff;
336 r[30] = (a->n[0] >> 8) & 0xff;
337 r[31] = a->n[0] & 0xff;
338}
339
340SECP256K1_INLINE static void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m) {
341 /* For all legal values of m (0..31), the following properties hold: */
342 VERIFY_CHECK(0x3FFFC2FUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
343 VERIFY_CHECK(0x3FFFFBFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
344 VERIFY_CHECK(0x3FFFFFFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m);
345 VERIFY_CHECK(0x03FFFFFUL * 2 * (m + 1) >= 0x03FFFFFUL * 2 * m);
346
347 /* Due to the properties above, the left hand in the subtractions below is never less than
348 * the right hand. */
349 r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0];
350 r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1];
351 r->n[2] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[2];
352 r->n[3] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[3];
353 r->n[4] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[4];
354 r->n[5] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[5];
355 r->n[6] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[6];
356 r->n[7] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[7];
357 r->n[8] = 0x3FFFFFFUL * 2 * (m + 1) - a->n[8];
358 r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
359}
360
361SECP256K1_INLINE static void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a) {
362 r->n[0] *= a;
363 r->n[1] *= a;
364 r->n[2] *= a;
365 r->n[3] *= a;
366 r->n[4] *= a;
367 r->n[5] *= a;
368 r->n[6] *= a;
369 r->n[7] *= a;
370 r->n[8] *= a;
371 r->n[9] *= a;
372}
373
374SECP256K1_INLINE static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a) {
375 r->n[0] += a->n[0];
376 r->n[1] += a->n[1];
377 r->n[2] += a->n[2];
378 r->n[3] += a->n[3];
379 r->n[4] += a->n[4];
380 r->n[5] += a->n[5];
381 r->n[6] += a->n[6];
382 r->n[7] += a->n[7];
383 r->n[8] += a->n[8];
384 r->n[9] += a->n[9];
385}
386
387SECP256K1_INLINE static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a) {
388 r->n[0] += a;
389}
390
391#if defined(USE_EXTERNAL_ASM)
392
393/* External assembler implementation */
394void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b);
395void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a);
396
397#else
398
399#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
400
401SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t * SECP256K1_RESTRICT b) {
402 uint64_t c, d;
403 uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
404 uint32_t t9, t1, t0, t2, t3, t4, t5, t6, t7;
405 const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
406
407 VERIFY_BITS(a[0], 30);
408 VERIFY_BITS(a[1], 30);
409 VERIFY_BITS(a[2], 30);
410 VERIFY_BITS(a[3], 30);
411 VERIFY_BITS(a[4], 30);
412 VERIFY_BITS(a[5], 30);
413 VERIFY_BITS(a[6], 30);
414 VERIFY_BITS(a[7], 30);
415 VERIFY_BITS(a[8], 30);
416 VERIFY_BITS(a[9], 26);
417 VERIFY_BITS(b[0], 30);
418 VERIFY_BITS(b[1], 30);
419 VERIFY_BITS(b[2], 30);
420 VERIFY_BITS(b[3], 30);
421 VERIFY_BITS(b[4], 30);
422 VERIFY_BITS(b[5], 30);
423 VERIFY_BITS(b[6], 30);
424 VERIFY_BITS(b[7], 30);
425 VERIFY_BITS(b[8], 30);
426 VERIFY_BITS(b[9], 26);
427
434 d = (uint64_t)a[0] * b[9]
435 + (uint64_t)a[1] * b[8]
436 + (uint64_t)a[2] * b[7]
437 + (uint64_t)a[3] * b[6]
438 + (uint64_t)a[4] * b[5]
439 + (uint64_t)a[5] * b[4]
440 + (uint64_t)a[6] * b[3]
441 + (uint64_t)a[7] * b[2]
442 + (uint64_t)a[8] * b[1]
443 + (uint64_t)a[9] * b[0];
444 /* VERIFY_BITS(d, 64); */
445 /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
446 t9 = d & M; d >>= 26;
447 VERIFY_BITS(t9, 26);
448 VERIFY_BITS(d, 38);
449 /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
450
451 c = (uint64_t)a[0] * b[0];
452 VERIFY_BITS(c, 60);
453 /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
454 d += (uint64_t)a[1] * b[9]
455 + (uint64_t)a[2] * b[8]
456 + (uint64_t)a[3] * b[7]
457 + (uint64_t)a[4] * b[6]
458 + (uint64_t)a[5] * b[5]
459 + (uint64_t)a[6] * b[4]
460 + (uint64_t)a[7] * b[3]
461 + (uint64_t)a[8] * b[2]
462 + (uint64_t)a[9] * b[1];
463 VERIFY_BITS(d, 63);
464 /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
465 u0 = d & M; d >>= 26; c += u0 * R0;
466 VERIFY_BITS(u0, 26);
467 VERIFY_BITS(d, 37);
468 VERIFY_BITS(c, 61);
469 /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
470 t0 = c & M; c >>= 26; c += u0 * R1;
471 VERIFY_BITS(t0, 26);
472 VERIFY_BITS(c, 37);
473 /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
474 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
475
476 c += (uint64_t)a[0] * b[1]
477 + (uint64_t)a[1] * b[0];
478 VERIFY_BITS(c, 62);
479 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
480 d += (uint64_t)a[2] * b[9]
481 + (uint64_t)a[3] * b[8]
482 + (uint64_t)a[4] * b[7]
483 + (uint64_t)a[5] * b[6]
484 + (uint64_t)a[6] * b[5]
485 + (uint64_t)a[7] * b[4]
486 + (uint64_t)a[8] * b[3]
487 + (uint64_t)a[9] * b[2];
488 VERIFY_BITS(d, 63);
489 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
490 u1 = d & M; d >>= 26; c += u1 * R0;
491 VERIFY_BITS(u1, 26);
492 VERIFY_BITS(d, 37);
493 VERIFY_BITS(c, 63);
494 /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
495 t1 = c & M; c >>= 26; c += u1 * R1;
496 VERIFY_BITS(t1, 26);
497 VERIFY_BITS(c, 38);
498 /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
499 /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
500
501 c += (uint64_t)a[0] * b[2]
502 + (uint64_t)a[1] * b[1]
503 + (uint64_t)a[2] * b[0];
504 VERIFY_BITS(c, 62);
505 /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
506 d += (uint64_t)a[3] * b[9]
507 + (uint64_t)a[4] * b[8]
508 + (uint64_t)a[5] * b[7]
509 + (uint64_t)a[6] * b[6]
510 + (uint64_t)a[7] * b[5]
511 + (uint64_t)a[8] * b[4]
512 + (uint64_t)a[9] * b[3];
513 VERIFY_BITS(d, 63);
514 /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
515 u2 = d & M; d >>= 26; c += u2 * R0;
516 VERIFY_BITS(u2, 26);
517 VERIFY_BITS(d, 37);
518 VERIFY_BITS(c, 63);
519 /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
520 t2 = c & M; c >>= 26; c += u2 * R1;
521 VERIFY_BITS(t2, 26);
522 VERIFY_BITS(c, 38);
523 /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
524 /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
525
526 c += (uint64_t)a[0] * b[3]
527 + (uint64_t)a[1] * b[2]
528 + (uint64_t)a[2] * b[1]
529 + (uint64_t)a[3] * b[0];
530 VERIFY_BITS(c, 63);
531 /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
532 d += (uint64_t)a[4] * b[9]
533 + (uint64_t)a[5] * b[8]
534 + (uint64_t)a[6] * b[7]
535 + (uint64_t)a[7] * b[6]
536 + (uint64_t)a[8] * b[5]
537 + (uint64_t)a[9] * b[4];
538 VERIFY_BITS(d, 63);
539 /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
540 u3 = d & M; d >>= 26; c += u3 * R0;
541 VERIFY_BITS(u3, 26);
542 VERIFY_BITS(d, 37);
543 /* VERIFY_BITS(c, 64); */
544 /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
545 t3 = c & M; c >>= 26; c += u3 * R1;
546 VERIFY_BITS(t3, 26);
547 VERIFY_BITS(c, 39);
548 /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
549 /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
550
551 c += (uint64_t)a[0] * b[4]
552 + (uint64_t)a[1] * b[3]
553 + (uint64_t)a[2] * b[2]
554 + (uint64_t)a[3] * b[1]
555 + (uint64_t)a[4] * b[0];
556 VERIFY_BITS(c, 63);
557 /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
558 d += (uint64_t)a[5] * b[9]
559 + (uint64_t)a[6] * b[8]
560 + (uint64_t)a[7] * b[7]
561 + (uint64_t)a[8] * b[6]
562 + (uint64_t)a[9] * b[5];
563 VERIFY_BITS(d, 62);
564 /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
565 u4 = d & M; d >>= 26; c += u4 * R0;
566 VERIFY_BITS(u4, 26);
567 VERIFY_BITS(d, 36);
568 /* VERIFY_BITS(c, 64); */
569 /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
570 t4 = c & M; c >>= 26; c += u4 * R1;
571 VERIFY_BITS(t4, 26);
572 VERIFY_BITS(c, 39);
573 /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
574 /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
575
576 c += (uint64_t)a[0] * b[5]
577 + (uint64_t)a[1] * b[4]
578 + (uint64_t)a[2] * b[3]
579 + (uint64_t)a[3] * b[2]
580 + (uint64_t)a[4] * b[1]
581 + (uint64_t)a[5] * b[0];
582 VERIFY_BITS(c, 63);
583 /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
584 d += (uint64_t)a[6] * b[9]
585 + (uint64_t)a[7] * b[8]
586 + (uint64_t)a[8] * b[7]
587 + (uint64_t)a[9] * b[6];
588 VERIFY_BITS(d, 62);
589 /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
590 u5 = d & M; d >>= 26; c += u5 * R0;
591 VERIFY_BITS(u5, 26);
592 VERIFY_BITS(d, 36);
593 /* VERIFY_BITS(c, 64); */
594 /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
595 t5 = c & M; c >>= 26; c += u5 * R1;
596 VERIFY_BITS(t5, 26);
597 VERIFY_BITS(c, 39);
598 /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
599 /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
600
601 c += (uint64_t)a[0] * b[6]
602 + (uint64_t)a[1] * b[5]
603 + (uint64_t)a[2] * b[4]
604 + (uint64_t)a[3] * b[3]
605 + (uint64_t)a[4] * b[2]
606 + (uint64_t)a[5] * b[1]
607 + (uint64_t)a[6] * b[0];
608 VERIFY_BITS(c, 63);
609 /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
610 d += (uint64_t)a[7] * b[9]
611 + (uint64_t)a[8] * b[8]
612 + (uint64_t)a[9] * b[7];
613 VERIFY_BITS(d, 61);
614 /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
615 u6 = d & M; d >>= 26; c += u6 * R0;
616 VERIFY_BITS(u6, 26);
617 VERIFY_BITS(d, 35);
618 /* VERIFY_BITS(c, 64); */
619 /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
620 t6 = c & M; c >>= 26; c += u6 * R1;
621 VERIFY_BITS(t6, 26);
622 VERIFY_BITS(c, 39);
623 /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
624 /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
625
626 c += (uint64_t)a[0] * b[7]
627 + (uint64_t)a[1] * b[6]
628 + (uint64_t)a[2] * b[5]
629 + (uint64_t)a[3] * b[4]
630 + (uint64_t)a[4] * b[3]
631 + (uint64_t)a[5] * b[2]
632 + (uint64_t)a[6] * b[1]
633 + (uint64_t)a[7] * b[0];
634 /* VERIFY_BITS(c, 64); */
635 VERIFY_CHECK(c <= 0x8000007C00000007ULL);
636 /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
637 d += (uint64_t)a[8] * b[9]
638 + (uint64_t)a[9] * b[8];
639 VERIFY_BITS(d, 58);
640 /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
641 u7 = d & M; d >>= 26; c += u7 * R0;
642 VERIFY_BITS(u7, 26);
643 VERIFY_BITS(d, 32);
644 /* VERIFY_BITS(c, 64); */
645 VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
646 /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
647 t7 = c & M; c >>= 26; c += u7 * R1;
648 VERIFY_BITS(t7, 26);
649 VERIFY_BITS(c, 38);
650 /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
651 /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
652
653 c += (uint64_t)a[0] * b[8]
654 + (uint64_t)a[1] * b[7]
655 + (uint64_t)a[2] * b[6]
656 + (uint64_t)a[3] * b[5]
657 + (uint64_t)a[4] * b[4]
658 + (uint64_t)a[5] * b[3]
659 + (uint64_t)a[6] * b[2]
660 + (uint64_t)a[7] * b[1]
661 + (uint64_t)a[8] * b[0];
662 /* VERIFY_BITS(c, 64); */
663 VERIFY_CHECK(c <= 0x9000007B80000008ULL);
664 /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
665 d += (uint64_t)a[9] * b[9];
666 VERIFY_BITS(d, 57);
667 /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
668 u8 = d & M; d >>= 26; c += u8 * R0;
669 VERIFY_BITS(u8, 26);
670 VERIFY_BITS(d, 31);
671 /* VERIFY_BITS(c, 64); */
672 VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
673 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
674
675 r[3] = t3;
676 VERIFY_BITS(r[3], 26);
677 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
678 r[4] = t4;
679 VERIFY_BITS(r[4], 26);
680 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
681 r[5] = t5;
682 VERIFY_BITS(r[5], 26);
683 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
684 r[6] = t6;
685 VERIFY_BITS(r[6], 26);
686 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
687 r[7] = t7;
688 VERIFY_BITS(r[7], 26);
689 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
690
691 r[8] = c & M; c >>= 26; c += u8 * R1;
692 VERIFY_BITS(r[8], 26);
693 VERIFY_BITS(c, 39);
694 /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
695 /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
696 c += d * R0 + t9;
697 VERIFY_BITS(c, 45);
698 /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
699 r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
700 VERIFY_BITS(r[9], 22);
701 VERIFY_BITS(c, 46);
702 /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
703 /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
704 /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
705
706 d = c * (R0 >> 4) + t0;
707 VERIFY_BITS(d, 56);
708 /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
709 r[0] = d & M; d >>= 26;
710 VERIFY_BITS(r[0], 26);
711 VERIFY_BITS(d, 30);
712 /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
713 d += c * (R1 >> 4) + t1;
714 VERIFY_BITS(d, 53);
715 VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
716 /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
717 /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
718 r[1] = d & M; d >>= 26;
719 VERIFY_BITS(r[1], 26);
720 VERIFY_BITS(d, 27);
721 VERIFY_CHECK(d <= 0x4000000ULL);
722 /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
723 d += t2;
724 VERIFY_BITS(d, 27);
725 /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
726 r[2] = d;
727 VERIFY_BITS(r[2], 27);
728 /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
729}
730
731SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a) {
732 uint64_t c, d;
733 uint64_t u0, u1, u2, u3, u4, u5, u6, u7, u8;
734 uint32_t t9, t0, t1, t2, t3, t4, t5, t6, t7;
735 const uint32_t M = 0x3FFFFFFUL, R0 = 0x3D10UL, R1 = 0x400UL;
736
737 VERIFY_BITS(a[0], 30);
738 VERIFY_BITS(a[1], 30);
739 VERIFY_BITS(a[2], 30);
740 VERIFY_BITS(a[3], 30);
741 VERIFY_BITS(a[4], 30);
742 VERIFY_BITS(a[5], 30);
743 VERIFY_BITS(a[6], 30);
744 VERIFY_BITS(a[7], 30);
745 VERIFY_BITS(a[8], 30);
746 VERIFY_BITS(a[9], 26);
747
753 d = (uint64_t)(a[0]*2) * a[9]
754 + (uint64_t)(a[1]*2) * a[8]
755 + (uint64_t)(a[2]*2) * a[7]
756 + (uint64_t)(a[3]*2) * a[6]
757 + (uint64_t)(a[4]*2) * a[5];
758 /* VERIFY_BITS(d, 64); */
759 /* [d 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
760 t9 = d & M; d >>= 26;
761 VERIFY_BITS(t9, 26);
762 VERIFY_BITS(d, 38);
763 /* [d t9 0 0 0 0 0 0 0 0 0] = [p9 0 0 0 0 0 0 0 0 0] */
764
765 c = (uint64_t)a[0] * a[0];
766 VERIFY_BITS(c, 60);
767 /* [d t9 0 0 0 0 0 0 0 0 c] = [p9 0 0 0 0 0 0 0 0 p0] */
768 d += (uint64_t)(a[1]*2) * a[9]
769 + (uint64_t)(a[2]*2) * a[8]
770 + (uint64_t)(a[3]*2) * a[7]
771 + (uint64_t)(a[4]*2) * a[6]
772 + (uint64_t)a[5] * a[5];
773 VERIFY_BITS(d, 63);
774 /* [d t9 0 0 0 0 0 0 0 0 c] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
775 u0 = d & M; d >>= 26; c += u0 * R0;
776 VERIFY_BITS(u0, 26);
777 VERIFY_BITS(d, 37);
778 VERIFY_BITS(c, 61);
779 /* [d u0 t9 0 0 0 0 0 0 0 0 c-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
780 t0 = c & M; c >>= 26; c += u0 * R1;
781 VERIFY_BITS(t0, 26);
782 VERIFY_BITS(c, 37);
783 /* [d u0 t9 0 0 0 0 0 0 0 c-u0*R1 t0-u0*R0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
784 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 0 p0] */
785
786 c += (uint64_t)(a[0]*2) * a[1];
787 VERIFY_BITS(c, 62);
788 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p10 p9 0 0 0 0 0 0 0 p1 p0] */
789 d += (uint64_t)(a[2]*2) * a[9]
790 + (uint64_t)(a[3]*2) * a[8]
791 + (uint64_t)(a[4]*2) * a[7]
792 + (uint64_t)(a[5]*2) * a[6];
793 VERIFY_BITS(d, 63);
794 /* [d 0 t9 0 0 0 0 0 0 0 c t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
795 u1 = d & M; d >>= 26; c += u1 * R0;
796 VERIFY_BITS(u1, 26);
797 VERIFY_BITS(d, 37);
798 VERIFY_BITS(c, 63);
799 /* [d u1 0 t9 0 0 0 0 0 0 0 c-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
800 t1 = c & M; c >>= 26; c += u1 * R1;
801 VERIFY_BITS(t1, 26);
802 VERIFY_BITS(c, 38);
803 /* [d u1 0 t9 0 0 0 0 0 0 c-u1*R1 t1-u1*R0 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
804 /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 0 p1 p0] */
805
806 c += (uint64_t)(a[0]*2) * a[2]
807 + (uint64_t)a[1] * a[1];
808 VERIFY_BITS(c, 62);
809 /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
810 d += (uint64_t)(a[3]*2) * a[9]
811 + (uint64_t)(a[4]*2) * a[8]
812 + (uint64_t)(a[5]*2) * a[7]
813 + (uint64_t)a[6] * a[6];
814 VERIFY_BITS(d, 63);
815 /* [d 0 0 t9 0 0 0 0 0 0 c t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
816 u2 = d & M; d >>= 26; c += u2 * R0;
817 VERIFY_BITS(u2, 26);
818 VERIFY_BITS(d, 37);
819 VERIFY_BITS(c, 63);
820 /* [d u2 0 0 t9 0 0 0 0 0 0 c-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
821 t2 = c & M; c >>= 26; c += u2 * R1;
822 VERIFY_BITS(t2, 26);
823 VERIFY_BITS(c, 38);
824 /* [d u2 0 0 t9 0 0 0 0 0 c-u2*R1 t2-u2*R0 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
825 /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 0 p2 p1 p0] */
826
827 c += (uint64_t)(a[0]*2) * a[3]
828 + (uint64_t)(a[1]*2) * a[2];
829 VERIFY_BITS(c, 63);
830 /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
831 d += (uint64_t)(a[4]*2) * a[9]
832 + (uint64_t)(a[5]*2) * a[8]
833 + (uint64_t)(a[6]*2) * a[7];
834 VERIFY_BITS(d, 63);
835 /* [d 0 0 0 t9 0 0 0 0 0 c t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
836 u3 = d & M; d >>= 26; c += u3 * R0;
837 VERIFY_BITS(u3, 26);
838 VERIFY_BITS(d, 37);
839 /* VERIFY_BITS(c, 64); */
840 /* [d u3 0 0 0 t9 0 0 0 0 0 c-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
841 t3 = c & M; c >>= 26; c += u3 * R1;
842 VERIFY_BITS(t3, 26);
843 VERIFY_BITS(c, 39);
844 /* [d u3 0 0 0 t9 0 0 0 0 c-u3*R1 t3-u3*R0 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
845 /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 0 p3 p2 p1 p0] */
846
847 c += (uint64_t)(a[0]*2) * a[4]
848 + (uint64_t)(a[1]*2) * a[3]
849 + (uint64_t)a[2] * a[2];
850 VERIFY_BITS(c, 63);
851 /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
852 d += (uint64_t)(a[5]*2) * a[9]
853 + (uint64_t)(a[6]*2) * a[8]
854 + (uint64_t)a[7] * a[7];
855 VERIFY_BITS(d, 62);
856 /* [d 0 0 0 0 t9 0 0 0 0 c t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
857 u4 = d & M; d >>= 26; c += u4 * R0;
858 VERIFY_BITS(u4, 26);
859 VERIFY_BITS(d, 36);
860 /* VERIFY_BITS(c, 64); */
861 /* [d u4 0 0 0 0 t9 0 0 0 0 c-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
862 t4 = c & M; c >>= 26; c += u4 * R1;
863 VERIFY_BITS(t4, 26);
864 VERIFY_BITS(c, 39);
865 /* [d u4 0 0 0 0 t9 0 0 0 c-u4*R1 t4-u4*R0 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
866 /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 0 p4 p3 p2 p1 p0] */
867
868 c += (uint64_t)(a[0]*2) * a[5]
869 + (uint64_t)(a[1]*2) * a[4]
870 + (uint64_t)(a[2]*2) * a[3];
871 VERIFY_BITS(c, 63);
872 /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
873 d += (uint64_t)(a[6]*2) * a[9]
874 + (uint64_t)(a[7]*2) * a[8];
875 VERIFY_BITS(d, 62);
876 /* [d 0 0 0 0 0 t9 0 0 0 c t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
877 u5 = d & M; d >>= 26; c += u5 * R0;
878 VERIFY_BITS(u5, 26);
879 VERIFY_BITS(d, 36);
880 /* VERIFY_BITS(c, 64); */
881 /* [d u5 0 0 0 0 0 t9 0 0 0 c-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
882 t5 = c & M; c >>= 26; c += u5 * R1;
883 VERIFY_BITS(t5, 26);
884 VERIFY_BITS(c, 39);
885 /* [d u5 0 0 0 0 0 t9 0 0 c-u5*R1 t5-u5*R0 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
886 /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 0 p5 p4 p3 p2 p1 p0] */
887
888 c += (uint64_t)(a[0]*2) * a[6]
889 + (uint64_t)(a[1]*2) * a[5]
890 + (uint64_t)(a[2]*2) * a[4]
891 + (uint64_t)a[3] * a[3];
892 VERIFY_BITS(c, 63);
893 /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
894 d += (uint64_t)(a[7]*2) * a[9]
895 + (uint64_t)a[8] * a[8];
896 VERIFY_BITS(d, 61);
897 /* [d 0 0 0 0 0 0 t9 0 0 c t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
898 u6 = d & M; d >>= 26; c += u6 * R0;
899 VERIFY_BITS(u6, 26);
900 VERIFY_BITS(d, 35);
901 /* VERIFY_BITS(c, 64); */
902 /* [d u6 0 0 0 0 0 0 t9 0 0 c-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
903 t6 = c & M; c >>= 26; c += u6 * R1;
904 VERIFY_BITS(t6, 26);
905 VERIFY_BITS(c, 39);
906 /* [d u6 0 0 0 0 0 0 t9 0 c-u6*R1 t6-u6*R0 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
907 /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 0 p6 p5 p4 p3 p2 p1 p0] */
908
909 c += (uint64_t)(a[0]*2) * a[7]
910 + (uint64_t)(a[1]*2) * a[6]
911 + (uint64_t)(a[2]*2) * a[5]
912 + (uint64_t)(a[3]*2) * a[4];
913 /* VERIFY_BITS(c, 64); */
914 VERIFY_CHECK(c <= 0x8000007C00000007ULL);
915 /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
916 d += (uint64_t)(a[8]*2) * a[9];
917 VERIFY_BITS(d, 58);
918 /* [d 0 0 0 0 0 0 0 t9 0 c t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
919 u7 = d & M; d >>= 26; c += u7 * R0;
920 VERIFY_BITS(u7, 26);
921 VERIFY_BITS(d, 32);
922 /* VERIFY_BITS(c, 64); */
923 VERIFY_CHECK(c <= 0x800001703FFFC2F7ULL);
924 /* [d u7 0 0 0 0 0 0 0 t9 0 c-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
925 t7 = c & M; c >>= 26; c += u7 * R1;
926 VERIFY_BITS(t7, 26);
927 VERIFY_BITS(c, 38);
928 /* [d u7 0 0 0 0 0 0 0 t9 c-u7*R1 t7-u7*R0 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
929 /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 0 p7 p6 p5 p4 p3 p2 p1 p0] */
930
931 c += (uint64_t)(a[0]*2) * a[8]
932 + (uint64_t)(a[1]*2) * a[7]
933 + (uint64_t)(a[2]*2) * a[6]
934 + (uint64_t)(a[3]*2) * a[5]
935 + (uint64_t)a[4] * a[4];
936 /* VERIFY_BITS(c, 64); */
937 VERIFY_CHECK(c <= 0x9000007B80000008ULL);
938 /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
939 d += (uint64_t)a[9] * a[9];
940 VERIFY_BITS(d, 57);
941 /* [d 0 0 0 0 0 0 0 0 t9 c t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
942 u8 = d & M; d >>= 26; c += u8 * R0;
943 VERIFY_BITS(u8, 26);
944 VERIFY_BITS(d, 31);
945 /* VERIFY_BITS(c, 64); */
946 VERIFY_CHECK(c <= 0x9000016FBFFFC2F8ULL);
947 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 t3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
948
949 r[3] = t3;
950 VERIFY_BITS(r[3], 26);
951 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 t4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
952 r[4] = t4;
953 VERIFY_BITS(r[4], 26);
954 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 t5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
955 r[5] = t5;
956 VERIFY_BITS(r[5], 26);
957 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 t6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
958 r[6] = t6;
959 VERIFY_BITS(r[6], 26);
960 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 t7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
961 r[7] = t7;
962 VERIFY_BITS(r[7], 26);
963 /* [d u8 0 0 0 0 0 0 0 0 t9 c-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
964
965 r[8] = c & M; c >>= 26; c += u8 * R1;
966 VERIFY_BITS(r[8], 26);
967 VERIFY_BITS(c, 39);
968 /* [d u8 0 0 0 0 0 0 0 0 t9+c-u8*R1 r8-u8*R0 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
969 /* [d 0 0 0 0 0 0 0 0 0 t9+c r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
970 c += d * R0 + t9;
971 VERIFY_BITS(c, 45);
972 /* [d 0 0 0 0 0 0 0 0 0 c-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
973 r[9] = c & (M >> 4); c >>= 22; c += d * (R1 << 4);
974 VERIFY_BITS(r[9], 22);
975 VERIFY_BITS(c, 46);
976 /* [d 0 0 0 0 0 0 0 0 r9+((c-d*R1<<4)<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
977 /* [d 0 0 0 0 0 0 0 -d*R1 r9+(c<<22)-d*R0 r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
978 /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 t0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
979
980 d = c * (R0 >> 4) + t0;
981 VERIFY_BITS(d, 56);
982 /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1 d-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
983 r[0] = d & M; d >>= 26;
984 VERIFY_BITS(r[0], 26);
985 VERIFY_BITS(d, 30);
986 /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 t1+d r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
987 d += c * (R1 >> 4) + t1;
988 VERIFY_BITS(d, 53);
989 VERIFY_CHECK(d <= 0x10000003FFFFBFULL);
990 /* [r9+(c<<22) r8 r7 r6 r5 r4 r3 t2 d-c*R1>>4 r0-c*R0>>4] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
991 /* [r9 r8 r7 r6 r5 r4 r3 t2 d r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
992 r[1] = d & M; d >>= 26;
993 VERIFY_BITS(r[1], 26);
994 VERIFY_BITS(d, 27);
995 VERIFY_CHECK(d <= 0x4000000ULL);
996 /* [r9 r8 r7 r6 r5 r4 r3 t2+d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
997 d += t2;
998 VERIFY_BITS(d, 27);
999 /* [r9 r8 r7 r6 r5 r4 r3 d r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
1000 r[2] = d;
1001 VERIFY_BITS(r[2], 27);
1002 /* [r9 r8 r7 r6 r5 r4 r3 r2 r1 r0] = [p18 p17 p16 p15 p14 p13 p12 p11 p10 p9 p8 p7 p6 p5 p4 p3 p2 p1 p0] */
1003}
1004#endif
1005
1009
1013
1014SECP256K1_INLINE static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
1015 uint32_t mask0, mask1;
1016 volatile int vflag = flag;
1017 VERIFY_CHECK(flag == 0 || flag == 1);
1018 SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
1019 mask0 = vflag + ~((uint32_t)0);
1020 mask1 = ~mask0;
1021 r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1022 r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1023 r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1024 r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1025 r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1026 r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1027 r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1028 r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1029 r->n[8] = (r->n[8] & mask0) | (a->n[8] & mask1);
1030 r->n[9] = (r->n[9] & mask0) | (a->n[9] & mask1);
1031}
1032
1033static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r) {
1034 uint32_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4],
1035 t5 = r->n[5], t6 = r->n[6], t7 = r->n[7], t8 = r->n[8], t9 = r->n[9];
1036 uint32_t one = (uint32_t)1;
1037 uint32_t mask = -(t0 & one) >> 6;
1038
1039 /* Bounds analysis (over the rationals).
1040 *
1041 * Let m = r->magnitude
1042 * C = 0x3FFFFFFUL * 2
1043 * D = 0x03FFFFFUL * 2
1044 *
1045 * Initial bounds: t0..t8 <= C * m
1046 * t9 <= D * m
1047 */
1048
1049 t0 += 0x3FFFC2FUL & mask;
1050 t1 += 0x3FFFFBFUL & mask;
1051 t2 += mask;
1052 t3 += mask;
1053 t4 += mask;
1054 t5 += mask;
1055 t6 += mask;
1056 t7 += mask;
1057 t8 += mask;
1058 t9 += mask >> 4;
1059
1060 VERIFY_CHECK((t0 & one) == 0);
1061
1062 /* t0..t8: added <= C/2
1063 * t9: added <= D/2
1064 *
1065 * Current bounds: t0..t8 <= C * (m + 1/2)
1066 * t9 <= D * (m + 1/2)
1067 */
1068
1069 r->n[0] = (t0 >> 1) + ((t1 & one) << 25);
1070 r->n[1] = (t1 >> 1) + ((t2 & one) << 25);
1071 r->n[2] = (t2 >> 1) + ((t3 & one) << 25);
1072 r->n[3] = (t3 >> 1) + ((t4 & one) << 25);
1073 r->n[4] = (t4 >> 1) + ((t5 & one) << 25);
1074 r->n[5] = (t5 >> 1) + ((t6 & one) << 25);
1075 r->n[6] = (t6 >> 1) + ((t7 & one) << 25);
1076 r->n[7] = (t7 >> 1) + ((t8 & one) << 25);
1077 r->n[8] = (t8 >> 1) + ((t9 & one) << 25);
1078 r->n[9] = (t9 >> 1);
1079
1080 /* t0..t8: shifted right and added <= C/4 + 1/2
1081 * t9: shifted right
1082 *
1083 * Current bounds: t0..t8 <= C * (m/2 + 1/2)
1084 * t9 <= D * (m/2 + 1/4)
1085 *
1086 * Therefore the output magnitude (M) has to be set such that:
1087 * t0..t8: C * M >= C * (m/2 + 1/2)
1088 * t9: D * M >= D * (m/2 + 1/4)
1089 *
1090 * It suffices for all limbs that, for any input magnitude m:
1091 * M >= m/2 + 1/2
1092 *
1093 * and since we want the smallest such integer value for M:
1094 * M == floor(m/2) + 1
1095 */
1096}
1097
1098static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
1099 uint32_t mask0, mask1;
1100 volatile int vflag = flag;
1101 VERIFY_CHECK(flag == 0 || flag == 1);
1102 SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
1103 mask0 = vflag + ~((uint32_t)0);
1104 mask1 = ~mask0;
1105 r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
1106 r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
1107 r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
1108 r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
1109 r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
1110 r->n[5] = (r->n[5] & mask0) | (a->n[5] & mask1);
1111 r->n[6] = (r->n[6] & mask0) | (a->n[6] & mask1);
1112 r->n[7] = (r->n[7] & mask0) | (a->n[7] & mask1);
1113}
1114
1115static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
1116 r->n[0] = a->n[0] | a->n[1] << 26;
1117 r->n[1] = a->n[1] >> 6 | a->n[2] << 20;
1118 r->n[2] = a->n[2] >> 12 | a->n[3] << 14;
1119 r->n[3] = a->n[3] >> 18 | a->n[4] << 8;
1120 r->n[4] = a->n[4] >> 24 | a->n[5] << 2 | a->n[6] << 28;
1121 r->n[5] = a->n[6] >> 4 | a->n[7] << 22;
1122 r->n[6] = a->n[7] >> 10 | a->n[8] << 16;
1123 r->n[7] = a->n[8] >> 16 | a->n[9] << 10;
1124}
1125
1126static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
1127 r->n[0] = a->n[0] & 0x3FFFFFFUL;
1128 r->n[1] = a->n[0] >> 26 | ((a->n[1] << 6) & 0x3FFFFFFUL);
1129 r->n[2] = a->n[1] >> 20 | ((a->n[2] << 12) & 0x3FFFFFFUL);
1130 r->n[3] = a->n[2] >> 14 | ((a->n[3] << 18) & 0x3FFFFFFUL);
1131 r->n[4] = a->n[3] >> 8 | ((a->n[4] << 24) & 0x3FFFFFFUL);
1132 r->n[5] = (a->n[4] >> 2) & 0x3FFFFFFUL;
1133 r->n[6] = a->n[4] >> 28 | ((a->n[5] << 4) & 0x3FFFFFFUL);
1134 r->n[7] = a->n[5] >> 22 | ((a->n[6] << 10) & 0x3FFFFFFUL);
1135 r->n[8] = a->n[6] >> 16 | ((a->n[7] << 16) & 0x3FFFFFFUL);
1136 r->n[9] = a->n[7] >> 10;
1137}
1138
1139static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a) {
1140 const uint32_t M26 = UINT32_MAX >> 6;
1141 const uint32_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4],
1142 a5 = a->v[5], a6 = a->v[6], a7 = a->v[7], a8 = a->v[8];
1143
1144 /* The output from secp256k1_modinv32{_var} should be normalized to range [0,modulus), and
1145 * have limbs in [0,2^30). The modulus is < 2^256, so the top limb must be below 2^(256-30*8).
1146 */
1147 VERIFY_CHECK(a0 >> 30 == 0);
1148 VERIFY_CHECK(a1 >> 30 == 0);
1149 VERIFY_CHECK(a2 >> 30 == 0);
1150 VERIFY_CHECK(a3 >> 30 == 0);
1151 VERIFY_CHECK(a4 >> 30 == 0);
1152 VERIFY_CHECK(a5 >> 30 == 0);
1153 VERIFY_CHECK(a6 >> 30 == 0);
1154 VERIFY_CHECK(a7 >> 30 == 0);
1155 VERIFY_CHECK(a8 >> 16 == 0);
1156
1157 r->n[0] = a0 & M26;
1158 r->n[1] = (a0 >> 26 | a1 << 4) & M26;
1159 r->n[2] = (a1 >> 22 | a2 << 8) & M26;
1160 r->n[3] = (a2 >> 18 | a3 << 12) & M26;
1161 r->n[4] = (a3 >> 14 | a4 << 16) & M26;
1162 r->n[5] = (a4 >> 10 | a5 << 20) & M26;
1163 r->n[6] = (a5 >> 6 | a6 << 24) & M26;
1164 r->n[7] = (a6 >> 2 ) & M26;
1165 r->n[8] = (a6 >> 28 | a7 << 2) & M26;
1166 r->n[9] = (a7 >> 24 | a8 << 6);
1167}
1168
1169static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a) {
1170 const uint32_t M30 = UINT32_MAX >> 2;
1171 const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4],
1172 a5 = a->n[5], a6 = a->n[6], a7 = a->n[7], a8 = a->n[8], a9 = a->n[9];
1173
1174 r->v[0] = (a0 | a1 << 26) & M30;
1175 r->v[1] = (a1 >> 4 | a2 << 22) & M30;
1176 r->v[2] = (a2 >> 8 | a3 << 18) & M30;
1177 r->v[3] = (a3 >> 12 | a4 << 14) & M30;
1178 r->v[4] = (a4 >> 16 | a5 << 10) & M30;
1179 r->v[5] = (a5 >> 20 | a6 << 6) & M30;
1180 r->v[6] = (a6 >> 24 | a7 << 2
1181 | a8 << 28) & M30;
1182 r->v[7] = (a8 >> 2 | a9 << 24) & M30;
1183 r->v[8] = a9 >> 6;
1184}
1185
1186static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe = {
1187 {{-0x3D1, -4, 0, 0, 0, 0, 0, 0, 65536}},
1188 0x2DDACACFL
1189};
1190
1200
1210
1211static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x) {
1212 secp256k1_fe tmp;
1213 secp256k1_modinv32_signed30 s;
1214 int jac, ret;
1215
1216 tmp = *x;
1217 secp256k1_fe_normalize_var(&tmp);
1218 /* secp256k1_jacobi32_maybe_var cannot deal with input 0. */
1219 if (secp256k1_fe_is_zero(&tmp)) return 1;
1220 secp256k1_fe_to_signed30(&s, &tmp);
1221 jac = secp256k1_jacobi32_maybe_var(&s, &secp256k1_const_modinfo_fe);
1222 if (jac == 0) {
1223 /* secp256k1_jacobi32_maybe_var failed to compute the Jacobi symbol. Fall back
1224 * to computing a square root. This should be extremely rare with random
1225 * input (except in VERIFY mode, where a lower iteration count is used). */
1226 secp256k1_fe dummy;
1227 ret = secp256k1_fe_sqrt(&dummy, &tmp);
1228 } else {
1229 ret = jac >= 0;
1230 }
1231 return ret;
1232}
1233
1234#endif /* SECP256K1_FIELD_REPR_IMPL_H */
ret
int ret
Definition bitcoin-cli.cpp:1350
SECP256K1_CHECKMEM_CHECK_VERIFY
#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len)
Definition checkmem.h:114
u8
unsigned char u8
Definition crypto_diff_fuzz_chacha20.cpp:21
secp256k1_fe_sqrt
static int secp256k1_fe_sqrt(secp256k1_fe *SECP256K1_RESTRICT r, const secp256k1_fe *SECP256K1_RESTRICT a)
Compute a square root of a field element.
secp256k1_fe_normalize_var
#define secp256k1_fe_normalize_var
Definition field.h:80
secp256k1_fe_is_zero
#define secp256k1_fe_is_zero
Definition field.h:84
secp256k1_fe_normalize
#define secp256k1_fe_normalize
Definition field.h:78
secp256k1_fe_impl_half
static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r)
Definition field_10x26_impl.h:1033
secp256k1_fe_impl_set_b32_mod
static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a)
Definition field_10x26_impl.h:286
secp256k1_fe_impl_normalize_weak
static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r)
Definition field_10x26_impl.h:102
secp256k1_fe_impl_is_square_var
static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x)
Definition field_10x26_impl.h:1211
secp256k1_fe_impl_get_b32
static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a)
Convert a field element to a 32-byte big endian value.
Definition field_10x26_impl.h:305
secp256k1_fe_impl_add
static SECP256K1_INLINE void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a)
Definition field_10x26_impl.h:374
secp256k1_fe_sqr_inner
static SECP256K1_INLINE void secp256k1_fe_sqr_inner(uint32_t *r, const uint32_t *a)
Definition field_10x26_impl.h:731
secp256k1_fe_impl_set_int
static SECP256K1_INLINE void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a)
Definition field_10x26_impl.h:259
secp256k1_const_modinfo_fe
static const secp256k1_modinv32_modinfo secp256k1_const_modinfo_fe
Definition field_10x26_impl.h:1186
secp256k1_fe_impl_is_zero
static SECP256K1_INLINE int secp256k1_fe_impl_is_zero(const secp256k1_fe *a)
Definition field_10x26_impl.h:264
secp256k1_fe_impl_get_bounds
static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m)
Definition field_10x26_impl.h:40
secp256k1_fe_impl_set_b32_limit
static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a)
Definition field_10x26_impl.h:299
secp256k1_fe_mul_inner
static SECP256K1_INLINE void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t *a, const uint32_t *SECP256K1_RESTRICT b)
Definition field_10x26_impl.h:401
secp256k1_fe_from_signed30
static void secp256k1_fe_from_signed30(secp256k1_fe *r, const secp256k1_modinv32_signed30 *a)
Definition field_10x26_impl.h:1139
secp256k1_fe_storage_cmov
static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag)
Definition field_10x26_impl.h:1098
secp256k1_fe_impl_negate_unchecked
static SECP256K1_INLINE void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m)
Definition field_10x26_impl.h:340
secp256k1_fe_impl_mul_int_unchecked
static SECP256K1_INLINE void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a)
Definition field_10x26_impl.h:361
secp256k1_fe_impl_cmp_var
static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b)
Definition field_10x26_impl.h:273
VERIFY_BITS
#define VERIFY_BITS(x, n)
Definition field_10x26_impl.h:399
secp256k1_fe_impl_normalizes_to_zero
static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r)
Definition field_10x26_impl.h:178
secp256k1_fe_impl_inv_var
static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x)
Definition field_10x26_impl.h:1201
secp256k1_fe_impl_sqr
static SECP256K1_INLINE void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a)
Definition field_10x26_impl.h:1010
secp256k1_fe_impl_from_storage
static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a)
Definition field_10x26_impl.h:1126
secp256k1_fe_to_signed30
static void secp256k1_fe_to_signed30(secp256k1_modinv32_signed30 *r, const secp256k1_fe *a)
Definition field_10x26_impl.h:1169
secp256k1_fe_impl_to_storage
static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a)
Definition field_10x26_impl.h:1115
secp256k1_fe_impl_add_int
static SECP256K1_INLINE void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a)
Definition field_10x26_impl.h:387
secp256k1_fe_impl_normalizes_to_zero_var
static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r)
Definition field_10x26_impl.h:207
secp256k1_fe_impl_normalize
static void secp256k1_fe_impl_normalize(secp256k1_fe *r)
Definition field_10x26_impl.h:53
secp256k1_fe_impl_cmov
static SECP256K1_INLINE void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag)
Definition field_10x26_impl.h:1014
secp256k1_fe_impl_inv
static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x)
Definition field_10x26_impl.h:1191
secp256k1_fe_impl_normalize_var
static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r)
Definition field_10x26_impl.h:128
secp256k1_fe_impl_is_odd
static SECP256K1_INLINE int secp256k1_fe_impl_is_odd(const secp256k1_fe *a)
Definition field_10x26_impl.h:269
secp256k1_fe_impl_mul
static SECP256K1_INLINE void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe *SECP256K1_RESTRICT b)
Definition field_10x26_impl.h:1006
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)
secp256k1_jacobi32_maybe_var
static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo)
modinv32_impl.h
SECP256K1_INLINE
#define SECP256K1_INLINE
Definition util.h:54
VERIFY_CHECK
#define VERIFY_CHECK(cond)
Definition util.h:159
SECP256K1_RESTRICT
#define SECP256K1_RESTRICT
Definition util.h:194
secp256k1_fe_storage
Definition field_10x26.h:50
secp256k1_fe_storage::n
uint32_t n[8]
Definition field_10x26.h:51
secp256k1_fe
This field implementation represents the value as 10 uint32_t limbs in base 2^26.
Definition field_10x26.h:14
secp256k1_fe::n
uint32_t n[10]
Definition field_10x26.h:22
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
Ticks
constexpr auto Ticks(Dur2 d)
Helper to count the seconds of a duration/time_point.
Definition time.h:73
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