Botan 3.6.1
Crypto and TLS for C&
ge.cpp
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1/*
2* Ed25519 group operations
3* (C) 2017 Ribose Inc
4*
5* Based on the public domain code from SUPERCOP ref10 by
6* Peter Schwabe, Daniel J. Bernstein, Niels Duif, Tanja Lange, Bo-Yin Yang
7*
8* Botan is released under the Simplified BSD License (see license.txt)
9*/
10
11#include <botan/internal/ed25519_internal.h>
12
13namespace Botan {
14
15namespace {
16
17/*
18Representations:
19 ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
20 ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
21 ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
22 ge_precomp (Duif): (y+x,y-x,2dxy)
23*/
24struct ge_p2 {
25 FE_25519 X;
26 FE_25519 Y;
27 FE_25519 Z;
28};
29
30struct ge_p1p1 {
31 FE_25519 X;
32 FE_25519 Y;
33 FE_25519 Z;
34 FE_25519 T;
35};
36
37struct ge_precomp {
38 FE_25519 yplusx;
39 FE_25519 yminusx;
40 FE_25519 xy2d;
41};
42
43struct ge_cached {
44 FE_25519 YplusX;
45 FE_25519 YminusX;
46 FE_25519 Z;
47 FE_25519 T2d;
48};
49
50/*
51r = p + q
52*/
53
54void ge_add(ge_p1p1* r, const ge_p3* p, const ge_cached* q) {
55 FE_25519 t0;
56 /* qhasm: YpX1 = Y1+X1 */
57 /* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
58 /* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
59 fe_add(r->X, p->Y, p->X);
60
61 /* qhasm: YmX1 = Y1-X1 */
62 /* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
63 /* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
64 fe_sub(r->Y, p->Y, p->X);
65
66 /* qhasm: A = YpX1*YpX2 */
67 /* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YpX2=fe#15); */
68 /* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YpX2=q->YplusX); */
69 fe_mul(r->Z, r->X, q->YplusX);
70
71 /* qhasm: B = YmX1*YmX2 */
72 /* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YmX2=fe#16); */
73 /* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YmX2=q->YminusX); */
74 fe_mul(r->Y, r->Y, q->YminusX);
75
76 /* qhasm: C = T2d2*T1 */
77 /* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
78 /* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
79 fe_mul(r->T, q->T2d, p->T);
80
81 /* qhasm: ZZ = Z1*Z2 */
82 /* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
83 /* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
84 fe_mul(r->X, p->Z, q->Z);
85
86 /* qhasm: D = 2*ZZ */
87 /* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
88 /* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
89 fe_add(t0, r->X, r->X);
90
91 /* qhasm: X3 = A-B */
92 /* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
93 /* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
94 fe_sub(r->X, r->Z, r->Y);
95
96 /* qhasm: Y3 = A+B */
97 /* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
98 /* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
99 fe_add(r->Y, r->Z, r->Y);
100
101 /* qhasm: Z3 = D+C */
102 /* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
103 /* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
104 fe_add(r->Z, t0, r->T);
105
106 /* qhasm: T3 = D-C */
107 /* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
108 /* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
109 fe_sub(r->T, t0, r->T);
110}
111
112/*
113r = p + q
114*/
115
116void ge_madd(ge_p1p1* r, const ge_p3* p, const ge_precomp* q) {
117 FE_25519 t0;
118 /* qhasm: YpX1 = Y1+X1 */
119 fe_add(r->X, p->Y, p->X);
120
121 /* qhasm: YmX1 = Y1-X1 */
122 fe_sub(r->Y, p->Y, p->X);
123
124 /* qhasm: A = YpX1*ypx2 */
125 fe_mul(r->Z, r->X, q->yplusx);
126
127 /* qhasm: B = YmX1*ymx2 */
128 fe_mul(r->Y, r->Y, q->yminusx);
129
130 /* qhasm: C = xy2d2*T1 */
131 fe_mul(r->T, q->xy2d, p->T);
132
133 /* qhasm: D = 2*Z1 */
134 fe_add(t0, p->Z, p->Z);
135
136 /* qhasm: X3 = A-B */
137 fe_sub(r->X, r->Z, r->Y);
138
139 /* qhasm: Y3 = A+B */
140 fe_add(r->Y, r->Z, r->Y);
141
142 /* qhasm: Z3 = D+C */
143 fe_add(r->Z, t0, r->T);
144
145 /* qhasm: T3 = D-C */
146 fe_sub(r->T, t0, r->T);
147}
148
149/*
150r = p - q
151*/
152
153void ge_msub(ge_p1p1* r, const ge_p3* p, const ge_precomp* q) {
154 FE_25519 t0;
155
156 /* qhasm: YpX1 = Y1+X1 */
157 /* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
158 /* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
159 fe_add(r->X, p->Y, p->X);
160
161 /* qhasm: YmX1 = Y1-X1 */
162 /* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
163 /* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
164 fe_sub(r->Y, p->Y, p->X);
165
166 /* qhasm: A = YpX1*ymx2 */
167 /* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ymx2=fe#16); */
168 /* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ymx2=q->yminusx); */
169 fe_mul(r->Z, r->X, q->yminusx);
170
171 /* qhasm: B = YmX1*ypx2 */
172 /* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ypx2=fe#15); */
173 /* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ypx2=q->yplusx); */
174 fe_mul(r->Y, r->Y, q->yplusx);
175
176 /* qhasm: C = xy2d2*T1 */
177 /* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
178 /* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
179 fe_mul(r->T, q->xy2d, p->T);
180
181 /* qhasm: D = 2*Z1 */
182 /* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
183 /* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
184 fe_add(t0, p->Z, p->Z);
185
186 /* qhasm: X3 = A-B */
187 /* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
188 /* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
189 fe_sub(r->X, r->Z, r->Y);
190
191 /* qhasm: Y3 = A+B */
192 /* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
193 /* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
194 fe_add(r->Y, r->Z, r->Y);
195
196 /* qhasm: Z3 = D-C */
197 /* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
198 /* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
199 fe_sub(r->Z, t0, r->T);
200
201 /* qhasm: T3 = D+C */
202 /* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
203 /* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
204 fe_add(r->T, t0, r->T);
205}
206
207/*
208r = p
209*/
210
211void ge_p1p1_to_p2(ge_p2* r, const ge_p1p1* p) {
212 fe_mul(r->X, p->X, p->T);
213 fe_mul(r->Y, p->Y, p->Z);
214 fe_mul(r->Z, p->Z, p->T);
215}
216
217/*
218r = p
219*/
220
221void ge_p1p1_to_p3(ge_p3* r, const ge_p1p1* p) {
222 fe_mul(r->X, p->X, p->T);
223 fe_mul(r->Y, p->Y, p->Z);
224 fe_mul(r->Z, p->Z, p->T);
225 fe_mul(r->T, p->X, p->Y);
226}
227
228/*
229r = 2 * p
230*/
231
232void ge_p2_dbl(ge_p1p1* r, const ge_p2* p) {
233 FE_25519 t0;
234 /* qhasm: XX=X1^2 */
235 /* asm 1: fe_sq(>XX=fe#1,<X1=fe#11); */
236 /* asm 2: fe_sq(>XX=r->X,<X1=p->X); */
237 fe_sq(r->X, p->X);
238
239 /* qhasm: YY=Y1^2 */
240 /* asm 1: fe_sq(>YY=fe#3,<Y1=fe#12); */
241 /* asm 2: fe_sq(>YY=r->Z,<Y1=p->Y); */
242 fe_sq(r->Z, p->Y);
243
244 /* qhasm: B=2*Z1^2 */
245 /* asm 1: fe_sq2(>B=fe#4,<Z1=fe#13); */
246 /* asm 2: fe_sq2(>B=r->T,<Z1=p->Z); */
247 fe_sq2(r->T, p->Z);
248
249 /* qhasm: A=X1+Y1 */
250 /* asm 1: fe_add(>A=fe#2,<X1=fe#11,<Y1=fe#12); */
251 /* asm 2: fe_add(>A=r->Y,<X1=p->X,<Y1=p->Y); */
252 fe_add(r->Y, p->X, p->Y);
253
254 /* qhasm: AA=A^2 */
255 /* asm 1: fe_sq(>AA=fe#5,<A=fe#2); */
256 /* asm 2: fe_sq(>AA=t0,<A=r->Y); */
257 fe_sq(t0, r->Y);
258
259 /* qhasm: Y3=YY+XX */
260 /* asm 1: fe_add(>Y3=fe#2,<YY=fe#3,<XX=fe#1); */
261 /* asm 2: fe_add(>Y3=r->Y,<YY=r->Z,<XX=r->X); */
262 fe_add(r->Y, r->Z, r->X);
263
264 /* qhasm: Z3=YY-XX */
265 /* asm 1: fe_sub(>Z3=fe#3,<YY=fe#3,<XX=fe#1); */
266 /* asm 2: fe_sub(>Z3=r->Z,<YY=r->Z,<XX=r->X); */
267 fe_sub(r->Z, r->Z, r->X);
268
269 /* qhasm: X3=AA-Y3 */
270 /* asm 1: fe_sub(>X3=fe#1,<AA=fe#5,<Y3=fe#2); */
271 /* asm 2: fe_sub(>X3=r->X,<AA=t0,<Y3=r->Y); */
272 fe_sub(r->X, t0, r->Y);
273
274 /* qhasm: T3=B-Z3 */
275 /* asm 1: fe_sub(>T3=fe#4,<B=fe#4,<Z3=fe#3); */
276 /* asm 2: fe_sub(>T3=r->T,<B=r->T,<Z3=r->Z); */
277 fe_sub(r->T, r->T, r->Z);
278}
279
280void ge_p3_0(ge_p3* h) {
281 fe_0(h->X);
282 fe_1(h->Y);
283 fe_1(h->Z);
284 fe_0(h->T);
285}
286
287/*
288r = 2 * p
289*/
290
291void ge_p3_dbl(ge_p1p1* r, const ge_p3* p) {
292 ge_p2 q;
293 // Convert to p2 rep
294 q.X = p->X;
295 q.Y = p->Y;
296 q.Z = p->Z;
297 ge_p2_dbl(r, &q);
298}
299
300/*
301r = p
302*/
303
304void ge_p3_to_cached(ge_cached* r, const ge_p3* p) {
305 static const FE_25519 d2 = {
306 -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199};
307 fe_add(r->YplusX, p->Y, p->X);
308 fe_sub(r->YminusX, p->Y, p->X);
309 fe_copy(r->Z, p->Z);
310 fe_mul(r->T2d, p->T, d2);
311}
312
313/*
314r = p - q
315*/
316
317void ge_sub(ge_p1p1* r, const ge_p3* p, const ge_cached* q) {
318 FE_25519 t0;
319 /* qhasm: YpX1 = Y1+X1 */
320 /* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
321 /* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
322 fe_add(r->X, p->Y, p->X);
323
324 /* qhasm: YmX1 = Y1-X1 */
325 /* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
326 /* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
327 fe_sub(r->Y, p->Y, p->X);
328
329 /* qhasm: A = YpX1*YmX2 */
330 /* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YmX2=fe#16); */
331 /* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YmX2=q->YminusX); */
332 fe_mul(r->Z, r->X, q->YminusX);
333
334 /* qhasm: B = YmX1*YpX2 */
335 /* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YpX2=fe#15); */
336 /* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YpX2=q->YplusX); */
337 fe_mul(r->Y, r->Y, q->YplusX);
338
339 /* qhasm: C = T2d2*T1 */
340 /* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
341 /* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
342 fe_mul(r->T, q->T2d, p->T);
343
344 /* qhasm: ZZ = Z1*Z2 */
345 /* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
346 /* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
347 fe_mul(r->X, p->Z, q->Z);
348
349 /* qhasm: D = 2*ZZ */
350 /* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
351 /* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
352 fe_add(t0, r->X, r->X);
353
354 /* qhasm: X3 = A-B */
355 /* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
356 /* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
357 fe_sub(r->X, r->Z, r->Y);
358
359 /* qhasm: Y3 = A+B */
360 /* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
361 /* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
362 fe_add(r->Y, r->Z, r->Y);
363
364 /* qhasm: Z3 = D-C */
365 /* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
366 /* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
367 fe_sub(r->Z, t0, r->T);
368
369 /* qhasm: T3 = D+C */
370 /* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
371 /* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
372 fe_add(r->T, t0, r->T);
373}
374
375void slide(int8_t* r, const uint8_t* a) {
376 for(size_t i = 0; i < 256; ++i) {
377 r[i] = 1 & (a[i >> 3] >> (i & 7));
378 }
379
380 for(size_t i = 0; i < 256; ++i) {
381 if(r[i]) {
382 for(size_t b = 1; b <= 6 && i + b < 256; ++b) {
383 if(r[i + b]) {
384 if(r[i] + (r[i + b] << b) <= 15) {
385 r[i] += r[i + b] << b;
386 r[i + b] = 0;
387 } else if(r[i] - (r[i + b] << b) >= -15) {
388 r[i] -= r[i + b] << b;
389 for(size_t k = i + b; k < 256; ++k) {
390 if(!r[k]) {
391 r[k] = 1;
392 break;
393 }
394 r[k] = 0;
395 }
396 } else {
397 break;
398 }
399 }
400 }
401 }
402 }
403}
404
405void ge_tobytes(uint8_t* s, const ge_p2* h) {
406 FE_25519 recip;
407 FE_25519 x;
408 FE_25519 y;
409
410 fe_invert(recip, h->Z);
411 fe_mul(x, h->X, recip);
412 fe_mul(y, h->Y, recip);
413 fe_tobytes(s, y);
414 s[31] ^= fe_isnegative(x) << 7;
415}
416
417void ge_p2_0(ge_p2* h) {
418 fe_0(h->X);
419 fe_1(h->Y);
420 fe_1(h->Z);
421}
422
423} // namespace
424
425int ge_frombytes_negate_vartime(ge_p3* h, const uint8_t* s) {
426 static const FE_25519 d = {
427 -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116};
428 static const FE_25519 sqrtm1 = {
429 -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482};
430
431 FE_25519 u;
432 FE_25519 v;
433 FE_25519 v3;
434 FE_25519 vxx;
435 FE_25519 check;
436
437 fe_frombytes(h->Y, s);
438 fe_1(h->Z);
439 fe_sq(u, h->Y);
440 fe_mul(v, u, d);
441 fe_sub(u, u, h->Z); /* u = y^2-1 */
442 fe_add(v, v, h->Z); /* v = dy^2+1 */
443
444 fe_sq(v3, v);
445 fe_mul(v3, v3, v); /* v3 = v^3 */
446 fe_sq(h->X, v3);
447 fe_mul(h->X, h->X, v);
448 fe_mul(h->X, h->X, u); /* x = uv^7 */
449
450 fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
451 fe_mul(h->X, h->X, v3);
452 fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
453
454 fe_sq(vxx, h->X);
455 fe_mul(vxx, vxx, v);
456 fe_sub(check, vxx, u); /* vx^2-u */
457 if(fe_isnonzero(check)) {
458 fe_add(check, vxx, u); /* vx^2+u */
459 if(fe_isnonzero(check)) {
460 return -1;
461 }
462 fe_mul(h->X, h->X, sqrtm1);
463 }
464
465 if(fe_isnegative(h->X) == (s[31] >> 7)) {
466 fe_neg(h->X, h->X);
467 }
468
469 fe_mul(h->T, h->X, h->Y);
470 return 0;
471}
472
473/*
474r = a * A + b * B
475where a = a[0]+256*a[1]+...+256^31 a[31].
476and b = b[0]+256*b[1]+...+256^31 b[31].
477B is the Ed25519 base point (x,4/5) with x positive.
478*/
479
480void ge_double_scalarmult_vartime(uint8_t out[32], const uint8_t* a, const ge_p3* A, const uint8_t* b) {
481 static const ge_precomp Bi[8] = {
482 {
483 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
484 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
485 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546},
486 },
487 {
488 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
489 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
490 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357},
491 },
492 {
493 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
494 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
495 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942},
496 },
497 {
498 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
499 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
500 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300},
501 },
502 {
503 {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877},
504 {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951},
505 {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784},
506 },
507 {
508 {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436},
509 {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918},
510 {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877},
511 },
512 {
513 {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800},
514 {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305},
515 {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300},
516 },
517 {
518 {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876},
519 {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619},
520 {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683},
521 },
522 };
523
524 int8_t aslide[256];
525 int8_t bslide[256];
526 ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
527 ge_p1p1 t;
528 ge_p3 u;
529 ge_p3 A2;
530 ge_p2 r;
531 int i;
532
533 slide(aslide, a);
534 slide(bslide, b);
535
536 ge_p3_to_cached(&Ai[0], A);
537 ge_p3_dbl(&t, A);
538 ge_p1p1_to_p3(&A2, &t);
539 ge_add(&t, &A2, &Ai[0]);
540 ge_p1p1_to_p3(&u, &t);
541 ge_p3_to_cached(&Ai[1], &u);
542 ge_add(&t, &A2, &Ai[1]);
543 ge_p1p1_to_p3(&u, &t);
544 ge_p3_to_cached(&Ai[2], &u);
545 ge_add(&t, &A2, &Ai[2]);
546 ge_p1p1_to_p3(&u, &t);
547 ge_p3_to_cached(&Ai[3], &u);
548 ge_add(&t, &A2, &Ai[3]);
549 ge_p1p1_to_p3(&u, &t);
550 ge_p3_to_cached(&Ai[4], &u);
551 ge_add(&t, &A2, &Ai[4]);
552 ge_p1p1_to_p3(&u, &t);
553 ge_p3_to_cached(&Ai[5], &u);
554 ge_add(&t, &A2, &Ai[5]);
555 ge_p1p1_to_p3(&u, &t);
556 ge_p3_to_cached(&Ai[6], &u);
557 ge_add(&t, &A2, &Ai[6]);
558 ge_p1p1_to_p3(&u, &t);
559 ge_p3_to_cached(&Ai[7], &u);
560
561 ge_p2_0(&r);
562
563 for(i = 255; i >= 0; --i) {
564 if(aslide[i] || bslide[i]) {
565 break;
566 }
567 }
568
569 for(; i >= 0; --i) {
570 ge_p2_dbl(&t, &r);
571
572 if(aslide[i] > 0) {
573 ge_p1p1_to_p3(&u, &t);
574 ge_add(&t, &u, &Ai[aslide[i] >> 1]);
575 } else if(aslide[i] < 0) {
576 ge_p1p1_to_p3(&u, &t);
577 ge_sub(&t, &u, &Ai[(-aslide[i]) >> 1]);
578 }
579
580 if(bslide[i] > 0) {
581 ge_p1p1_to_p3(&u, &t);
582 ge_madd(&t, &u, &Bi[bslide[i] >> 1]);
583 } else if(bslide[i] < 0) {
584 ge_p1p1_to_p3(&u, &t);
585 ge_msub(&t, &u, &Bi[(-bslide[i]) >> 1]);
586 }
587
588 ge_p1p1_to_p2(&r, &t);
589 }
590
591 ge_tobytes(out, &r);
592}
593
594/* base[i][j] = (j+1)*256^i*B */
595static const ge_precomp B_precomp[32][8] = {
596 {
597 {
598 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
599 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
600 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546},
601 },
602 {
603 {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303},
604 {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081},
605 {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697},
606 },
607 {
608 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
609 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
610 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357},
611 },
612 {
613 {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540},
614 {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397},
615 {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325},
616 },
617 {
618 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
619 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
620 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942},
621 },
622 {
623 {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777},
624 {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737},
625 {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652},
626 },
627 {
628 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
629 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
630 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300},
631 },
632 {
633 {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726},
634 {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955},
635 {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425},
636 },
637 },
638 {
639 {
640 {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171},
641 {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510},
642 {17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660},
643 },
644 {
645 {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639},
646 {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963},
647 {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950},
648 },
649 {
650 {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568},
651 {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335},
652 {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628},
653 },
654 {
655 {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007},
656 {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772},
657 {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653},
658 },
659 {
660 {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567},
661 {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686},
662 {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372},
663 },
664 {
665 {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887},
666 {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954},
667 {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953},
668 },
669 {
670 {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833},
671 {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532},
672 {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876},
673 },
674 {
675 {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268},
676 {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214},
677 {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038},
678 },
679 },
680 {
681 {
682 {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800},
683 {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645},
684 {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664},
685 },
686 {
687 {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933},
688 {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182},
689 {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222},
690 },
691 {
692 {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991},
693 {20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880},
694 {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092},
695 },
696 {
697 {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295},
698 {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788},
699 {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553},
700 },
701 {
702 {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026},
703 {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347},
704 {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033},
705 },
706 {
707 {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395},
708 {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278},
709 {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890},
710 },
711 {
712 {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995},
713 {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596},
714 {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891},
715 },
716 {
717 {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060},
718 {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608},
719 {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606},
720 },
721 },
722 {
723 {
724 {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389},
725 {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016},
726 {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341},
727 },
728 {
729 {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505},
730 {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553},
731 {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655},
732 },
733 {
734 {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220},
735 {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631},
736 {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099},
737 },
738 {
739 {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556},
740 {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749},
741 {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930},
742 },
743 {
744 {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391},
745 {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253},
746 {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066},
747 },
748 {
749 {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958},
750 {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082},
751 {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383},
752 },
753 {
754 {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521},
755 {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807},
756 {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948},
757 },
758 {
759 {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134},
760 {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455},
761 {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629},
762 },
763 },
764 {
765 {
766 {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069},
767 {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746},
768 {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919},
769 },
770 {
771 {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837},
772 {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906},
773 {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771},
774 },
775 {
776 {-25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817},
777 {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098},
778 {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409},
779 },
780 {
781 {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504},
782 {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727},
783 {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420},
784 },
785 {
786 {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003},
787 {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605},
788 {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384},
789 },
790 {
791 {-26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701},
792 {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683},
793 {29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708},
794 },
795 {
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1829 },
1830 {
1831 {31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275},
1832 {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511},
1833 {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095},
1834 },
1835 {
1836 {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439},
1837 {23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939},
1838 {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424},
1839 },
1840 {
1841 {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310},
1842 {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608},
1843 {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079},
1844 },
1845 {
1846 {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101},
1847 {21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418},
1848 {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576},
1849 },
1850 {
1851 {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356},
1852 {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996},
1853 {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099},
1854 },
1855 },
1856 {
1857 {
1858 {-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728},
1859 {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658},
1860 {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242},
1861 },
1862 {
1863 {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001},
1864 {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766},
1865 {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373},
1866 },
1867 {
1868 {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458},
1869 {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628},
1870 {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657},
1871 },
1872 {
1873 {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062},
1874 {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616},
1875 {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014},
1876 },
1877 {
1878 {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383},
1879 {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814},
1880 {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718},
1881 },
1882 {
1883 {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417},
1884 {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222},
1885 {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444},
1886 },
1887 {
1888 {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597},
1889 {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970},
1890 {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799},
1891 },
1892 {
1893 {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647},
1894 {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511},
1895 {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032},
1896 },
1897 },
1898 {
1899 {
1900 {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834},
1901 {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461},
1902 {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062},
1903 },
1904 {
1905 {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516},
1906 {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547},
1907 {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240},
1908 },
1909 {
1910 {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038},
1911 {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741},
1912 {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103},
1913 },
1914 {
1915 {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747},
1916 {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323},
1917 {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016},
1918 },
1919 {
1920 {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373},
1921 {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228},
1922 {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141},
1923 },
1924 {
1925 {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399},
1926 {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831},
1927 {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376},
1928 },
1929 {
1930 {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313},
1931 {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958},
1932 {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577},
1933 },
1934 {
1935 {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743},
1936 {29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684},
1937 {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476},
1938 },
1939 },
1940};
1941
1942namespace {
1943
1944inline uint8_t equal(int8_t b, int8_t c) {
1945 uint8_t ub = b;
1946 uint8_t uc = c;
1947 uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
1948 uint32_t y = x; /* 0: yes; 1..255: no */
1949 y -= 1; /* 4294967295: yes; 0..254: no */
1950 y >>= 31; /* 1: yes; 0: no */
1951 return static_cast<uint8_t>(y);
1952}
1953
1954inline int32_t equal32(int8_t b, int8_t c) {
1955 return -static_cast<int32_t>(equal(b, c));
1956}
1957
1958inline uint8_t negative(int8_t b) {
1959 /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
1960 uint64_t x = b; // NOLINT(bugprone-signed-char-misuse,cert-str34-c)
1961 x >>= 63; /* 1: yes; 0: no */
1962 return static_cast<uint8_t>(x);
1963}
1964
1965inline void ge_precomp_0(ge_precomp* h) {
1966 fe_1(h->yplusx);
1967 fe_1(h->yminusx);
1968 fe_0(h->xy2d);
1969}
1970
1971inline void select(ge_precomp* t, const ge_precomp* base, int8_t b) {
1972 const uint8_t bnegative = negative(b);
1973 const uint8_t babs = b - ((-static_cast<int>(bnegative) & b) * 2);
1974 const int32_t neg_mask = equal32(bnegative, 1);
1975
1976 const int32_t mask1 = equal32(babs, 1);
1977 const int32_t mask2 = equal32(babs, 2);
1978 const int32_t mask3 = equal32(babs, 3);
1979 const int32_t mask4 = equal32(babs, 4);
1980 const int32_t mask5 = equal32(babs, 5);
1981 const int32_t mask6 = equal32(babs, 6);
1982 const int32_t mask7 = equal32(babs, 7);
1983 const int32_t mask8 = equal32(babs, 8);
1984
1985 ge_precomp_0(t);
1986
1987 for(size_t i = 0; i != 10; ++i) {
1988 t->yplusx[i] = t->yplusx[i] ^ ((t->yplusx[i] ^ base[0].yplusx[i]) & mask1) ^
1989 ((t->yplusx[i] ^ base[1].yplusx[i]) & mask2) ^ ((t->yplusx[i] ^ base[2].yplusx[i]) & mask3) ^
1990 ((t->yplusx[i] ^ base[3].yplusx[i]) & mask4) ^ ((t->yplusx[i] ^ base[4].yplusx[i]) & mask5) ^
1991 ((t->yplusx[i] ^ base[5].yplusx[i]) & mask6) ^ ((t->yplusx[i] ^ base[6].yplusx[i]) & mask7) ^
1992 ((t->yplusx[i] ^ base[7].yplusx[i]) & mask8);
1993
1994 t->yminusx[i] = t->yminusx[i] ^ ((t->yminusx[i] ^ base[0].yminusx[i]) & mask1) ^
1995 ((t->yminusx[i] ^ base[1].yminusx[i]) & mask2) ^ ((t->yminusx[i] ^ base[2].yminusx[i]) & mask3) ^
1996 ((t->yminusx[i] ^ base[3].yminusx[i]) & mask4) ^ ((t->yminusx[i] ^ base[4].yminusx[i]) & mask5) ^
1997 ((t->yminusx[i] ^ base[5].yminusx[i]) & mask6) ^ ((t->yminusx[i] ^ base[6].yminusx[i]) & mask7) ^
1998 ((t->yminusx[i] ^ base[7].yminusx[i]) & mask8);
1999
2000 t->xy2d[i] = t->xy2d[i] ^ ((t->xy2d[i] ^ base[0].xy2d[i]) & mask1) ^ ((t->xy2d[i] ^ base[1].xy2d[i]) & mask2) ^
2001 ((t->xy2d[i] ^ base[2].xy2d[i]) & mask3) ^ ((t->xy2d[i] ^ base[3].xy2d[i]) & mask4) ^
2002 ((t->xy2d[i] ^ base[4].xy2d[i]) & mask5) ^ ((t->xy2d[i] ^ base[5].xy2d[i]) & mask6) ^
2003 ((t->xy2d[i] ^ base[6].xy2d[i]) & mask7) ^ ((t->xy2d[i] ^ base[7].xy2d[i]) & mask8);
2004 }
2005
2006 FE_25519 minus_xy2d;
2007 fe_neg(minus_xy2d, t->xy2d);
2008
2009 // If negative have to swap yminusx and yplusx
2010 for(size_t i = 0; i != 10; ++i) {
2011 int32_t t_yplusx = t->yplusx[i] ^ ((t->yplusx[i] ^ t->yminusx[i]) & neg_mask);
2012 int32_t t_yminusx = t->yminusx[i] ^ ((t->yminusx[i] ^ t->yplusx[i]) & neg_mask);
2013
2014 t->yplusx[i] = t_yplusx;
2015 t->yminusx[i] = t_yminusx;
2016 t->xy2d[i] = t->xy2d[i] ^ ((t->xy2d[i] ^ minus_xy2d[i]) & neg_mask);
2017 }
2018}
2019
2020void ge_p3_tobytes(uint8_t* s, const ge_p3* h) {
2021 FE_25519 recip;
2022 FE_25519 x;
2023 FE_25519 y;
2024
2025 fe_invert(recip, h->Z);
2026 fe_mul(x, h->X, recip);
2027 fe_mul(y, h->Y, recip);
2028 fe_tobytes(s, y);
2029 s[31] ^= fe_isnegative(x) << 7;
2030}
2031
2032} // namespace
2033
2034/*
2035h = a * B
2036where a = a[0]+256*a[1]+...+256^31 a[31]
2037B is the Ed25519 base point (x,4/5) with x positive.
2038
2039Preconditions:
2040 a[31] <= 127
2041*/
2042
2043void ge_scalarmult_base(uint8_t out[32], const uint8_t a[32]) {
2044 int8_t e[64];
2045 int8_t carry;
2046 ge_p1p1 r;
2047 ge_p2 s;
2048 ge_p3 h;
2049 ge_precomp t;
2050 int i;
2051
2052 for(i = 0; i < 32; ++i) {
2053 e[2 * i + 0] = (a[i] >> 0) & 15;
2054 e[2 * i + 1] = (a[i] >> 4) & 15;
2055 }
2056 /* each e[i] is between 0 and 15 */
2057 /* e[63] is between 0 and 7 */
2058
2059 carry = 0;
2060 for(i = 0; i < 63; ++i) {
2061 e[i] += carry;
2062 carry = e[i] + 8;
2063 carry >>= 4;
2064 e[i] -= carry << 4;
2065 }
2066 e[63] += carry;
2067 /* each e[i] is between -8 and 8 */
2068
2069 ge_p3_0(&h);
2070 for(i = 1; i < 64; i += 2) {
2071 select(&t, B_precomp[i / 2], e[i]);
2072 ge_madd(&r, &h, &t);
2073 ge_p1p1_to_p3(&h, &r);
2074 }
2075
2076 ge_p3_dbl(&r, &h);
2077 ge_p1p1_to_p2(&s, &r);
2078 ge_p2_dbl(&r, &s);
2079 ge_p1p1_to_p2(&s, &r);
2080 ge_p2_dbl(&r, &s);
2081 ge_p1p1_to_p2(&s, &r);
2082 ge_p2_dbl(&r, &s);
2083 ge_p1p1_to_p3(&h, &r);
2084
2085 for(i = 0; i < 64; i += 2) {
2086 select(&t, B_precomp[i / 2], e[i]);
2087 ge_madd(&r, &h, &t);
2088 ge_p1p1_to_p3(&h, &r);
2089 }
2090
2091 ge_p3_tobytes(out, &h);
2092}
2093
2094} // namespace Botan
Botan::FE_25519
Definition ed25519_fe.h:22
yplusx
FE_25519 yplusx
Definition ge.cpp:38
Y
FE_25519 Y
Definition ge.cpp:26
Z
FE_25519 Z
Definition ge.cpp:27
YminusX
FE_25519 YminusX
Definition ge.cpp:45
X
FE_25519 X
Definition ge.cpp:25
YplusX
FE_25519 YplusX
Definition ge.cpp:44
T
FE_25519 T
Definition ge.cpp:34
yminusx
FE_25519 yminusx
Definition ge.cpp:39
T2d
FE_25519 T2d
Definition ge.cpp:47
xy2d
FE_25519 xy2d
Definition ge.cpp:40
Botan::fe_sq2
void fe_sq2(fe &x, const fe &z)
Definition ed25519_fe.h:202
Botan::fe_0
void fe_0(fe &x)
Definition ed25519_fe.h:170
Botan::fe_isnegative
int fe_isnegative(const fe &x)
Definition ed25519_fe.h:166
Botan::fe_isnonzero
int fe_isnonzero(const fe &x)
Definition ed25519_fe.h:162
Botan::fe_1
void fe_1(fe &x)
Definition ed25519_fe.h:174
Botan::fe_mul
void fe_mul(fe &x, const fe &a, const fe &b)
Definition ed25519_fe.h:190
Botan::fe_sq
void fe_sq(fe &x, const fe &z)
Definition ed25519_fe.h:194
Botan::ge_frombytes_negate_vartime
int ge_frombytes_negate_vartime(ge_p3 *v, const uint8_t *)
Definition ge.cpp:425
Botan::fe_neg
void fe_neg(fe &x, const fe &z)
Definition ed25519_fe.h:186
Botan::ge_scalarmult_base
void ge_scalarmult_base(uint8_t out[32], const uint8_t in[32])
Definition ge.cpp:2043
Botan::fe_copy
void fe_copy(fe &a, const fe &b)
Definition ed25519_fe.h:158
Botan::fe_add
void fe_add(fe &x, const fe &a, const fe &b)
Definition ed25519_fe.h:178
Botan::carry
void carry(int64_t &h0, int64_t &h1)
Definition ed25519_internal.h:28
Botan::fe_sub
void fe_sub(fe &x, const fe &a, const fe &b)
Definition ed25519_fe.h:182
Botan::fe_tobytes
void fe_tobytes(uint8_t *b, const fe &x)
Definition ed25519_fe.h:154
Botan::fe_pow22523
void fe_pow22523(fe &x, const fe &y)
Definition ed25519_fe.h:210
Botan::b
const SIMD_8x32 & b
Definition simd_avx2_gfni.h:63
Botan::fe_invert
void fe_invert(fe &x, const fe &z)
Definition ed25519_fe.h:206
Botan::fe_frombytes
void fe_frombytes(fe &x, const uint8_t *b)
Definition ed25519_fe.h:150
Botan::ge_double_scalarmult_vartime
void ge_double_scalarmult_vartime(uint8_t out[32], const uint8_t a[], const ge_p3 *A, const uint8_t b[])
Botan::ge_p3
Definition ed25519_internal.h:79
Botan::ge_p3::Z
FE_25519 Z
Definition ed25519_internal.h:82
Botan::ge_p3::T
FE_25519 T
Definition ed25519_internal.h:83
Botan::ge_p3::X
FE_25519 X
Definition ed25519_internal.h:80
Botan::ge_p3::Y
FE_25519 Y
Definition ed25519_internal.h:81
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