/src/botan/src/lib/pubkey/ed25519/ge.cpp

Line	Count	Source (jump to first uncovered line)
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
13		namespace Botan {
14
15		namespace {
16
17		/*
18		Representations:
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		*/
24		struct ge_p2
25		{
26		fe X;
27		fe Y;
28		fe Z;
29		};
30
31		struct ge_p1p1
32		{
33		fe X;
34		fe Y;
35		fe Z;
36		fe T;
37		};
38
39		struct ge_precomp
40		{
41		fe yplusx;
42		fe yminusx;
43		fe xy2d;
44		};
45
46		struct ge_cached
47		{
48		fe YplusX;
49		fe YminusX;
50		fe Z;
51		fe T2d;
52		};
53
54		/*
55		r = p + q
56		*/
57
58		void ge_add(ge_p1p1* r, const ge_p3* p, const ge_cached* q)
59	0	{
60	0	fe t0;
61		/* qhasm: YpX1 = Y1+X1 */
62		/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
63		/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
64	0	fe_add(r->X, p->Y, p->X);
65
66		/* qhasm: YmX1 = Y1-X1 */
67		/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
68		/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
69	0	fe_sub(r->Y, p->Y, p->X);
70
71		/* qhasm: A = YpX1YpX2 /
72		/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YpX2=fe#15); */
73		/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YpX2=q->YplusX); */
74	0	fe_mul(r->Z, r->X, q->YplusX);
75
76		/* qhasm: B = YmX1YmX2 /
77		/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YmX2=fe#16); */
78		/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YmX2=q->YminusX); */
79	0	fe_mul(r->Y, r->Y, q->YminusX);
80
81		/* qhasm: C = T2d2T1 /
82		/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
83		/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
84	0	fe_mul(r->T, q->T2d, p->T);
85
86		/* qhasm: ZZ = Z1Z2 /
87		/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
88		/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
89	0	fe_mul(r->X, p->Z, q->Z);
90
91		/* qhasm: D = 2ZZ /
92		/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
93		/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
94	0	fe_add(t0, r->X, r->X);
95
96		/* qhasm: X3 = A-B */
97		/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
98		/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
99	0	fe_sub(r->X, r->Z, r->Y);
100
101		/* qhasm: Y3 = A+B */
102		/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
103		/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
104	0	fe_add(r->Y, r->Z, r->Y);
105
106		/* qhasm: Z3 = D+C */
107		/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
108		/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
109	0	fe_add(r->Z, t0, r->T);
110
111		/* qhasm: T3 = D-C */
112		/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
113		/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
114	0	fe_sub(r->T, t0, r->T);
115	0	}
116
117		/*
118		r = p + q
119		*/
120
121		void ge_madd(ge_p1p1* r, const ge_p3* p, const ge_precomp* q)
122	192	{
123	192	fe t0;
124		/* qhasm: YpX1 = Y1+X1 */
125	192	fe_add(r->X, p->Y, p->X);
126
127		/* qhasm: YmX1 = Y1-X1 */
128	192	fe_sub(r->Y, p->Y, p->X);
129
130		/* qhasm: A = YpX1ypx2 /
131	192	fe_mul(r->Z, r->X, q->yplusx);
132
133		/* qhasm: B = YmX1ymx2 /
134	192	fe_mul(r->Y, r->Y, q->yminusx);
135
136		/* qhasm: C = xy2d2T1 /
137	192	fe_mul(r->T, q->xy2d, p->T);
138
139		/* qhasm: D = 2Z1 /
140	192	fe_add(t0, p->Z, p->Z);
141
142		/* qhasm: X3 = A-B */
143	192	fe_sub(r->X, r->Z, r->Y);
144
145		/* qhasm: Y3 = A+B */
146	192	fe_add(r->Y, r->Z, r->Y);
147
148		/* qhasm: Z3 = D+C */
149	192	fe_add(r->Z, t0, r->T);
150
151		/* qhasm: T3 = D-C */
152	192	fe_sub(r->T, t0, r->T);
153	192	}
154
155		/*
156		r = p - q
157		*/
158
159		void ge_msub(ge_p1p1* r, const ge_p3* p, const ge_precomp* q)
160	0	{
161	0	fe t0;
162
163		/* qhasm: YpX1 = Y1+X1 */
164		/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
165		/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
166	0	fe_add(r->X, p->Y, p->X);
167
168		/* qhasm: YmX1 = Y1-X1 */
169		/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
170		/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
171	0	fe_sub(r->Y, p->Y, p->X);
172
173		/* qhasm: A = YpX1ymx2 /
174		/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ymx2=fe#16); */
175		/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ymx2=q->yminusx); */
176	0	fe_mul(r->Z, r->X, q->yminusx);
177
178		/* qhasm: B = YmX1ypx2 /
179		/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ypx2=fe#15); */
180		/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ypx2=q->yplusx); */
181	0	fe_mul(r->Y, r->Y, q->yplusx);
182
183		/* qhasm: C = xy2d2T1 /
184		/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
185		/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
186	0	fe_mul(r->T, q->xy2d, p->T);
187
188		/* qhasm: D = 2Z1 /
189		/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
190		/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
191	0	fe_add(t0, p->Z, p->Z);
192
193		/* qhasm: X3 = A-B */
194		/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
195		/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
196	0	fe_sub(r->X, r->Z, r->Y);
197
198		/* qhasm: Y3 = A+B */
199		/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
200		/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
201	0	fe_add(r->Y, r->Z, r->Y);
202
203		/* qhasm: Z3 = D-C */
204		/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
205		/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
206	0	fe_sub(r->Z, t0, r->T);
207
208		/* qhasm: T3 = D+C */
209		/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
210		/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
211	0	fe_add(r->T, t0, r->T);
212
213	0	}
214
215		/*
216		r = p
217		*/
218
219		void ge_p1p1_to_p2(ge_p2* r, const ge_p1p1* p)
220	9	{
221	9	fe_mul(r->X, p->X, p->T);
222	9	fe_mul(r->Y, p->Y, p->Z);
223	9	fe_mul(r->Z, p->Z, p->T);
224	9	}
225
226		/*
227		r = p
228		*/
229
230		void ge_p1p1_to_p3(ge_p3* r, const ge_p1p1* p)
231	195	{
232	195	fe_mul(r->X, p->X, p->T);
233	195	fe_mul(r->Y, p->Y, p->Z);
234	195	fe_mul(r->Z, p->Z, p->T);
235	195	fe_mul(r->T, p->X, p->Y);
236	195	}
237
238		/*
239		r = 2 * p
240		*/
241
242		void ge_p2_dbl(ge_p1p1* r, const ge_p2* p)
243	12	{
244	12	fe t0;
245		/* qhasm: XX=X1^2 */
246		/* asm 1: fe_sq(>XX=fe#1,<X1=fe#11); */
247		/* asm 2: fe_sq(>XX=r->X,<X1=p->X); */
248	12	fe_sq(r->X, p->X);
249
250		/* qhasm: YY=Y1^2 */
251		/* asm 1: fe_sq(>YY=fe#3,<Y1=fe#12); */
252		/* asm 2: fe_sq(>YY=r->Z,<Y1=p->Y); */
253	12	fe_sq(r->Z, p->Y);
254
255		/* qhasm: B=2Z1^2 /
256		/* asm 1: fe_sq2(>B=fe#4,<Z1=fe#13); */
257		/* asm 2: fe_sq2(>B=r->T,<Z1=p->Z); */
258	12	fe_sq2(r->T, p->Z);
259
260		/* qhasm: A=X1+Y1 */
261		/* asm 1: fe_add(>A=fe#2,<X1=fe#11,<Y1=fe#12); */
262		/* asm 2: fe_add(>A=r->Y,<X1=p->X,<Y1=p->Y); */
263	12	fe_add(r->Y, p->X, p->Y);
264
265		/* qhasm: AA=A^2 */
266		/* asm 1: fe_sq(>AA=fe#5,<A=fe#2); */
267		/* asm 2: fe_sq(>AA=t0,<A=r->Y); */
268	12	fe_sq(t0, r->Y);
269
270		/* qhasm: Y3=YY+XX */
271		/* asm 1: fe_add(>Y3=fe#2,<YY=fe#3,<XX=fe#1); */
272		/* asm 2: fe_add(>Y3=r->Y,<YY=r->Z,<XX=r->X); */
273	12	fe_add(r->Y, r->Z, r->X);
274
275		/* qhasm: Z3=YY-XX */
276		/* asm 1: fe_sub(>Z3=fe#3,<YY=fe#3,<XX=fe#1); */
277		/* asm 2: fe_sub(>Z3=r->Z,<YY=r->Z,<XX=r->X); */
278	12	fe_sub(r->Z, r->Z, r->X);
279
280		/* qhasm: X3=AA-Y3 */
281		/* asm 1: fe_sub(>X3=fe#1,<AA=fe#5,<Y3=fe#2); */
282		/* asm 2: fe_sub(>X3=r->X,<AA=t0,<Y3=r->Y); */
283	12	fe_sub(r->X, t0, r->Y);
284
285		/* qhasm: T3=B-Z3 */
286		/* asm 1: fe_sub(>T3=fe#4,<B=fe#4,<Z3=fe#3); */
287		/* asm 2: fe_sub(>T3=r->T,<B=r->T,<Z3=r->Z); */
288	12	fe_sub(r->T, r->T, r->Z);
289	12	}
290
291		void ge_p3_0(ge_p3* h)
292	3	{
293	3	fe_0(h->X);
294	3	fe_1(h->Y);
295	3	fe_1(h->Z);
296	3	fe_0(h->T);
297	3	}
298
299		/*
300		r = 2 * p
301		*/
302
303		void ge_p3_dbl(ge_p1p1* r, const ge_p3* p)
304	3	{
305	3	ge_p2 q;
306		// Convert to p2 rep
307	3	q.X = p->X;
308	3	q.Y = p->Y;
309	3	q.Z = p->Z;
310	3	ge_p2_dbl(r, &q);
311	3	}
312
313		/*
314		r = p
315		*/
316
317
318		void ge_p3_to_cached(ge_cached* r, const ge_p3* p)
319	0	{
320	0	static const fe d2 =
321	0	{
322	0	-21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199
323	0	} ;
324	0	fe_add(r->YplusX, p->Y, p->X);
325	0	fe_sub(r->YminusX, p->Y, p->X);
326	0	fe_copy(r->Z, p->Z);
327	0	fe_mul(r->T2d, p->T, d2);
328	0	}
329
330		/*
331		r = p - q
332		*/
333
334		void ge_sub(ge_p1p1* r, const ge_p3* p, const ge_cached* q)
335	0	{
336	0	fe t0;
337		/* qhasm: YpX1 = Y1+X1 */
338		/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
339		/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
340	0	fe_add(r->X, p->Y, p->X);
341
342		/* qhasm: YmX1 = Y1-X1 */
343		/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
344		/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
345	0	fe_sub(r->Y, p->Y, p->X);
346
347		/* qhasm: A = YpX1YmX2 /
348		/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YmX2=fe#16); */
349		/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YmX2=q->YminusX); */
350	0	fe_mul(r->Z, r->X, q->YminusX);
351
352		/* qhasm: B = YmX1YpX2 /
353		/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YpX2=fe#15); */
354		/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YpX2=q->YplusX); */
355	0	fe_mul(r->Y, r->Y, q->YplusX);
356
357		/* qhasm: C = T2d2T1 /
358		/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
359		/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
360	0	fe_mul(r->T, q->T2d, p->T);
361
362		/* qhasm: ZZ = Z1Z2 /
363		/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
364		/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
365	0	fe_mul(r->X, p->Z, q->Z);
366
367		/* qhasm: D = 2ZZ /
368		/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
369		/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
370	0	fe_add(t0, r->X, r->X);
371
372		/* qhasm: X3 = A-B */
373		/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
374		/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
375	0	fe_sub(r->X, r->Z, r->Y);
376
377		/* qhasm: Y3 = A+B */
378		/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
379		/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
380	0	fe_add(r->Y, r->Z, r->Y);
381
382		/* qhasm: Z3 = D-C */
383		/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
384		/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
385	0	fe_sub(r->Z, t0, r->T);
386
387		/* qhasm: T3 = D+C */
388		/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
389		/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
390	0	fe_add(r->T, t0, r->T);
391
392	0	}
393
394		void slide(int8_t* r, const uint8_t* a)
395	0	{
396	0	for(size_t i = 0; i < 256; ++i)
397	0	{
398	0	r[i] = 1 & (a[i >> 3] >> (i & 7));
399	0	}
400
401	0	for(size_t i = 0; i < 256; ++i)
402	0	{
403	0	if(r[i])
404	0	{
405	0	for(size_t b = 1; b <= 6 && i + b < 256; ++b)
406	0	{
407	0	if(r[i + b])
408	0	{
409	0	if(r[i] + (r[i + b] << b) <= 15)
410	0	{
411	0	r[i] += r[i + b] << b;
412	0	r[i + b] = 0;
413	0	}
414	0	else if(r[i] - (r[i + b] << b) >= -15)
415	0	{
416	0	r[i] -= r[i + b] << b;
417	0	for(size_t k = i + b; k < 256; ++k)
418	0	{
419	0	if(!r[k])
420	0	{
421	0	r[k] = 1;
422	0	break;
423	0	}
424	0	r[k] = 0;
425	0	}
426	0	}
427	0	else
428	0	{ break; }
429	0	}
430	0	}
431	0	}
432	0	}
433	0	}
434
435		void ge_tobytes(uint8_t* s, const ge_p2* h)
436	0	{
437	0	fe recip;
438	0	fe x;
439	0	fe y;
440
441	0	fe_invert(recip, h->Z);
442	0	fe_mul(x, h->X, recip);
443	0	fe_mul(y, h->Y, recip);
444	0	fe_tobytes(s, y);
445	0	s[31] ^= fe_isnegative(x) << 7;
446	0	}
447
448		void ge_p2_0(ge_p2* h)
449	0	{
450	0	fe_0(h->X);
451	0	fe_1(h->Y);
452	0	fe_1(h->Z);
453	0	}
454
455		}
456
457		int ge_frombytes_negate_vartime(ge_p3* h, const uint8_t* s)
458	0	{
459	0	static const fe d =
460	0	{
461	0	-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116
462	0	} ;
463	0	static const fe sqrtm1 =
464	0	{
465	0	-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482
466	0	} ;
467
468	0	fe u;
469	0	fe v;
470	0	fe v3;
471	0	fe vxx;
472	0	fe check;
473
474	0	fe_frombytes(h->Y, s);
475	0	fe_1(h->Z);
476	0	fe_sq(u, h->Y);
477	0	fe_mul(v, u, d);
478	0	fe_sub(u, u, h->Z); /* u = y^2-1 */
479	0	fe_add(v, v, h->Z); /* v = dy^2+1 */
480
481	0	fe_sq(v3, v);
482	0	fe_mul(v3, v3, v); /* v3 = v^3 */
483	0	fe_sq(h->X, v3);
484	0	fe_mul(h->X, h->X, v);
485	0	fe_mul(h->X, h->X, u); /* x = uv^7 */
486
487	0	fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
488	0	fe_mul(h->X, h->X, v3);
489	0	fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
490
491	0	fe_sq(vxx, h->X);
492	0	fe_mul(vxx, vxx, v);
493	0	fe_sub(check, vxx, u); /* vx^2-u */
494	0	if(fe_isnonzero(check))
495	0	{
496	0	fe_add(check, vxx, u); /* vx^2+u */
497	0	if(fe_isnonzero(check))
498	0	{
499	0	return -1;
500	0	}
501	0	fe_mul(h->X, h->X, sqrtm1);
502	0	}
503
504	0	if(fe_isnegative(h->X) == (s[31] >> 7))
505	0	{ fe_neg(h->X, h->X); }
506
507	0	fe_mul(h->T, h->X, h->Y);
508	0	return 0;
509	0	}
510
511		/*
512		r = a * A + b * B
513		where a = a[0]+256*a[1]+...+256^31 a[31].
514		and b = b[0]+256*b[1]+...+256^31 b[31].
515		B is the Ed25519 base point (x,4/5) with x positive.
516		*/
517
518		void ge_double_scalarmult_vartime(
519		uint8_t out[32],
520		const uint8_t* a, const ge_p3* A, const uint8_t* b)
521	0	{
522	0	static const ge_precomp Bi[8] =
523	0	{
524	0	{
525	0	{ 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
526	0	{ -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
527	0	{ -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
528	0	},
529	0	{
530	0	{ 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
531	0	{ 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
532	0	{ 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
533	0	},
534	0	{
535	0	{ 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
536	0	{ 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
537	0	{ 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
538	0	},
539	0	{
540	0	{ 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
541	0	{ -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
542	0	{ 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
543	0	},
544	0	{
545	0	{ -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877 },
546	0	{ -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951 },
547	0	{ 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784 },
548	0	},
549	0	{
550	0	{ -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436 },
551	0	{ 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918 },
552	0	{ 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877 },
553	0	},
554	0	{
555	0	{ -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800 },
556	0	{ -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305 },
557	0	{ -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300 },
558	0	},
559	0	{
560	0	{ -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876 },
561	0	{ -24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619 },
562	0	{ -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683 },
563	0	},
564	0	} ;
565
566	0	int8_t aslide[256];
567	0	int8_t bslide[256];
568	0	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
569	0	ge_p1p1 t;
570	0	ge_p3 u;
571	0	ge_p3 A2;
572	0	ge_p2 r;
573	0	int i;
574
575	0	slide(aslide, a);
576	0	slide(bslide, b);
577
578	0	ge_p3_to_cached(&Ai[0], A);
579	0	ge_p3_dbl(&t, A);
580	0	ge_p1p1_to_p3(&A2, &t);
581	0	ge_add(&t, &A2, &Ai[0]);
582	0	ge_p1p1_to_p3(&u, &t);
583	0	ge_p3_to_cached(&Ai[1], &u);
584	0	ge_add(&t, &A2, &Ai[1]);
585	0	ge_p1p1_to_p3(&u, &t);
586	0	ge_p3_to_cached(&Ai[2], &u);
587	0	ge_add(&t, &A2, &Ai[2]);
588	0	ge_p1p1_to_p3(&u, &t);
589	0	ge_p3_to_cached(&Ai[3], &u);
590	0	ge_add(&t, &A2, &Ai[3]);
591	0	ge_p1p1_to_p3(&u, &t);
592	0	ge_p3_to_cached(&Ai[4], &u);
593	0	ge_add(&t, &A2, &Ai[4]);
594	0	ge_p1p1_to_p3(&u, &t);
595	0	ge_p3_to_cached(&Ai[5], &u);
596	0	ge_add(&t, &A2, &Ai[5]);
597	0	ge_p1p1_to_p3(&u, &t);
598	0	ge_p3_to_cached(&Ai[6], &u);
599	0	ge_add(&t, &A2, &Ai[6]);
600	0	ge_p1p1_to_p3(&u, &t);
601	0	ge_p3_to_cached(&Ai[7], &u);
602
603	0	ge_p2_0(&r);
604
605	0	for(i = 255; i >= 0; --i)
606	0	{
607	0	if(aslide[i] \|\| bslide[i])
608	0	{
609	0	break;
610	0	}
611	0	}
612
613	0	for(; i >= 0; --i)
614	0	{
615	0	ge_p2_dbl(&t, &r);
616
617	0	if(aslide[i] > 0)
618	0	{
619	0	ge_p1p1_to_p3(&u, &t);
620	0	ge_add(&t, &u, &Ai[aslide[i] >> 1]);
621	0	}
622	0	else if(aslide[i] < 0)
623	0	{
624	0	ge_p1p1_to_p3(&u, &t);
625	0	ge_sub(&t, &u, &Ai[(-aslide[i]) >> 1]);
626	0	}
627
628	0	if(bslide[i] > 0)
629	0	{
630	0	ge_p1p1_to_p3(&u, &t);
631	0	ge_madd(&t, &u, &Bi[bslide[i] >> 1]);
632	0	}
633	0	else if(bslide[i] < 0)
634	0	{
635	0	ge_p1p1_to_p3(&u, &t);
636	0	ge_msub(&t, &u, &Bi[(-bslide[i]) >> 1]);
637	0	}
638
639	0	ge_p1p1_to_p2(&r, &t);
640	0	}
641
642	0	ge_tobytes(out, &r);
643	0	}
644
645		/* base[i][j] = (j+1)256^iB */
646		static const ge_precomp B_precomp[32][8] =
647		{
648		{
649		{
650		{ 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605 },
651		{ -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378 },
652		{ -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546 },
653		},
654		{
655		{ -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303 },
656		{ -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081 },
657		{ 26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697 },
658		},
659		{
660		{ 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024 },
661		{ 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574 },
662		{ 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357 },
663		},
664		{
665		{ -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540 },
666		{ 23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397 },
667		{ 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325 },
668		},
669		{
670		{ 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380 },
671		{ 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306 },
672		{ 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942 },
673		},
674		{
675		{ -15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777 },
676		{ -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737 },
677		{ -18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652 },
678		},
679		{
680		{ 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766 },
681		{ -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701 },
682		{ 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300 },
683		},
684		{
685		{ 14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726 },
686		{ -7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955 },
687		{ 27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425 },
688		},
689		},
690		{
691		{
692		{ -13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171 },
693		{ 27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510 },
694		{ 17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660 },
695		},
696		{
697		{ -10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639 },
698		{ 29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963 },
699		{ 5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950 },
700		},
701		{
702		{ -27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568 },
703		{ 12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335 },
704		{ 25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628 },
705		},
706		{
707		{ -26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007 },
708		{ -2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772 },
709		{ -22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653 },
710		},
711		{
712		{ 2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567 },
713		{ 13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686 },
714		{ 21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372 },
715		},
716		{
717		{ -13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887 },
718		{ -23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954 },
719		{ -29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953 },
720		},
721		{
722		{ 24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833 },
723		{ -16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532 },
724		{ -22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876 },
725		},
726		{
727		{ 2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268 },
728		{ 33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214 },
729		{ 1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038 },
730		},
731		},
732		{
733		{
734		{ 6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800 },
735		{ 4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645 },
736		{ -4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664 },
737		},
738		{
739		{ 1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933 },
740		{ -25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182 },
741		{ -17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222 },
742		},
743		{
744		{ -18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991 },
745		{ 20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880 },
746		{ 9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092 },
747		},
748		{
749		{ -16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295 },
750		{ 19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788 },
751		{ 8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553 },
752		},
753		{
754		{ -15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026 },
755		{ 11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347 },
756		{ -18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033 },
757		},
758		{
759		{ -23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395 },
760		{ -27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278 },
761		{ 1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890 },
762		},
763		{
764		{ 32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995 },
765		{ -30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596 },
766		{ -11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891 },
767		},
768		{
769		{ 31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060 },
770		{ 11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608 },
771		{ -20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606 },
772		},
773		},
774		{
775		{
776		{ 7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389 },
777		{ -19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016 },
778		{ -11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341 },
779		},
780		{
781		{ -22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505 },
782		{ 14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553 },
783		{ -28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655 },
784		},
785		{
786		{ 15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220 },
787		{ 12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631 },
788		{ -4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099 },
789		},
790		{
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1035		{ -6928835, -16430795, 10361374, 5642961, 4910474, 12345252, -31638386, -494430, 10530747, 1053335 },
1036		},
1037		{
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1039		{ -22592535, -3145277, -2289276, 5953843, -13440189, 9425631, 25310643, 13003497, -2314791, -15145616 },
1040		{ -27419985, -603321, -8043984, -1669117, -26092265, 13987819, -27297622, 187899, -23166419, -2531735 },
1041		},
1042		{
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1044		{ 29370922, -6053998, 7334071, -15342259, 9385287, 2247707, -13661962, -4839461, 30007388, -15823341 },
1045		{ -936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, 730663, 9835848, 4555336 },
1046		},
1047		{
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1049		{ 31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -5118685, -4096706, 29120153, 13924425 },
1050		{ -17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -9383939, -11317700, 7240931, -237388 },
1051		},
1052		{
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1054		{ -16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -24319580, 7733547, 12796905, -6335822 },
1055		{ -8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -28253339, 3647836, 3222231, -11160462 },
1056		},
1057		{
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1059		{ 9255317, -3131197, -12156162, -1004256, 13098013, -9214866, 16377220, -2102812, -19802075, -3034702 },
1060		{ -22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -31718148, 9936966, -30097688, -10618797 },
1061		},
1062		{
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1064		{ 27736861, 10103576, 12500508, 8502413, -3413016, -9633558, 10436918, -1550276, -23659143, -8132100 },
1065		{ 19492550, -12104365, -29681976, -852630, -3208171, 12403437, 30066266, 8367329, 13243957, 8709688 },
1066		},
1067		},
1068		{
1069		{
1070		{ 12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -11194191, -5645734, 5150968, 7274186 },
1071		{ 2831366, -12492146, 1478975, 6122054, 23825128, -12733586, 31097299, 6083058, 31021603, -9793610 },
1072		{ -2529932, -2229646, 445613, 10720828, -13849527, -11505937, -23507731, 16354465, 15067285, -14147707 },
1073		},
1074		{
1075		{ 7840942, 14037873, -33364863, 15934016, -728213, -3642706, 21403988, 1057586, -19379462, -12403220 },
1076		{ 915865, -16469274, 15608285, -8789130, -24357026, 6060030, -17371319, 8410997, -7220461, 16527025 },
1077		{ 32922597, -556987, 20336074, -16184568, 10903705, -5384487, 16957574, 52992, 23834301, 6588044 },
1078		},
1079		{
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1081		{ -4689649, 9166776, -25710296, -10847306, 11576752, 12733943, 7924251, -2752281, 1976123, -7249027 },
1082		{ 21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -3371252, 12331345, -8237197 },
1083		},
1084		{
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1086		{ 31486080, 15114593, -14261250, 12951354, 14369431, -7387845, 16347321, -13662089, 8684155, -10532952 },
1087		{ 19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -26263207, -6086921, 31316348, 14219878 },
1088		},
1089		{
1090		{ -28594490, 1193785, 32245219, 11392485, 31092169, 15722801, 27146014, 6992409, 29126555, 9207390 },
1091		{ 32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -4980517, 10843782, -7957600, -14435730 },
1092		{ 2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -21494559, 8550130, 28346258, 1994730 },
1093		},
1094		{
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1096		{ -30405132, 955511, -11133838, -15078069, -32447087, -13278079, -25651578, 3317160, -9943017, 930272 },
1097		{ -15303681, -6833769, 28856490, 1357446, 23421993, 1057177, 24091212, -1388970, -22765376, -10650715 },
1098		},
1099		{
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1101		{ -31969310, 2106403, -4736360, 1362501, 12813763, 16200670, 22981545, -6291273, 18009408, -15772772 },
1102		{ -17220923, -9545221, -27784654, 14166835, 29815394, 7444469, 29551787, -3727419, 19288549, 1325865 },
1103		},
1104		{
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1107		{ 32529814, -11074689, 30361439, -16689753, -9135940, 1513226, 22922121, 6382134, -5766928, 8371348 },
1108		},
1109		},
1110		{
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1113		{ -22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, 2610596, -23921530, -11455195 },
1114		{ 5408411, -1136691, -4969122, 10561668, 24145918, 14240566, 31319731, -4235541, 19985175, -3436086 },
1115		},
1116		{
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1118		{ -8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -19442942, 6922164, 12743482, -9800518 },
1119		{ -2361371, 12678785, 28815050, 4759974, -23893047, 4884717, 23783145, 11038569, 18800704, 255233 },
1120		},
1121		{
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1123		{ -2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -31934921, 2209390, -1524053, 2055794 },
1124		{ 580882, 16705327, 5468415, -2683018, -30926419, -14696000, -7203346, -8994389, -30021019, 7394435 },
1125		},
1126		{
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1129		{ 2286874, -4435931, -20042458, -2008336, -13696227, 5038122, 11006906, -15760352, 8205061, 1607563 },
1130		},
1131		{
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1133		{ -27688051, 1585953, -10775053, 931069, -29120221, -11002319, -14410829, 12029093, 9944378, 8024 },
1134		{ 4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -16114594, -999085, -8142388, 5640030 },
1135		},
1136		{
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1138		{ 27425505, -5719081, 3055006, 10660664, 23458024, 595578, -15398605, -1173195, -18342183, 9742717 },
1139		{ 6744077, 2427284, 26042789, 2720740, -847906, 1118974, 32324614, 7406442, 12420155, 1994844 },
1140		},
1141		{
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1143		{ 16412690, -4507367, 10772641, 15929391, -17068788, -4658621, 10555945, -10484049, -30102368, -4739048 },
1144		{ 22397382, -7767684, -9293161, -12792868, 17166287, -9755136, -27333065, 6199366, 21880021, -12250760 },
1145		},
1146		{
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1148		{ -15447727, 709327, -6919446, -10870178, -29777922, 6522332, -21720181, 12130072, -14796503, 5005757 },
1149		{ -2114751, -14308128, 23019042, 15765735, -25269683, 6002752, 10183197, -13239326, -16395286, -2176112 },
1150		},
1151		},
1152		{
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1155		{ 3065073, -1412761, -25598674, -361432, -17683065, -5703415, -8164212, 11248527, -3691214, -7414184 },
1156		{ 10379208, -6045554, 8877319, 1473647, -29291284, -12507580, 16690915, 2553332, -3132688, 16400289 },
1157		},
1158		{
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1160		{ 24158887, 12938817, 11085297, -8177598, -28063478, -4457083, -30576463, 64452, -6817084, -2692882 },
1161		{ 13488534, 7794716, 22236231, 5989356, 25426474, -12578208, 2350710, -3418511, -4688006, 2364226 },
1162		},
1163		{
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1165		{ 29004207, -7867081, 28661402, -640412, -12794003, -7943086, 31863255, -4135540, -278050, -15759279 },
1166		{ -6122061, -14866665, -28614905, 14569919, -10857999, -3591829, 10343412, -6976290, -29828287, -10815811 },
1167		},
1168		{
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1170		{ 20263915, 11434237, -5765435, 11236810, 13505955, -10857102, -16111345, 6493122, -19384511, 7639714 },
1171		{ -2830798, -14839232, 25403038, -8215196, -8317012, -16173699, 18006287, -16043750, 29994677, -15808121 },
1172		},
1173		{
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1175		{ 12286395, 13076066, -21775189, -1176622, -25003198, 4057652, -32018128, -8890874, 16102007, 13205847 },
1176		{ 13733362, 5599946, 10557076, 3195751, -5557991, 8536970, -25540170, 8525972, 10151379, 10394400 },
1177		},
1178		{
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1180		{ -15879800, -4525240, -8580747, -2934061, 14634845, -698278, -9449077, 3137094, -11536886, 11721158 },
1181		{ 17555939, -5013938, 8268606, 2331751, -22738815, 9761013, 9319229, 8835153, -9205489, -1280045 },
1182		},
1183		{
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1185		{ -5070281, 12367917, -30663534, 3234473, 32617080, -8422642, 29880583, -13483331, -26898490, -7867459 },
1186		{ -31975283, 5726539, 26934134, 10237677, -3173717, -605053, 24199304, 3795095, 7592688, -14992079 },
1187		},
1188		{
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1190		{ -20650503, -11961496, -27236275, 570498, 3767144, -1717540, 13891942, -1569194, 13717174, 10805743 },
1191		{ -14676630, -15644296, 15287174, 11927123, 24177847, -8175568, -796431, 14860609, -26938930, -5863836 },
1192		},
1193		},
1194		{
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1197		{ 18512079, 11319350, -20123124, 15090309, 18818594, 5271736, -22727904, 3666879, -23967430, -3299429 },
1198		{ -6789020, -3146043, 16192429, 13241070, 15898607, -14206114, -10084880, -6661110, -2403099, 5276065 },
1199		},
1200		{
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1202		{ 10342826, 3098505, 2119311, 193222, 25702612, 12233820, 23697382, 15056736, -21016438, -8202000 },
1203		{ -33150110, 3261608, 22745853, 7948688, 19370557, -15177665, -26171976, 6482814, -10300080, -11060101 },
1204		},
1205		{
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1207		{ 29506923, 4457497, 3377935, -9796444, -30510046, 12935080, 1561737, 3841096, -29003639, -6657642 },
1208		{ 10340844, -6630377, -18656632, -2278430, 12621151, -13339055, 30878497, -11824370, -25584551, 5181966 },
1209		},
1210		{
1211		{ 25940115, -12658025, 17324188, -10307374, -8671468, 15029094, 24396252, -16450922, -2322852, -12388574 },
1212		{ -21765684, 9916823, -1300409, 4079498, -1028346, 11909559, 1782390, 12641087, 20603771, -6561742 },
1213		{ -18882287, -11673380, 24849422, 11501709, 13161720, -4768874, 1925523, 11914390, 4662781, 7820689 },
1214		},
1215		{
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1217		{ -10349955, -14680563, -8211979, 2330220, -17662549, -14545780, 10658213, 6671822, 19012087, 3772772 },
1218		{ 3753511, -3421066, 10617074, 2028709, 14841030, -6721664, 28718732, -15762884, 20527771, 12988982 },
1219		},
1220		{
1221		{ -14822485, -5797269, -3707987, 12689773, -898983, -10914866, -24183046, -10564943, 3299665, -12424953 },
1222		{ -16777703, -15253301, -9642417, 4978983, 3308785, 8755439, 6943197, 6461331, -25583147, 8991218 },
1223		{ -17226263, 1816362, -1673288, -6086439, 31783888, -8175991, -32948145, 7417950, -30242287, 1507265 },
1224		},
1225		{
1226		{ 29692663, 6829891, -10498800, 4334896, 20945975, -11906496, -28887608, 8209391, 14606362, -10647073 },
1227		{ -3481570, 8707081, 32188102, 5672294, 22096700, 1711240, -33020695, 9761487, 4170404, -2085325 },
1228		{ -11587470, 14855945, -4127778, -1531857, -26649089, 15084046, 22186522, 16002000, -14276837, -8400798 },
1229		},
1230		{
1231		{ -4811456, 13761029, -31703877, -2483919, -3312471, 7869047, -7113572, -9620092, 13240845, 10965870 },
1232		{ -7742563, -8256762, -14768334, -13656260, -23232383, 12387166, 4498947, 14147411, 29514390, 4302863 },
1233		{ -13413405, -12407859, 20757302, -13801832, 14785143, 8976368, -5061276, -2144373, 17846988, -13971927 },
1234		},
1235		},
1236		{
1237		{
1238		{ -2244452, -754728, -4597030, -1066309, -6247172, 1455299, -21647728, -9214789, -5222701, 12650267 },
1239		{ -9906797, -16070310, 21134160, 12198166, -27064575, 708126, 387813, 13770293, -19134326, 10958663 },
1240		{ 22470984, 12369526, 23446014, -5441109, -21520802, -9698723, -11772496, -11574455, -25083830, 4271862 },
1241		},
1242		{
1243		{ -25169565, -10053642, -19909332, 15361595, -5984358, 2159192, 75375, -4278529, -32526221, 8469673 },
1244		{ 15854970, 4148314, -8893890, 7259002, 11666551, 13824734, -30531198, 2697372, 24154791, -9460943 },
1245		{ 15446137, -15806644, 29759747, 14019369, 30811221, -9610191, -31582008, 12840104, 24913809, 9815020 },
1246		},
1247		{
1248		{ -4709286, -5614269, -31841498, -12288893, -14443537, 10799414, -9103676, 13438769, 18735128, 9466238 },
1249		{ 11933045, 9281483, 5081055, -5183824, -2628162, -4905629, -7727821, -10896103, -22728655, 16199064 },
1250		{ 14576810, 379472, -26786533, -8317236, -29426508, -10812974, -102766, 1876699, 30801119, 2164795 },
1251		},
1252		{
1253		{ 15995086, 3199873, 13672555, 13712240, -19378835, -4647646, -13081610, -15496269, -13492807, 1268052 },
1254		{ -10290614, -3659039, -3286592, 10948818, 23037027, 3794475, -3470338, -12600221, -17055369, 3565904 },
1255		{ 29210088, -9419337, -5919792, -4952785, 10834811, -13327726, -16512102, -10820713, -27162222, -14030531 },
1256		},
1257		{
1258		{ -13161890, 15508588, 16663704, -8156150, -28349942, 9019123, -29183421, -3769423, 2244111, -14001979 },
1259		{ -5152875, -3800936, -9306475, -6071583, 16243069, 14684434, -25673088, -16180800, 13491506, 4641841 },
1260		{ 10813417, 643330, -19188515, -728916, 30292062, -16600078, 27548447, -7721242, 14476989, -12767431 },
1261		},
1262		{
1263		{ 10292079, 9984945, 6481436, 8279905, -7251514, 7032743, 27282937, -1644259, -27912810, 12651324 },
1264		{ -31185513, -813383, 22271204, 11835308, 10201545, 15351028, 17099662, 3988035, 21721536, -3148940 },
1265		{ 10202177, -6545839, -31373232, -9574638, -32150642, -8119683, -12906320, 3852694, 13216206, 14842320 },
1266		},
1267		{
1268		{ -15815640, -10601066, -6538952, -7258995, -6984659, -6581778, -31500847, 13765824, -27434397, 9900184 },
1269		{ 14465505, -13833331, -32133984, -14738873, -27443187, 12990492, 33046193, 15796406, -7051866, -8040114 },
1270		{ 30924417, -8279620, 6359016, -12816335, 16508377, 9071735, -25488601, 15413635, 9524356, -7018878 },
1271		},
1272		{
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1752		{ -23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989 },
1753		{ -30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523 },
1754		{ 4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278 },
1755		},
1756		{
1757		{ 31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045 },
1758		{ 19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377 },
1759		{ 24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480 },
1760		},
1761		{
1762		{ 17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016 },
1763		{ 510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426 },
1764		{ 18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525 },
1765		},
1766		{
1767		{ 13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396 },
1768		{ 9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080 },
1769		{ 12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892 },
1770		},
1771		{
1772		{ 15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275 },
1773		{ 11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074 },
1774		{ 20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140 },
1775		},
1776		{
1777		{ -16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717 },
1778		{ -1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101 },
1779		{ 24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127 },
1780		},
1781		},
1782		{
1783		{
1784		{ -12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632 },
1785		{ -26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415 },
1786		{ -31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160 },
1787		},
1788		{
1789		{ 31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876 },
1790		{ 22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625 },
1791		{ -15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478 },
1792		},
1793		{
1794		{ 27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164 },
1795		{ 26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595 },
1796		{ -7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248 },
1797		},
1798		{
1799		{ -16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858 },
1800		{ 15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193 },
1801		{ 8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184 },
1802		},
1803		{
1804		{ -18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942 },
1805		{ -1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635 },
1806		{ 21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948 },
1807		},
1808		{
1809		{ 11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935 },
1810		{ -25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415 },
1811		{ -15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416 },
1812		},
1813		{
1814		{ -7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018 },
1815		{ 4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778 },
1816		{ 366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659 },
1817		},
1818		{
1819		{ -24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385 },
1820		{ 18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503 },
1821		{ 476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329 },
1822		},
1823		},
1824		{
1825		{
1826		{ 20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056 },
1827		{ -13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838 },
1828		{ 24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948 },
1829		},
1830		{
1831		{ -3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691 },
1832		{ -15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118 },
1833		{ -23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517 },
1834		},
1835		{
1836		{ -20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269 },
1837		{ -6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904 },
1838		{ -23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589 },
1839		},
1840		{
1841		{ -28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193 },
1842		{ -7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910 },
1843		{ -30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930 },
1844		},
1845		{
1846		{ -7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667 },
1847		{ 25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481 },
1848		{ -9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876 },
1849		},
1850		{
1851		{ 22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640 },
1852		{ -8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278 },
1853		{ -21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112 },
1854		},
1855		{
1856		{ 26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272 },
1857		{ 17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012 },
1858		{ -10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221 },
1859		},
1860		{
1861		{ 30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046 },
1862		{ 13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345 },
1863		{ -19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310 },
1864		},
1865		},
1866		{
1867		{
1868		{ 19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937 },
1869		{ 31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636 },
1870		{ -9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008 },
1871		},
1872		{
1873		{ -2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429 },
1874		{ -15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576 },
1875		{ 31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066 },
1876		},
1877		{
1878		{ -9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490 },
1879		{ -12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104 },
1880		{ 33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053 },
1881		},
1882		{
1883		{ 31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275 },
1884		{ -20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511 },
1885		{ 22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095 },
1886		},
1887		{
1888		{ -28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439 },
1889		{ 23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939 },
1890		{ -23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424 },
1891		},
1892		{
1893		{ 2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310 },
1894		{ 3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608 },
1895		{ -32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079 },
1896		},
1897		{
1898		{ -23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101 },
1899		{ 21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418 },
1900		{ 18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576 },
1901		},
1902		{
1903		{ 30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356 },
1904		{ 9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996 },
1905		{ -26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099 },
1906		},
1907		},
1908		{
1909		{
1910		{ -26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728 },
1911		{ -13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658 },
1912		{ -10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242 },
1913		},
1914		{
1915		{ -21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001 },
1916		{ -4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766 },
1917		{ 18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373 },
1918		},
1919		{
1920		{ 26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458 },
1921		{ -17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628 },
1922		{ -13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657 },
1923		},
1924		{
1925		{ -23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062 },
1926		{ 25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616 },
1927		{ 31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014 },
1928		},
1929		{
1930		{ 24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383 },
1931		{ -25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814 },
1932		{ -20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718 },
1933		},
1934		{
1935		{ 30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417 },
1936		{ 2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222 },
1937		{ 33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444 },
1938		},
1939		{
1940		{ -20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597 },
1941		{ 23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970 },
1942		{ 1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799 },
1943		},
1944		{
1945		{ -5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647 },
1946		{ 13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511 },
1947		{ -29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032 },
1948		},
1949		},
1950		{
1951		{
1952		{ 9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834 },
1953		{ -23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461 },
1954		{ 29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062 },
1955		},
1956		{
1957		{ -25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516 },
1958		{ -20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547 },
1959		{ -24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240 },
1960		},
1961		{
1962		{ -17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038 },
1963		{ -33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741 },
1964		{ 16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103 },
1965		},
1966		{
1967		{ -19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747 },
1968		{ -1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323 },
1969		{ 31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016 },
1970		},
1971		{
1972		{ -14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373 },
1973		{ 15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228 },
1974		{ -2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141 },
1975		},
1976		{
1977		{ 16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399 },
1978		{ 11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831 },
1979		{ -185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376 },
1980		},
1981		{
1982		{ -32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313 },
1983		{ -18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958 },
1984		{ -6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577 },
1985		},
1986		{
1987		{ -22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743 },
1988		{ 29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684 },
1989		{ -20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476 },
1990		},
1991		},
1992		} ;
1993
1994		namespace {
1995
1996		inline uint8_t equal(int8_t b, int8_t c)
1997	1.72k	{
1998	1.72k	uint8_t ub = b;
1999	1.72k	uint8_t uc = c;
2000	1.72k	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2001	1.72k	uint32_t y = x; /* 0: yes; 1..255: no */
2002	1.72k	y -= 1; /* 4294967295: yes; 0..254: no */
2003	1.72k	y >>= 31; /* 1: yes; 0: no */
2004	1.72k	return static_cast<uint8_t>(y);
2005	1.72k	}
2006
2007		inline int32_t equal32(int8_t b, int8_t c)
2008	1.72k	{
2009	1.72k	return -static_cast<int32_t>(equal(b, c));
2010	1.72k	}
2011
2012		inline uint8_t negative(int8_t b)
2013	192	{
2014	192	uint64_t x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
2015	192	x >>= 63; /* 1: yes; 0: no */
2016	192	return static_cast<uint8_t>(x);
2017	192	}
2018
2019		inline void ge_precomp_0(ge_precomp* h)
2020	192	{
2021	192	fe_1(h->yplusx);
2022	192	fe_1(h->yminusx);
2023	192	fe_0(h->xy2d);
2024	192	}
2025
2026		inline void select(ge_precomp* t,
2027		const ge_precomp* base,
2028		int8_t b)
2029	192	{
2030	192	const uint8_t bnegative = negative(b);
2031	192	const uint8_t babs = b - ((-static_cast<int>(bnegative) & b) * 2);
2032	192	const int32_t neg_mask = equal32(bnegative, 1);
2033
2034	192	const int32_t mask1 = equal32(babs, 1);
2035	192	const int32_t mask2 = equal32(babs, 2);
2036	192	const int32_t mask3 = equal32(babs, 3);
2037	192	const int32_t mask4 = equal32(babs, 4);
2038	192	const int32_t mask5 = equal32(babs, 5);
2039	192	const int32_t mask6 = equal32(babs, 6);
2040	192	const int32_t mask7 = equal32(babs, 7);
2041	192	const int32_t mask8 = equal32(babs, 8);
2042
2043	192	ge_precomp_0(t);
2044
2045	2.11k	for(size_t i = 0; i != 10; ++i)
2046	1.92k	{
2047	1.92k	t->yplusx[i] = t->yplusx[i] ^
2048	1.92k	((t->yplusx[i] ^ base[0].yplusx[i]) & mask1) ^
2049	1.92k	((t->yplusx[i] ^ base[1].yplusx[i]) & mask2) ^
2050	1.92k	((t->yplusx[i] ^ base[2].yplusx[i]) & mask3) ^
2051	1.92k	((t->yplusx[i] ^ base[3].yplusx[i]) & mask4) ^
2052	1.92k	((t->yplusx[i] ^ base[4].yplusx[i]) & mask5) ^
2053	1.92k	((t->yplusx[i] ^ base[5].yplusx[i]) & mask6) ^
2054	1.92k	((t->yplusx[i] ^ base[6].yplusx[i]) & mask7) ^
2055	1.92k	((t->yplusx[i] ^ base[7].yplusx[i]) & mask8);
2056
2057	1.92k	t->yminusx[i] = t->yminusx[i] ^
2058	1.92k	((t->yminusx[i] ^ base[0].yminusx[i]) & mask1) ^
2059	1.92k	((t->yminusx[i] ^ base[1].yminusx[i]) & mask2) ^
2060	1.92k	((t->yminusx[i] ^ base[2].yminusx[i]) & mask3) ^
2061	1.92k	((t->yminusx[i] ^ base[3].yminusx[i]) & mask4) ^
2062	1.92k	((t->yminusx[i] ^ base[4].yminusx[i]) & mask5) ^
2063	1.92k	((t->yminusx[i] ^ base[5].yminusx[i]) & mask6) ^
2064	1.92k	((t->yminusx[i] ^ base[6].yminusx[i]) & mask7) ^
2065	1.92k	((t->yminusx[i] ^ base[7].yminusx[i]) & mask8);
2066
2067	1.92k	t->xy2d[i] = t->xy2d[i] ^
2068	1.92k	((t->xy2d[i] ^ base[0].xy2d[i]) & mask1) ^
2069	1.92k	((t->xy2d[i] ^ base[1].xy2d[i]) & mask2) ^
2070	1.92k	((t->xy2d[i] ^ base[2].xy2d[i]) & mask3) ^
2071	1.92k	((t->xy2d[i] ^ base[3].xy2d[i]) & mask4) ^
2072	1.92k	((t->xy2d[i] ^ base[4].xy2d[i]) & mask5) ^
2073	1.92k	((t->xy2d[i] ^ base[5].xy2d[i]) & mask6) ^
2074	1.92k	((t->xy2d[i] ^ base[6].xy2d[i]) & mask7) ^
2075	1.92k	((t->xy2d[i] ^ base[7].xy2d[i]) & mask8);
2076	1.92k	}
2077
2078	192	fe minus_xy2d;
2079	192	fe_neg(minus_xy2d, t->xy2d);
2080
2081		// If negative have to swap yminusx and yplusx
2082	2.11k	for(size_t i = 0; i != 10; ++i)
2083	1.92k	{
2084	1.92k	int32_t t_yplusx = t->yplusx[i] ^ ((t->yplusx[i] ^ t->yminusx[i]) & neg_mask);
2085	1.92k	int32_t t_yminusx = t->yminusx[i] ^ ((t->yminusx[i] ^ t->yplusx[i]) & neg_mask);
2086
2087	1.92k	t->yplusx[i] = t_yplusx;
2088	1.92k	t->yminusx[i] = t_yminusx;
2089	1.92k	t->xy2d[i] = t->xy2d[i] ^ ((t->xy2d[i] ^ minus_xy2d[i]) & neg_mask);
2090	1.92k	}
2091	192	}
2092
2093		void ge_p3_tobytes(uint8_t* s, const ge_p3* h)
2094	3	{
2095	3	fe recip;
2096	3	fe x;
2097	3	fe y;
2098
2099	3	fe_invert(recip, h->Z);
2100	3	fe_mul(x, h->X, recip);
2101	3	fe_mul(y, h->Y, recip);
2102	3	fe_tobytes(s, y);
2103	3	s[31] ^= fe_isnegative(x) << 7;
2104	3	}
2105
2106		}
2107
2108		/*
2109		h = a * B
2110		where a = a[0]+256*a[1]+...+256^31 a[31]
2111		B is the Ed25519 base point (x,4/5) with x positive.
2112
2113		Preconditions:
2114		a[31] <= 127
2115		*/
2116
2117		void ge_scalarmult_base(uint8_t out[32], const uint8_t a[32])
2118	3	{
2119	3	int8_t e[64];
2120	3	int8_t carry;
2121	3	ge_p1p1 r;
2122	3	ge_p2 s;
2123	3	ge_p3 h;
2124	3	ge_precomp t;
2125	3	int i;
2126
2127	99	for(i = 0; i < 32; ++i)
2128	96	{
2129	96	e[2 * i + 0] = (a[i] >> 0) & 15;
2130	96	e[2 * i + 1] = (a[i] >> 4) & 15;
2131	96	}
2132		/* each e[i] is between 0 and 15 */
2133		/* e[63] is between 0 and 7 */
2134
2135	3	carry = 0;
2136	192	for(i = 0; i < 63; ++i)
2137	189	{
2138	189	e[i] += carry;
2139	189	carry = e[i] + 8;
2140	189	carry >>= 4;
2141	189	e[i] -= carry << 4;
2142	189	}
2143	3	e[63] += carry;
2144		/* each e[i] is between -8 and 8 */
2145
2146	3	ge_p3_0(&h);
2147	99	for(i = 1; i < 64; i += 2)
2148	96	{
2149	96	select(&t, B_precomp[i / 2], e[i]);
2150	96	ge_madd(&r, &h, &t);
2151	96	ge_p1p1_to_p3(&h, &r);
2152	96	}
2153
2154	3	ge_p3_dbl(&r, &h);
2155	3	ge_p1p1_to_p2(&s, &r);
2156	3	ge_p2_dbl(&r, &s);
2157	3	ge_p1p1_to_p2(&s, &r);
2158	3	ge_p2_dbl(&r, &s);
2159	3	ge_p1p1_to_p2(&s, &r);
2160	3	ge_p2_dbl(&r, &s);
2161	3	ge_p1p1_to_p3(&h, &r);
2162
2163	99	for(i = 0; i < 64; i += 2)
2164	96	{
2165	96	select(&t, B_precomp[i / 2], e[i]);
2166	96	ge_madd(&r, &h, &t);
2167	96	ge_p1p1_to_p3(&h, &r);
2168	96	}
2169
2170	3	ge_p3_tobytes(out, &h);
2171	3	}
2172
2173		}

Coverage Report

Created: 2022-05-14 06:06