Botan 2.19.1
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#include <assert.h>
13
14namespace Botan {
15
16namespace {
17
18/*
19Representations:
20 ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
21 ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
22 ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
23 ge_precomp (Duif): (y+x,y-x,2dxy)
24*/
25typedef struct
26 {
30 } ge_p2;
31
32typedef struct
33 {
34 fe X;
35 fe Y;
36 fe Z;
38 } ge_p1p1;
39
40typedef struct
41 {
45 } ge_precomp;
46
47typedef struct
48 {
51 fe Z;
53 } ge_cached;
54
55/*
56r = p + q
57*/
58
59void ge_add(ge_p1p1* r, const ge_p3* p, const ge_cached* q)
60 {
61 fe t0;
62 /* qhasm: YpX1 = Y1+X1 */
63 /* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
64 /* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
65 fe_add(r->X, p->Y, p->X);
66
67 /* qhasm: YmX1 = Y1-X1 */
68 /* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
69 /* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
70 fe_sub(r->Y, p->Y, p->X);
71
72 /* qhasm: A = YpX1*YpX2 */
73 /* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YpX2=fe#15); */
74 /* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YpX2=q->YplusX); */
75 fe_mul(r->Z, r->X, q->YplusX);
76
77 /* qhasm: B = YmX1*YmX2 */
78 /* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YmX2=fe#16); */
79 /* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YmX2=q->YminusX); */
80 fe_mul(r->Y, r->Y, q->YminusX);
81
82 /* qhasm: C = T2d2*T1 */
83 /* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
84 /* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
85 fe_mul(r->T, q->T2d, p->T);
86
87 /* qhasm: ZZ = Z1*Z2 */
88 /* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
89 /* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
90 fe_mul(r->X, p->Z, q->Z);
91
92 /* qhasm: D = 2*ZZ */
93 /* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
94 /* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
95 fe_add(t0, r->X, r->X);
96
97 /* qhasm: X3 = A-B */
98 /* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
99 /* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
100 fe_sub(r->X, r->Z, r->Y);
101
102 /* qhasm: Y3 = A+B */
103 /* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
104 /* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
105 fe_add(r->Y, r->Z, r->Y);
106
107 /* qhasm: Z3 = D+C */
108 /* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
109 /* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
110 fe_add(r->Z, t0, r->T);
111
112 /* qhasm: T3 = D-C */
113 /* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
114 /* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
115 fe_sub(r->T, t0, r->T);
116 }
117
118/*
119r = p + q
120*/
121
122void ge_madd(ge_p1p1* r, const ge_p3* p, const ge_precomp* q)
123 {
124 fe t0;
125 /* qhasm: YpX1 = Y1+X1 */
126 fe_add(r->X, p->Y, p->X);
127
128 /* qhasm: YmX1 = Y1-X1 */
129 fe_sub(r->Y, p->Y, p->X);
130
131 /* qhasm: A = YpX1*ypx2 */
132 fe_mul(r->Z, r->X, q->yplusx);
133
134 /* qhasm: B = YmX1*ymx2 */
135 fe_mul(r->Y, r->Y, q->yminusx);
136
137 /* qhasm: C = xy2d2*T1 */
138 fe_mul(r->T, q->xy2d, p->T);
139
140 /* qhasm: D = 2*Z1 */
141 fe_add(t0, p->Z, p->Z);
142
143 /* qhasm: X3 = A-B */
144 fe_sub(r->X, r->Z, r->Y);
145
146 /* qhasm: Y3 = A+B */
147 fe_add(r->Y, r->Z, r->Y);
148
149 /* qhasm: Z3 = D+C */
150 fe_add(r->Z, t0, r->T);
151
152 /* qhasm: T3 = D-C */
153 fe_sub(r->T, t0, r->T);
154 }
155
156/*
157r = p - q
158*/
159
160void ge_msub(ge_p1p1* r, const ge_p3* p, const ge_precomp* q)
161 {
162 fe t0;
163
164 /* qhasm: YpX1 = Y1+X1 */
165 /* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
166 /* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
167 fe_add(r->X, p->Y, p->X);
168
169 /* qhasm: YmX1 = Y1-X1 */
170 /* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
171 /* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
172 fe_sub(r->Y, p->Y, p->X);
173
174 /* qhasm: A = YpX1*ymx2 */
175 /* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ymx2=fe#16); */
176 /* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ymx2=q->yminusx); */
177 fe_mul(r->Z, r->X, q->yminusx);
178
179 /* qhasm: B = YmX1*ypx2 */
180 /* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ypx2=fe#15); */
181 /* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ypx2=q->yplusx); */
182 fe_mul(r->Y, r->Y, q->yplusx);
183
184 /* qhasm: C = xy2d2*T1 */
185 /* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
186 /* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
187 fe_mul(r->T, q->xy2d, p->T);
188
189 /* qhasm: D = 2*Z1 */
190 /* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
191 /* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
192 fe_add(t0, p->Z, p->Z);
193
194 /* qhasm: X3 = A-B */
195 /* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
196 /* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
197 fe_sub(r->X, r->Z, r->Y);
198
199 /* qhasm: Y3 = A+B */
200 /* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
201 /* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
202 fe_add(r->Y, r->Z, r->Y);
203
204 /* qhasm: Z3 = D-C */
205 /* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
206 /* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
207 fe_sub(r->Z, t0, r->T);
208
209 /* qhasm: T3 = D+C */
210 /* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
211 /* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
212 fe_add(r->T, t0, r->T);
213
214 }
215
216/*
217r = p
218*/
219
220void ge_p1p1_to_p2(ge_p2* r, const ge_p1p1* p)
221 {
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 }
226
227/*
228r = p
229*/
230
231void ge_p1p1_to_p3(ge_p3* r, const ge_p1p1* p)
232 {
233 fe_mul(r->X, p->X, p->T);
234 fe_mul(r->Y, p->Y, p->Z);
235 fe_mul(r->Z, p->Z, p->T);
236 fe_mul(r->T, p->X, p->Y);
237 }
238
239/*
240r = 2 * p
241*/
242
243void ge_p2_dbl(ge_p1p1* r, const ge_p2* p)
244 {
245 fe t0;
246 /* qhasm: XX=X1^2 */
247 /* asm 1: fe_sq(>XX=fe#1,<X1=fe#11); */
248 /* asm 2: fe_sq(>XX=r->X,<X1=p->X); */
249 fe_sq(r->X, p->X);
250
251 /* qhasm: YY=Y1^2 */
252 /* asm 1: fe_sq(>YY=fe#3,<Y1=fe#12); */
253 /* asm 2: fe_sq(>YY=r->Z,<Y1=p->Y); */
254 fe_sq(r->Z, p->Y);
255
256 /* qhasm: B=2*Z1^2 */
257 /* asm 1: fe_sq2(>B=fe#4,<Z1=fe#13); */
258 /* asm 2: fe_sq2(>B=r->T,<Z1=p->Z); */
259 fe_sq2(r->T, p->Z);
260
261 /* qhasm: A=X1+Y1 */
262 /* asm 1: fe_add(>A=fe#2,<X1=fe#11,<Y1=fe#12); */
263 /* asm 2: fe_add(>A=r->Y,<X1=p->X,<Y1=p->Y); */
264 fe_add(r->Y, p->X, p->Y);
265
266 /* qhasm: AA=A^2 */
267 /* asm 1: fe_sq(>AA=fe#5,<A=fe#2); */
268 /* asm 2: fe_sq(>AA=t0,<A=r->Y); */
269 fe_sq(t0, r->Y);
270
271 /* qhasm: Y3=YY+XX */
272 /* asm 1: fe_add(>Y3=fe#2,<YY=fe#3,<XX=fe#1); */
273 /* asm 2: fe_add(>Y3=r->Y,<YY=r->Z,<XX=r->X); */
274 fe_add(r->Y, r->Z, r->X);
275
276 /* qhasm: Z3=YY-XX */
277 /* asm 1: fe_sub(>Z3=fe#3,<YY=fe#3,<XX=fe#1); */
278 /* asm 2: fe_sub(>Z3=r->Z,<YY=r->Z,<XX=r->X); */
279 fe_sub(r->Z, r->Z, r->X);
280
281 /* qhasm: X3=AA-Y3 */
282 /* asm 1: fe_sub(>X3=fe#1,<AA=fe#5,<Y3=fe#2); */
283 /* asm 2: fe_sub(>X3=r->X,<AA=t0,<Y3=r->Y); */
284 fe_sub(r->X, t0, r->Y);
285
286 /* qhasm: T3=B-Z3 */
287 /* asm 1: fe_sub(>T3=fe#4,<B=fe#4,<Z3=fe#3); */
288 /* asm 2: fe_sub(>T3=r->T,<B=r->T,<Z3=r->Z); */
289 fe_sub(r->T, r->T, r->Z);
290 }
291
292void ge_p3_0(ge_p3* h)
293 {
294 fe_0(h->X);
295 fe_1(h->Y);
296 fe_1(h->Z);
297 fe_0(h->T);
298 }
299
300/*
301r = 2 * p
302*/
303
304void ge_p3_dbl(ge_p1p1* r, const ge_p3* p)
305 {
306 ge_p2 q;
307 // Convert to p2 rep
308 q.X = p->X;
309 q.Y = p->Y;
310 q.Z = p->Z;
311 ge_p2_dbl(r, &q);
312 }
313
314/*
315r = p
316*/
317
318
319void ge_p3_to_cached(ge_cached* r, const ge_p3* p)
320 {
321 static const fe d2 =
322 {
323 -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199
324 } ;
325 fe_add(r->YplusX, p->Y, p->X);
326 fe_sub(r->YminusX, p->Y, p->X);
327 fe_copy(r->Z, p->Z);
328 fe_mul(r->T2d, p->T, d2);
329 }
330
331/*
332r = p - q
333*/
334
335void ge_sub(ge_p1p1* r, const ge_p3* p, const ge_cached* q)
336 {
337 fe t0;
338 /* qhasm: YpX1 = Y1+X1 */
339 /* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
340 /* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
341 fe_add(r->X, p->Y, p->X);
342
343 /* qhasm: YmX1 = Y1-X1 */
344 /* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
345 /* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
346 fe_sub(r->Y, p->Y, p->X);
347
348 /* qhasm: A = YpX1*YmX2 */
349 /* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YmX2=fe#16); */
350 /* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YmX2=q->YminusX); */
351 fe_mul(r->Z, r->X, q->YminusX);
352
353 /* qhasm: B = YmX1*YpX2 */
354 /* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YpX2=fe#15); */
355 /* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YpX2=q->YplusX); */
356 fe_mul(r->Y, r->Y, q->YplusX);
357
358 /* qhasm: C = T2d2*T1 */
359 /* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
360 /* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
361 fe_mul(r->T, q->T2d, p->T);
362
363 /* qhasm: ZZ = Z1*Z2 */
364 /* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
365 /* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
366 fe_mul(r->X, p->Z, q->Z);
367
368 /* qhasm: D = 2*ZZ */
369 /* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
370 /* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
371 fe_add(t0, r->X, r->X);
372
373 /* qhasm: X3 = A-B */
374 /* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
375 /* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
376 fe_sub(r->X, r->Z, r->Y);
377
378 /* qhasm: Y3 = A+B */
379 /* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
380 /* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
381 fe_add(r->Y, r->Z, r->Y);
382
383 /* qhasm: Z3 = D-C */
384 /* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
385 /* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
386 fe_sub(r->Z, t0, r->T);
387
388 /* qhasm: T3 = D+C */
389 /* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
390 /* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
391 fe_add(r->T, t0, r->T);
392
393 }
394
395void slide(int8_t* r, const uint8_t* a)
396 {
397 for(size_t i = 0; i < 256; ++i)
398 {
399 r[i] = 1 & (a[i >> 3] >> (i & 7));
400 }
401
402 for(size_t i = 0; i < 256; ++i)
403 {
404 if(r[i])
405 {
406 for(size_t b = 1; b <= 6 && i + b < 256; ++b)
407 {
408 if(r[i + b])
409 {
410 if(r[i] + (r[i + b] << b) <= 15)
411 {
412 r[i] += r[i + b] << b;
413 r[i + b] = 0;
414 }
415 else if(r[i] - (r[i + b] << b) >= -15)
416 {
417 r[i] -= r[i + b] << b;
418 for(size_t k = i + b; k < 256; ++k)
419 {
420 if(!r[k])
421 {
422 r[k] = 1;
423 break;
424 }
425 r[k] = 0;
426 }
427 }
428 else
429 { break; }
430 }
431 }
432 }
433 }
434 }
435
436void ge_tobytes(uint8_t* s, const ge_p2* h)
437 {
438 fe recip;
439 fe x;
440 fe y;
441
442 fe_invert(recip, h->Z);
443 fe_mul(x, h->X, recip);
444 fe_mul(y, h->Y, recip);
445 fe_tobytes(s, y);
446 s[31] ^= fe_isnegative(x) << 7;
447 }
448
449void ge_p2_0(ge_p2* h)
450 {
451 fe_0(h->X);
452 fe_1(h->Y);
453 fe_1(h->Z);
454 }
455
456}
457
458int ge_frombytes_negate_vartime(ge_p3* h, const uint8_t* s)
459 {
460 static const fe d =
461 {
462 -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116
463 } ;
464 static const fe sqrtm1 =
465 {
466 -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482
467 } ;
468
469 fe u;
470 fe v;
471 fe v3;
472 fe vxx;
473 fe check;
474
475 fe_frombytes(h->Y, s);
476 fe_1(h->Z);
477 fe_sq(u, h->Y);
478 fe_mul(v, u, d);
479 fe_sub(u, u, h->Z); /* u = y^2-1 */
480 fe_add(v, v, h->Z); /* v = dy^2+1 */
481
482 fe_sq(v3, v);
483 fe_mul(v3, v3, v); /* v3 = v^3 */
484 fe_sq(h->X, v3);
485 fe_mul(h->X, h->X, v);
486 fe_mul(h->X, h->X, u); /* x = uv^7 */
487
488 fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
489 fe_mul(h->X, h->X, v3);
490 fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
491
492 fe_sq(vxx, h->X);
493 fe_mul(vxx, vxx, v);
494 fe_sub(check, vxx, u); /* vx^2-u */
495 if(fe_isnonzero(check))
496 {
497 fe_add(check, vxx, u); /* vx^2+u */
498 if(fe_isnonzero(check))
499 {
500 return -1;
501 }
502 fe_mul(h->X, h->X, sqrtm1);
503 }
504
505 if(fe_isnegative(h->X) == (s[31] >> 7))
506 { fe_neg(h->X, h->X); }
507
508 fe_mul(h->T, h->X, h->Y);
509 return 0;
510 }
511
512/*
513r = a * A + b * B
514where a = a[0]+256*a[1]+...+256^31 a[31].
515and b = b[0]+256*b[1]+...+256^31 b[31].
516B is the Ed25519 base point (x,4/5) with x positive.
517*/
518
520 uint8_t out[32],
521 const uint8_t* a, const ge_p3* A, const uint8_t* b)
522 {
523 static const ge_precomp Bi[8] =
524 {
525 {
526 { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
527 { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
528 { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
529 },
530 {
531 { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
532 { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
533 { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
534 },
535 {
536 { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
537 { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
538 { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
539 },
540 {
541 { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
542 { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
543 { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
544 },
545 {
546 { -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877 },
547 { -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951 },
548 { 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784 },
549 },
550 {
551 { -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436 },
552 { 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918 },
553 { 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877 },
554 },
555 {
556 { -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800 },
557 { -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305 },
558 { -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300 },
559 },
560 {
561 { -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876 },
562 { -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619 },
563 { -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683 },
564 },
565 } ;
566
567 int8_t aslide[256];
568 int8_t bslide[256];
569 ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
570 ge_p1p1 t;
571 ge_p3 u;
572 ge_p3 A2;
573 ge_p2 r;
574 int i;
575
576 slide(aslide, a);
577 slide(bslide, b);
578
579 ge_p3_to_cached(&Ai[0], A);
580 ge_p3_dbl(&t, A);
581 ge_p1p1_to_p3(&A2, &t);
582 ge_add(&t, &A2, &Ai[0]);
583 ge_p1p1_to_p3(&u, &t);
584 ge_p3_to_cached(&Ai[1], &u);
585 ge_add(&t, &A2, &Ai[1]);
586 ge_p1p1_to_p3(&u, &t);
587 ge_p3_to_cached(&Ai[2], &u);
588 ge_add(&t, &A2, &Ai[2]);
589 ge_p1p1_to_p3(&u, &t);
590 ge_p3_to_cached(&Ai[3], &u);
591 ge_add(&t, &A2, &Ai[3]);
592 ge_p1p1_to_p3(&u, &t);
593 ge_p3_to_cached(&Ai[4], &u);
594 ge_add(&t, &A2, &Ai[4]);
595 ge_p1p1_to_p3(&u, &t);
596 ge_p3_to_cached(&Ai[5], &u);
597 ge_add(&t, &A2, &Ai[5]);
598 ge_p1p1_to_p3(&u, &t);
599 ge_p3_to_cached(&Ai[6], &u);
600 ge_add(&t, &A2, &Ai[6]);
601 ge_p1p1_to_p3(&u, &t);
602 ge_p3_to_cached(&Ai[7], &u);
603
604 ge_p2_0(&r);
605
606 for(i = 255; i >= 0; --i)
607 {
608 if(aslide[i] || bslide[i])
609 {
610 break;
611 }
612 }
613
614 for(; i >= 0; --i)
615 {
616 ge_p2_dbl(&t, &r);
617
618 if(aslide[i] > 0)
619 {
620 ge_p1p1_to_p3(&u, &t);
621 ge_add(&t, &u, &Ai[aslide[i] >> 1]);
622 }
623 else if(aslide[i] < 0)
624 {
625 ge_p1p1_to_p3(&u, &t);
626 ge_sub(&t, &u, &Ai[(-aslide[i]) >> 1]);
627 }
628
629 if(bslide[i] > 0)
630 {
631 ge_p1p1_to_p3(&u, &t);
632 ge_madd(&t, &u, &Bi[bslide[i] >> 1]);
633 }
634 else if(bslide[i] < 0)
635 {
636 ge_p1p1_to_p3(&u, &t);
637 ge_msub(&t, &u, &Bi[(-bslide[i]) >> 1]);
638 }
639
640 ge_p1p1_to_p2(&r, &t);
641 }
642
643 ge_tobytes(out, &r);
644 }
645
646/* base[i][j] = (j+1)*256^i*B */
647static const ge_precomp B_precomp[32][8] =
648 {
649 {
650 {
651 { 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
652 { -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
653 { -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
654 },
655 {
656 { -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303 },
657 { -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081 },
658 { 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697 },
659 },
660 {
661 { 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
662 { 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
663 { 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
664 },
665 {
666 { -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540 },
667 { 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397 },
668 { 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325 },
669 },
670 {
671 { 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
672 { 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
673 { 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
674 },
675 {
676 { -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777 },
677 { -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737 },
678 { -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652 },
679 },
680 {
681 { 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
682 { -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
683 { 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
684 },
685 {
686 { 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726 },
687 { -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955 },
688 { 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425 },
689 },
690 },
691 {
692 {
693 { -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171 },
694 { 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510 },
695 { 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660 },
696 },
697 {
698 { -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639 },
699 { 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963 },
700 { 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950 },
701 },
702 {
703 { -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568 },
704 { 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335 },
705 { 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628 },
706 },
707 {
708 { -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007 },
709 { -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772 },
710 { -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653 },
711 },
712 {
713 { 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567 },
714 { 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686 },
715 { 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372 },
716 },
717 {
718 { -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887 },
719 { -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954 },
720 { -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953 },
721 },
722 {
723 { 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833 },
724 { -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532 },
725 { -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876 },
726 },
727 {
728 { 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268 },
729 { 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214 },
730 { 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038 },
731 },
732 },
733 {
734 {
735 { 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800 },
736 { 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645 },
737 { -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664 },
738 },
739 {
740 { 1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933 },
741 { -25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182 },
742 { -17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222 },
743 },
744 {
745 { -18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991 },
746 { 20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880 },
747 { 9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092 },
748 },
749 {
750 { -16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295 },
751 { 19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788 },
752 { 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553 },
753 },
754 {
755 { -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026 },
756 { 11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347 },
757 { -18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033 },
758 },
759 {
760 { -23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395 },
761 { -27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278 },
762 { 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890 },
763 },
764 {
765 { 32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995 },
766 { -30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596 },
767 { -11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891 },
768 },
769 {
770 { 31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060 },
771 { 11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608 },
772 { -20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606 },
773 },
774 },
775 {
776 {
777 { 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389 },
778 { -19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016 },
779 { -11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341 },
780 },
781 {
782 { -22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505 },
783 { 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553 },
784 { -28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655 },
785 },
786 {
787 { 15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220 },
788 { 12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631 },
789 { -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099 },
790 },
791 {
792 { 26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556 },
793 { 14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749 },
794 { 236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930 },
795 },
796 {
797 { 1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391 },
798 { 5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253 },
799 { 20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066 },
800 },
801 {
802 { 24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958 },
803 { -11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082 },
804 { -28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383 },
805 },
806 {
807 { -30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521 },
808 { -11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807 },
809 { 23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948 },
810 },
811 {
812 { 9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134 },
813 { -32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455 },
814 { 27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629 },
815 },
816 },
817 {
818 {
819 { -8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069 },
820 { -32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746 },
821 { 24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919 },
822 },
823 {
824 { 11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837 },
825 { 8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906 },
826 { -28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771 },
827 },
828 {
829 { -25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817 },
830 { 10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098 },
831 { 10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409 },
832 },
833 {
834 { -12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504 },
835 { -26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727 },
836 { 28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420 },
837 },
838 {
839 { -32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003 },
840 { -1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605 },
841 { -30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384 },
842 },
843 {
844 { -26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701 },
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1863 { 13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345 },
1864 { -19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310 },
1865 },
1866 },
1867 {
1868 {
1869 { 19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937 },
1870 { 31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636 },
1871 { -9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008 },
1872 },
1873 {
1874 { -2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429 },
1875 { -15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576 },
1876 { 31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066 },
1877 },
1878 {
1879 { -9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490 },
1880 { -12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104 },
1881 { 33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053 },
1882 },
1883 {
1884 { 31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275 },
1885 { -20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511 },
1886 { 22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095 },
1887 },
1888 {
1889 { -28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439 },
1890 { 23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939 },
1891 { -23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424 },
1892 },
1893 {
1894 { 2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310 },
1895 { 3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608 },
1896 { -32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079 },
1897 },
1898 {
1899 { -23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101 },
1900 { 21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418 },
1901 { 18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576 },
1902 },
1903 {
1904 { 30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356 },
1905 { 9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996 },
1906 { -26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099 },
1907 },
1908 },
1909 {
1910 {
1911 { -26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728 },
1912 { -13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658 },
1913 { -10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242 },
1914 },
1915 {
1916 { -21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001 },
1917 { -4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766 },
1918 { 18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373 },
1919 },
1920 {
1921 { 26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458 },
1922 { -17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628 },
1923 { -13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657 },
1924 },
1925 {
1926 { -23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062 },
1927 { 25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616 },
1928 { 31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014 },
1929 },
1930 {
1931 { 24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383 },
1932 { -25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814 },
1933 { -20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718 },
1934 },
1935 {
1936 { 30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417 },
1937 { 2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222 },
1938 { 33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444 },
1939 },
1940 {
1941 { -20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597 },
1942 { 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970 },
1943 { 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799 },
1944 },
1945 {
1946 { -5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647 },
1947 { 13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511 },
1948 { -29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032 },
1949 },
1950 },
1951 {
1952 {
1953 { 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834 },
1954 { -23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461 },
1955 { 29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062 },
1956 },
1957 {
1958 { -25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516 },
1959 { -20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547 },
1960 { -24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240 },
1961 },
1962 {
1963 { -17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038 },
1964 { -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741 },
1965 { 16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103 },
1966 },
1967 {
1968 { -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747 },
1969 { -1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323 },
1970 { 31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016 },
1971 },
1972 {
1973 { -14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373 },
1974 { 15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228 },
1975 { -2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141 },
1976 },
1977 {
1978 { 16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399 },
1979 { 11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831 },
1980 { -185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376 },
1981 },
1982 {
1983 { -32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 },
1984 { -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 },
1985 { -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 },
1986 },
1987 {
1988 { -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 },
1989 { 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 },
1990 { -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 },
1991 },
1992 },
1993 } ;
1994
1995namespace {
1996
1997inline uint8_t equal(int8_t b, int8_t c)
1998 {
1999 uint8_t ub = b;
2000 uint8_t uc = c;
2001 uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2002 uint32_t y = x; /* 0: yes; 1..255: no */
2003 y -= 1; /* 4294967295: yes; 0..254: no */
2004 y >>= 31; /* 1: yes; 0: no */
2005 return static_cast<uint8_t>(y);
2006 }
2007
2008inline int32_t equal32(int8_t b, int8_t c)
2009 {
2010 return -static_cast<int32_t>(equal(b, c));
2011 }
2012
2013inline uint8_t negative(int8_t b)
2014 {
2015 uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
2016 x >>= 63; /* 1: yes; 0: no */
2017 return static_cast<uint8_t>(x);
2018 }
2019
2020inline void ge_precomp_0(ge_precomp* h)
2021 {
2022 fe_1(h->yplusx);
2023 fe_1(h->yminusx);
2024 fe_0(h->xy2d);
2025 }
2026
2027inline void select(ge_precomp* t,
2028 const ge_precomp* base,
2029 int8_t b)
2030 {
2031 const uint8_t bnegative = negative(b);
2032 const uint8_t babs = b - ((-static_cast<int>(bnegative) & b) * 2);
2033 const int32_t neg_mask = equal32(bnegative, 1);
2034
2035 const int32_t mask1 = equal32(babs, 1);
2036 const int32_t mask2 = equal32(babs, 2);
2037 const int32_t mask3 = equal32(babs, 3);
2038 const int32_t mask4 = equal32(babs, 4);
2039 const int32_t mask5 = equal32(babs, 5);
2040 const int32_t mask6 = equal32(babs, 6);
2041 const int32_t mask7 = equal32(babs, 7);
2042 const int32_t mask8 = equal32(babs, 8);
2043
2044 ge_precomp_0(t);
2045
2046 for(size_t i = 0; i != 10; ++i)
2047 {
2048 t->yplusx[i] = t->yplusx[i] ^
2049 ((t->yplusx[i] ^ base[0].yplusx[i]) & mask1) ^
2050 ((t->yplusx[i] ^ base[1].yplusx[i]) & mask2) ^
2051 ((t->yplusx[i] ^ base[2].yplusx[i]) & mask3) ^
2052 ((t->yplusx[i] ^ base[3].yplusx[i]) & mask4) ^
2053 ((t->yplusx[i] ^ base[4].yplusx[i]) & mask5) ^
2054 ((t->yplusx[i] ^ base[5].yplusx[i]) & mask6) ^
2055 ((t->yplusx[i] ^ base[6].yplusx[i]) & mask7) ^
2056 ((t->yplusx[i] ^ base[7].yplusx[i]) & mask8);
2057
2058 t->yminusx[i] = t->yminusx[i] ^
2059 ((t->yminusx[i] ^ base[0].yminusx[i]) & mask1) ^
2060 ((t->yminusx[i] ^ base[1].yminusx[i]) & mask2) ^
2061 ((t->yminusx[i] ^ base[2].yminusx[i]) & mask3) ^
2062 ((t->yminusx[i] ^ base[3].yminusx[i]) & mask4) ^
2063 ((t->yminusx[i] ^ base[4].yminusx[i]) & mask5) ^
2064 ((t->yminusx[i] ^ base[5].yminusx[i]) & mask6) ^
2065 ((t->yminusx[i] ^ base[6].yminusx[i]) & mask7) ^
2066 ((t->yminusx[i] ^ base[7].yminusx[i]) & mask8);
2067
2068 t->xy2d[i] = t->xy2d[i] ^
2069 ((t->xy2d[i] ^ base[0].xy2d[i]) & mask1) ^
2070 ((t->xy2d[i] ^ base[1].xy2d[i]) & mask2) ^
2071 ((t->xy2d[i] ^ base[2].xy2d[i]) & mask3) ^
2072 ((t->xy2d[i] ^ base[3].xy2d[i]) & mask4) ^
2073 ((t->xy2d[i] ^ base[4].xy2d[i]) & mask5) ^
2074 ((t->xy2d[i] ^ base[5].xy2d[i]) & mask6) ^
2075 ((t->xy2d[i] ^ base[6].xy2d[i]) & mask7) ^
2076 ((t->xy2d[i] ^ base[7].xy2d[i]) & mask8);
2077 }
2078
2079 fe minus_xy2d;
2080 fe_neg(minus_xy2d, t->xy2d);
2081
2082 // If negative have to swap yminusx and yplusx
2083 for(size_t i = 0; i != 10; ++i)
2084 {
2085 int32_t t_yplusx = t->yplusx[i] ^ ((t->yplusx[i] ^ t->yminusx[i]) & neg_mask);
2086 int32_t t_yminusx = t->yminusx[i] ^ ((t->yminusx[i] ^ t->yplusx[i]) & neg_mask);
2087
2088 t->yplusx[i] = t_yplusx;
2089 t->yminusx[i] = t_yminusx;
2090 t->xy2d[i] = t->xy2d[i] ^ ((t->xy2d[i] ^ minus_xy2d[i]) & neg_mask);
2091 }
2092 }
2093
2094void ge_p3_tobytes(uint8_t* s, const ge_p3* h)
2095 {
2096 fe recip;
2097 fe x;
2098 fe y;
2099
2100 fe_invert(recip, h->Z);
2101 fe_mul(x, h->X, recip);
2102 fe_mul(y, h->Y, recip);
2103 fe_tobytes(s, y);
2104 s[31] ^= fe_isnegative(x) << 7;
2105 }
2106
2107}
2108
2109/*
2110h = a * B
2111where a = a[0]+256*a[1]+...+256^31 a[31]
2112B is the Ed25519 base point (x,4/5) with x positive.
2113
2114Preconditions:
2115 a[31] <= 127
2116*/
2117
2118void ge_scalarmult_base(uint8_t out[32], const uint8_t a[32])
2119 {
2120 int8_t e[64];
2121 int8_t carry;
2122 ge_p1p1 r;
2123 ge_p2 s;
2124 ge_p3 h;
2125 ge_precomp t;
2126 int i;
2127
2128 for(i = 0; i < 32; ++i)
2129 {
2130 e[2 * i + 0] = (a[i] >> 0) & 15;
2131 e[2 * i + 1] = (a[i] >> 4) & 15;
2132 }
2133 /* each e[i] is between 0 and 15 */
2134 /* e[63] is between 0 and 7 */
2135
2136 carry = 0;
2137 for(i = 0; i < 63; ++i)
2138 {
2139 e[i] += carry;
2140 carry = e[i] + 8;
2141 carry >>= 4;
2142 e[i] -= carry << 4;
2143 }
2144 e[63] += carry;
2145 /* each e[i] is between -8 and 8 */
2146
2147 ge_p3_0(&h);
2148 for(i = 1; i < 64; i += 2)
2149 {
2150 select(&t, B_precomp[i / 2], e[i]);
2151 ge_madd(&r, &h, &t);
2152 ge_p1p1_to_p3(&h, &r);
2153 }
2154
2155 ge_p3_dbl(&r, &h);
2156 ge_p1p1_to_p2(&s, &r);
2157 ge_p2_dbl(&r, &s);
2158 ge_p1p1_to_p2(&s, &r);
2159 ge_p2_dbl(&r, &s);
2160 ge_p1p1_to_p2(&s, &r);
2161 ge_p2_dbl(&r, &s);
2162 ge_p1p1_to_p3(&h, &r);
2163
2164 for(i = 0; i < 64; i += 2)
2165 {
2166 select(&t, B_precomp[i / 2], e[i]);
2167 ge_madd(&r, &h, &t);
2168 ge_p1p1_to_p3(&h, &r);
2169 }
2170
2171 ge_p3_tobytes(out, &h);
2172 }
2173
2174}
fe yminusx
Definition: ge.cpp:43
fe YplusX
Definition: ge.cpp:49
fe yplusx
Definition: ge.cpp:42
fe Y
Definition: ge.cpp:28
fe Z
Definition: ge.cpp:29
fe xy2d
Definition: ge.cpp:44
fe T2d
Definition: ge.cpp:52
fe YminusX
Definition: ge.cpp:50
fe T
Definition: ge.cpp:37
fe X
Definition: ge.cpp:27
Definition: alg_id.cpp:13
void fe_sq2(fe &x, const fe &z)
Definition: ed25519_fe.h:210
void fe_0(fe &x)
Definition: ed25519_fe.h:170
int fe_isnegative(const fe &x)
Definition: ed25519_fe.h:164
int fe_isnonzero(const fe &x)
Definition: ed25519_fe.h:159
void fe_1(fe &x)
Definition: ed25519_fe.h:175
void fe_mul(fe &x, const fe &a, const fe &b)
Definition: ed25519_fe.h:195
void fe_sq(fe &x, const fe &z)
Definition: ed25519_fe.h:200
void fe_neg(fe &x, const fe &z)
Definition: ed25519_fe.h:190
FE_25519 fe
Definition: ed25519_fe.h:134
void carry(int64_t &h0, int64_t &h1)
void ge_scalarmult_base(uint8_t out[32], const uint8_t in[32])
Definition: ge.cpp:2118
void fe_copy(fe &a, const fe &b)
Definition: ed25519_fe.h:154
void fe_add(fe &x, const fe &a, const fe &b)
Definition: ed25519_fe.h:180
int ge_frombytes_negate_vartime(ge_p3 *, const uint8_t *)
Definition: ge.cpp:458
void fe_sub(fe &x, const fe &a, const fe &b)
Definition: ed25519_fe.h:185
void fe_tobytes(uint8_t *b, const fe &x)
Definition: ed25519_fe.h:149
void fe_pow22523(fe &x, const fe &y)
Definition: ed25519_fe.h:220
void fe_invert(fe &x, const fe &z)
Definition: ed25519_fe.h:215
void fe_frombytes(fe &x, const uint8_t *b)
Definition: ed25519_fe.h:144
void ge_double_scalarmult_vartime(uint8_t out[32], const uint8_t a[], const ge_p3 *A, const uint8_t b[])