/src/openssl/crypto/ec/curve25519.c

Line	Count	Source
1		/*
2		* Copyright 2016-2024 The OpenSSL Project Authors. All Rights Reserved.
3		*
4		* Licensed under the Apache License 2.0 (the "License"). You may not use
5		* this file except in compliance with the License. You can obtain a copy
6		* in the file LICENSE in the source distribution or at
7		* https://www.openssl.org/source/license.html
8		*/
9
10		/*
11		* ECDSA low level APIs are deprecated for public use, but still ok for
12		* internal use.
13		*/
14		#include "internal/deprecated.h"
15
16		#include <string.h>
17		#include "crypto/ecx.h"
18		#include "ec_local.h"
19		#include <openssl/evp.h>
20		#include <openssl/sha.h>
21
22		#include "internal/numbers.h"
23
24		#if defined(X25519_ASM) && (defined(__x86_64) \|\| defined(__x86_64__) \|\| defined(_M_AMD64) \|\| defined(_M_X64))
25
26		#define BASE_2_64_IMPLEMENTED
27
28		typedef uint64_t fe64[4];
29
30		int x25519_fe64_eligible(void);
31
32		/*
33		* Following subroutines perform corresponding operations modulo
34		* 2^256-38, i.e. double the curve modulus. However, inputs and
35		* outputs are permitted to be partially reduced, i.e. to remain
36		* in [0..2^256) range. It's all tied up in final fe64_tobytes
37		* that performs full reduction modulo 2^255-19.
38		*
39		* There are no reference C implementations for these.
40		*/
41		void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
42		void x25519_fe64_sqr(fe64 h, const fe64 f);
43		void x25519_fe64_mul121666(fe64 h, fe64 f);
44		void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
45		void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
46		void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
47		#define fe64_mul x25519_fe64_mul
48		#define fe64_sqr x25519_fe64_sqr
49		#define fe64_mul121666 x25519_fe64_mul121666
50		#define fe64_add x25519_fe64_add
51		#define fe64_sub x25519_fe64_sub
52		#define fe64_tobytes x25519_fe64_tobytes
53
54		static uint64_t load_8(const uint8_t *in)
55		{
56		uint64_t result;
57
58		result = in[0];
59		result \|= ((uint64_t)in[1]) << 8;
60		result \|= ((uint64_t)in[2]) << 16;
61		result \|= ((uint64_t)in[3]) << 24;
62		result \|= ((uint64_t)in[4]) << 32;
63		result \|= ((uint64_t)in[5]) << 40;
64		result \|= ((uint64_t)in[6]) << 48;
65		result \|= ((uint64_t)in[7]) << 56;
66
67		return result;
68		}
69
70		static void fe64_frombytes(fe64 h, const uint8_t *s)
71		{
72		h[0] = load_8(s);
73		h[1] = load_8(s + 8);
74		h[2] = load_8(s + 16);
75		h[3] = load_8(s + 24) & 0x7fffffffffffffff;
76		}
77
78		static void fe64_0(fe64 h)
79		{
80		h[0] = 0;
81		h[1] = 0;
82		h[2] = 0;
83		h[3] = 0;
84		}
85
86		static void fe64_1(fe64 h)
87		{
88		h[0] = 1;
89		h[1] = 0;
90		h[2] = 0;
91		h[3] = 0;
92		}
93
94		static void fe64_copy(fe64 h, const fe64 f)
95		{
96		h[0] = f[0];
97		h[1] = f[1];
98		h[2] = f[2];
99		h[3] = f[3];
100		}
101
102		static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
103		{
104		int i;
105		uint64_t mask = 0 - (uint64_t)b;
106
107		for (i = 0; i < 4; i++) {
108		uint64_t x = f[i] ^ g[i];
109		x &= mask;
110		f[i] ^= x;
111		g[i] ^= x;
112		}
113		}
114
115		static void fe64_invert(fe64 out, const fe64 z)
116		{
117		fe64 t0;
118		fe64 t1;
119		fe64 t2;
120		fe64 t3;
121		int i;
122
123		/*
124		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
125		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
126		*/
127
128		/* t0 = z ** 2 */
129		fe64_sqr(t0, z);
130
131		/* t1 = t0 (2 2) = z ** 8 */
132		fe64_sqr(t1, t0);
133		fe64_sqr(t1, t1);
134
135		/* t1 = z * t1 = z ** 9 */
136		fe64_mul(t1, z, t1);
137		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
138		fe64_mul(t0, t0, t1);
139
140		/* t2 = t0 2 = z 22 */
141		fe64_sqr(t2, t0);
142
143		/* t1 = t1 * t2 = z (2 5 - 1) */
144		fe64_mul(t1, t1, t2);
145
146		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
147		fe64_sqr(t2, t1);
148		for (i = 1; i < 5; ++i)
149		fe64_sqr(t2, t2);
150
151		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
152		fe64_mul(t1, t2, t1);
153
154		/* Continuing similarly... */
155
156		/* t2 = z (2 20 - 1) */
157		fe64_sqr(t2, t1);
158		for (i = 1; i < 10; ++i)
159		fe64_sqr(t2, t2);
160
161		fe64_mul(t2, t2, t1);
162
163		/* t2 = z (2 40 - 1) */
164		fe64_sqr(t3, t2);
165		for (i = 1; i < 20; ++i)
166		fe64_sqr(t3, t3);
167
168		fe64_mul(t2, t3, t2);
169
170		/* t2 = z (2 10) * (2 ** 40 - 1) */
171		for (i = 0; i < 10; ++i)
172		fe64_sqr(t2, t2);
173
174		/* t1 = z (2 50 - 1) */
175		fe64_mul(t1, t2, t1);
176
177		/* t2 = z (2 100 - 1) */
178		fe64_sqr(t2, t1);
179		for (i = 1; i < 50; ++i)
180		fe64_sqr(t2, t2);
181
182		fe64_mul(t2, t2, t1);
183
184		/* t2 = z (2 200 - 1) */
185		fe64_sqr(t3, t2);
186		for (i = 1; i < 100; ++i)
187		fe64_sqr(t3, t3);
188
189		fe64_mul(t2, t3, t2);
190
191		/* t2 = z ((2 50) * (2 ** 200 - 1) */
192		for (i = 0; i < 50; ++i)
193		fe64_sqr(t2, t2);
194
195		/* t1 = z (2 250 - 1) */
196		fe64_mul(t1, t2, t1);
197
198		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
199		for (i = 0; i < 5; ++i)
200		fe64_sqr(t1, t1);
201
202		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
203		fe64_mul(out, t1, t0);
204		}
205
206		/*
207		* Duplicate of original x25519_scalar_mult_generic, but using
208		* fe64_* subroutines.
209		*/
210		static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
211		const uint8_t point[32])
212		{
213		fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
214		uint8_t e[32];
215		unsigned swap = 0;
216		int pos;
217
218		memcpy(e, scalar, 32);
219		e[0] &= 0xf8;
220		e[31] &= 0x7f;
221		e[31] \|= 0x40;
222		fe64_frombytes(x1, point);
223		fe64_1(x2);
224		fe64_0(z2);
225		fe64_copy(x3, x1);
226		fe64_1(z3);
227
228		for (pos = 254; pos >= 0; --pos) {
229		unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
230
231		swap ^= b;
232		fe64_cswap(x2, x3, swap);
233		fe64_cswap(z2, z3, swap);
234		swap = b;
235		fe64_sub(tmp0, x3, z3);
236		fe64_sub(tmp1, x2, z2);
237		fe64_add(x2, x2, z2);
238		fe64_add(z2, x3, z3);
239		/* The original copy in x25519_scalar_mult_generic uses argument order
240		* fe_mul(z3, tmp0, x2), with the input arguments swapped.
241		*
242		* The assembly implementation of fe64_mul used here runs faster in
243		* parallel with its nearby instructions when an earlier-computable
244		* input (like tmp0) is passed as the 2nd input because it consumes
245		* the 2nd input at a faster rate than the 1st input. */
246		fe64_mul(z3, x2, tmp0);
247		fe64_mul(z2, z2, tmp1);
248		fe64_sqr(tmp0, tmp1);
249		fe64_sqr(tmp1, x2);
250		fe64_add(x3, z3, z2);
251		fe64_sub(z2, z3, z2);
252		fe64_mul(x2, tmp1, tmp0);
253		fe64_sub(tmp1, tmp1, tmp0);
254		fe64_sqr(z2, z2);
255		fe64_mul121666(z3, tmp1);
256		fe64_sqr(x3, x3);
257		fe64_add(tmp0, tmp0, z3);
258		fe64_mul(z3, x1, z2);
259		fe64_mul(z2, tmp1, tmp0);
260		}
261
262		fe64_invert(z2, z2);
263		fe64_mul(x2, x2, z2);
264		fe64_tobytes(out, x2);
265
266		OPENSSL_cleanse(e, sizeof(e));
267		}
268		#endif
269
270		#if defined(X25519_ASM) \
271		\|\| (defined(INT128_MAX) \
272		&& !defined(__sparc__) \
273		&& (!defined(__SIZEOF_LONG__) \|\| (__SIZEOF_LONG__ == 8)) \
274		&& !(defined(__ANDROID__) && !defined(__clang__)))
275		/*
276		* Base 2^51 implementation. It's virtually no different from reference
277		* base 2^25.5 implementation in respect to lax boundary conditions for
278		* intermediate values and even individual limbs. So that whatever you
279		* know about the reference, applies even here...
280		*/
281		#define BASE_2_51_IMPLEMENTED
282
283		typedef uint64_t fe51[5];
284
285		static const uint64_t MASK51 = 0x7ffffffffffff;
286
287		static uint64_t load_7(const uint8_t *in)
288	0	{
289	0	uint64_t result;
290
291	0	result = in[0];
292	0	result \|= ((uint64_t)in[1]) << 8;
293	0	result \|= ((uint64_t)in[2]) << 16;
294	0	result \|= ((uint64_t)in[3]) << 24;
295	0	result \|= ((uint64_t)in[4]) << 32;
296	0	result \|= ((uint64_t)in[5]) << 40;
297	0	result \|= ((uint64_t)in[6]) << 48;
298
299	0	return result;
300	0	}
301
302		static uint64_t load_6(const uint8_t *in)
303	0	{
304	0	uint64_t result;
305
306	0	result = in[0];
307	0	result \|= ((uint64_t)in[1]) << 8;
308	0	result \|= ((uint64_t)in[2]) << 16;
309	0	result \|= ((uint64_t)in[3]) << 24;
310	0	result \|= ((uint64_t)in[4]) << 32;
311	0	result \|= ((uint64_t)in[5]) << 40;
312
313	0	return result;
314	0	}
315
316		static void fe51_frombytes(fe51 h, const uint8_t *s)
317	0	{
318	0	uint64_t h0 = load_7(s); /* 56 bits */
319	0	uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
320	0	uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
321	0	uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
322	0	uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
323
324	0	h1 \|= h0 >> 51;
325	0	h0 &= MASK51;
326	0	h2 \|= h1 >> 51;
327	0	h1 &= MASK51;
328	0	h3 \|= h2 >> 51;
329	0	h2 &= MASK51;
330	0	h4 \|= h3 >> 51;
331	0	h3 &= MASK51;
332
333	0	h[0] = h0;
334	0	h[1] = h1;
335	0	h[2] = h2;
336	0	h[3] = h3;
337	0	h[4] = h4;
338	0	}
339
340		static void fe51_tobytes(uint8_t *s, const fe51 h)
341	0	{
342	0	uint64_t h0 = h[0];
343	0	uint64_t h1 = h[1];
344	0	uint64_t h2 = h[2];
345	0	uint64_t h3 = h[3];
346	0	uint64_t h4 = h[4];
347	0	uint64_t q;
348
349		/* compare to modulus */
350	0	q = (h0 + 19) >> 51;
351	0	q = (h1 + q) >> 51;
352	0	q = (h2 + q) >> 51;
353	0	q = (h3 + q) >> 51;
354	0	q = (h4 + q) >> 51;
355
356		/* full reduce */
357	0	h0 += 19 * q;
358	0	h1 += h0 >> 51;
359	0	h0 &= MASK51;
360	0	h2 += h1 >> 51;
361	0	h1 &= MASK51;
362	0	h3 += h2 >> 51;
363	0	h2 &= MASK51;
364	0	h4 += h3 >> 51;
365	0	h3 &= MASK51;
366	0	h4 &= MASK51;
367
368		/* smash */
369	0	s[0] = (uint8_t)(h0 >> 0);
370	0	s[1] = (uint8_t)(h0 >> 8);
371	0	s[2] = (uint8_t)(h0 >> 16);
372	0	s[3] = (uint8_t)(h0 >> 24);
373	0	s[4] = (uint8_t)(h0 >> 32);
374	0	s[5] = (uint8_t)(h0 >> 40);
375	0	s[6] = (uint8_t)((h0 >> 48) \| ((uint32_t)h1 << 3));
376	0	s[7] = (uint8_t)(h1 >> 5);
377	0	s[8] = (uint8_t)(h1 >> 13);
378	0	s[9] = (uint8_t)(h1 >> 21);
379	0	s[10] = (uint8_t)(h1 >> 29);
380	0	s[11] = (uint8_t)(h1 >> 37);
381	0	s[12] = (uint8_t)((h1 >> 45) \| ((uint32_t)h2 << 6));
382	0	s[13] = (uint8_t)(h2 >> 2);
383	0	s[14] = (uint8_t)(h2 >> 10);
384	0	s[15] = (uint8_t)(h2 >> 18);
385	0	s[16] = (uint8_t)(h2 >> 26);
386	0	s[17] = (uint8_t)(h2 >> 34);
387	0	s[18] = (uint8_t)(h2 >> 42);
388	0	s[19] = (uint8_t)((h2 >> 50) \| ((uint32_t)h3 << 1));
389	0	s[20] = (uint8_t)(h3 >> 7);
390	0	s[21] = (uint8_t)(h3 >> 15);
391	0	s[22] = (uint8_t)(h3 >> 23);
392	0	s[23] = (uint8_t)(h3 >> 31);
393	0	s[24] = (uint8_t)(h3 >> 39);
394	0	s[25] = (uint8_t)((h3 >> 47) \| ((uint32_t)h4 << 4));
395	0	s[26] = (uint8_t)(h4 >> 4);
396	0	s[27] = (uint8_t)(h4 >> 12);
397	0	s[28] = (uint8_t)(h4 >> 20);
398	0	s[29] = (uint8_t)(h4 >> 28);
399	0	s[30] = (uint8_t)(h4 >> 36);
400	0	s[31] = (uint8_t)(h4 >> 44);
401	0	}
402
403		#if defined(X25519_ASM)
404		void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
405		void x25519_fe51_sqr(fe51 h, const fe51 f);
406		void x25519_fe51_mul121666(fe51 h, fe51 f);
407		#define fe51_mul x25519_fe51_mul
408		#define fe51_sq x25519_fe51_sqr
409		#define fe51_mul121666 x25519_fe51_mul121666
410		#else
411
412		typedef uint128_t u128;
413
414		static void fe51_mul(fe51 h, const fe51 f, const fe51 g)
415	0	{
416	0	u128 h0, h1, h2, h3, h4;
417	0	uint64_t f_i, g0, g1, g2, g3, g4;
418
419	0	f_i = f[0];
420	0	h0 = (u128)f_i * (g0 = g[0]);
421	0	h1 = (u128)f_i * (g1 = g[1]);
422	0	h2 = (u128)f_i * (g2 = g[2]);
423	0	h3 = (u128)f_i * (g3 = g[3]);
424	0	h4 = (u128)f_i * (g4 = g[4]);
425
426	0	f_i = f[1];
427	0	h0 += (u128)f_i * (g4 *= 19);
428	0	h1 += (u128)f_i * g0;
429	0	h2 += (u128)f_i * g1;
430	0	h3 += (u128)f_i * g2;
431	0	h4 += (u128)f_i * g3;
432
433	0	f_i = f[2];
434	0	h0 += (u128)f_i * (g3 *= 19);
435	0	h1 += (u128)f_i * g4;
436	0	h2 += (u128)f_i * g0;
437	0	h3 += (u128)f_i * g1;
438	0	h4 += (u128)f_i * g2;
439
440	0	f_i = f[3];
441	0	h0 += (u128)f_i * (g2 *= 19);
442	0	h1 += (u128)f_i * g3;
443	0	h2 += (u128)f_i * g4;
444	0	h3 += (u128)f_i * g0;
445	0	h4 += (u128)f_i * g1;
446
447	0	f_i = f[4];
448	0	h0 += (u128)f_i * (g1 *= 19);
449	0	h1 += (u128)f_i * g2;
450	0	h2 += (u128)f_i * g3;
451	0	h3 += (u128)f_i * g4;
452	0	h4 += (u128)f_i * g0;
453
454		/* partial [lazy] reduction */
455	0	h3 += (uint64_t)(h2 >> 51);
456	0	g2 = (uint64_t)h2 & MASK51;
457	0	h1 += (uint64_t)(h0 >> 51);
458	0	g0 = (uint64_t)h0 & MASK51;
459
460	0	h4 += (uint64_t)(h3 >> 51);
461	0	g3 = (uint64_t)h3 & MASK51;
462	0	g2 += (uint64_t)(h1 >> 51);
463	0	g1 = (uint64_t)h1 & MASK51;
464
465	0	g0 += (uint64_t)(h4 >> 51) * 19;
466	0	g4 = (uint64_t)h4 & MASK51;
467	0	g3 += g2 >> 51;
468	0	g2 &= MASK51;
469	0	g1 += g0 >> 51;
470	0	g0 &= MASK51;
471
472	0	h[0] = g0;
473	0	h[1] = g1;
474	0	h[2] = g2;
475	0	h[3] = g3;
476	0	h[4] = g4;
477	0	}
478
479		static void fe51_sq(fe51 h, const fe51 f)
480	0	{
481		#if defined(OPENSSL_SMALL_FOOTPRINT)
482		fe51_mul(h, f, f);
483		#else
484		/* dedicated squaring gives 16-25% overall improvement */
485	0	uint64_t g0 = f[0];
486	0	uint64_t g1 = f[1];
487	0	uint64_t g2 = f[2];
488	0	uint64_t g3 = f[3];
489	0	uint64_t g4 = f[4];
490	0	u128 h0, h1, h2, h3, h4;
491
492	0	h0 = (u128)g0 * g0;
493	0	g0 *= 2;
494	0	h1 = (u128)g0 * g1;
495	0	h2 = (u128)g0 * g2;
496	0	h3 = (u128)g0 * g3;
497	0	h4 = (u128)g0 * g4;
498
499	0	g0 = g4; /* borrow g0 */
500	0	h3 += (u128)g0 * (g4 *= 19);
501
502	0	h2 += (u128)g1 * g1;
503	0	g1 *= 2;
504	0	h3 += (u128)g1 * g2;
505	0	h4 += (u128)g1 * g3;
506	0	h0 += (u128)g1 * g4;
507
508	0	g0 = g3; /* borrow g0 */
509	0	h1 += (u128)g0 * (g3 *= 19);
510	0	h2 += (u128)(g0 * 2) * g4;
511
512	0	h4 += (u128)g2 * g2;
513	0	g2 *= 2;
514	0	h0 += (u128)g2 * g3;
515	0	h1 += (u128)g2 * g4;
516
517		/* partial [lazy] reduction */
518	0	h3 += (uint64_t)(h2 >> 51);
519	0	g2 = (uint64_t)h2 & MASK51;
520	0	h1 += (uint64_t)(h0 >> 51);
521	0	g0 = (uint64_t)h0 & MASK51;
522
523	0	h4 += (uint64_t)(h3 >> 51);
524	0	g3 = (uint64_t)h3 & MASK51;
525	0	g2 += (uint64_t)(h1 >> 51);
526	0	g1 = (uint64_t)h1 & MASK51;
527
528	0	g0 += (uint64_t)(h4 >> 51) * 19;
529	0	g4 = (uint64_t)h4 & MASK51;
530	0	g3 += g2 >> 51;
531	0	g2 &= MASK51;
532	0	g1 += g0 >> 51;
533	0	g0 &= MASK51;
534
535	0	h[0] = g0;
536	0	h[1] = g1;
537	0	h[2] = g2;
538	0	h[3] = g3;
539	0	h[4] = g4;
540	0	#endif
541	0	}
542
543		static void fe51_mul121666(fe51 h, fe51 f)
544	0	{
545	0	u128 h0 = f[0] * (u128)121666;
546	0	u128 h1 = f[1] * (u128)121666;
547	0	u128 h2 = f[2] * (u128)121666;
548	0	u128 h3 = f[3] * (u128)121666;
549	0	u128 h4 = f[4] * (u128)121666;
550	0	uint64_t g0, g1, g2, g3, g4;
551
552	0	h3 += (uint64_t)(h2 >> 51);
553	0	g2 = (uint64_t)h2 & MASK51;
554	0	h1 += (uint64_t)(h0 >> 51);
555	0	g0 = (uint64_t)h0 & MASK51;
556
557	0	h4 += (uint64_t)(h3 >> 51);
558	0	g3 = (uint64_t)h3 & MASK51;
559	0	g2 += (uint64_t)(h1 >> 51);
560	0	g1 = (uint64_t)h1 & MASK51;
561
562	0	g0 += (uint64_t)(h4 >> 51) * 19;
563	0	g4 = (uint64_t)h4 & MASK51;
564	0	g3 += g2 >> 51;
565	0	g2 &= MASK51;
566	0	g1 += g0 >> 51;
567	0	g0 &= MASK51;
568
569	0	h[0] = g0;
570	0	h[1] = g1;
571	0	h[2] = g2;
572	0	h[3] = g3;
573	0	h[4] = g4;
574	0	}
575		#endif
576
577		static void fe51_add(fe51 h, const fe51 f, const fe51 g)
578	0	{
579	0	h[0] = f[0] + g[0];
580	0	h[1] = f[1] + g[1];
581	0	h[2] = f[2] + g[2];
582	0	h[3] = f[3] + g[3];
583	0	h[4] = f[4] + g[4];
584	0	}
585
586		static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
587	0	{
588		/*
589		* Add 2*modulus to ensure that result remains positive
590		* even if subtrahend is partially reduced.
591		*/
592	0	h[0] = (f[0] + 0xfffffffffffda) - g[0];
593	0	h[1] = (f[1] + 0xffffffffffffe) - g[1];
594	0	h[2] = (f[2] + 0xffffffffffffe) - g[2];
595	0	h[3] = (f[3] + 0xffffffffffffe) - g[3];
596	0	h[4] = (f[4] + 0xffffffffffffe) - g[4];
597	0	}
598
599		static void fe51_0(fe51 h)
600	0	{
601	0	h[0] = 0;
602	0	h[1] = 0;
603	0	h[2] = 0;
604	0	h[3] = 0;
605	0	h[4] = 0;
606	0	}
607
608		static void fe51_1(fe51 h)
609	0	{
610	0	h[0] = 1;
611	0	h[1] = 0;
612	0	h[2] = 0;
613	0	h[3] = 0;
614	0	h[4] = 0;
615	0	}
616
617		static void fe51_copy(fe51 h, const fe51 f)
618	0	{
619	0	h[0] = f[0];
620	0	h[1] = f[1];
621	0	h[2] = f[2];
622	0	h[3] = f[3];
623	0	h[4] = f[4];
624	0	}
625
626		static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
627	0	{
628	0	int i;
629	0	uint64_t mask = 0 - (uint64_t)b;
630
631	0	for (i = 0; i < 5; i++) {
632	0	int64_t x = f[i] ^ g[i];
633	0	x &= mask;
634	0	f[i] ^= x;
635	0	g[i] ^= x;
636	0	}
637	0	}
638
639		static void fe51_invert(fe51 out, const fe51 z)
640	0	{
641	0	fe51 t0;
642	0	fe51 t1;
643	0	fe51 t2;
644	0	fe51 t3;
645	0	int i;
646
647		/*
648		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
649		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
650		*/
651
652		/* t0 = z ** 2 */
653	0	fe51_sq(t0, z);
654
655		/* t1 = t0 (2 2) = z ** 8 */
656	0	fe51_sq(t1, t0);
657	0	fe51_sq(t1, t1);
658
659		/* t1 = z * t1 = z ** 9 */
660	0	fe51_mul(t1, z, t1);
661		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
662	0	fe51_mul(t0, t0, t1);
663
664		/* t2 = t0 2 = z 22 */
665	0	fe51_sq(t2, t0);
666
667		/* t1 = t1 * t2 = z (2 5 - 1) */
668	0	fe51_mul(t1, t1, t2);
669
670		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
671	0	fe51_sq(t2, t1);
672	0	for (i = 1; i < 5; ++i)
673	0	fe51_sq(t2, t2);
674
675		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
676	0	fe51_mul(t1, t2, t1);
677
678		/* Continuing similarly... */
679
680		/* t2 = z (2 20 - 1) */
681	0	fe51_sq(t2, t1);
682	0	for (i = 1; i < 10; ++i)
683	0	fe51_sq(t2, t2);
684
685	0	fe51_mul(t2, t2, t1);
686
687		/* t2 = z (2 40 - 1) */
688	0	fe51_sq(t3, t2);
689	0	for (i = 1; i < 20; ++i)
690	0	fe51_sq(t3, t3);
691
692	0	fe51_mul(t2, t3, t2);
693
694		/* t2 = z (2 10) * (2 ** 40 - 1) */
695	0	for (i = 0; i < 10; ++i)
696	0	fe51_sq(t2, t2);
697
698		/* t1 = z (2 50 - 1) */
699	0	fe51_mul(t1, t2, t1);
700
701		/* t2 = z (2 100 - 1) */
702	0	fe51_sq(t2, t1);
703	0	for (i = 1; i < 50; ++i)
704	0	fe51_sq(t2, t2);
705
706	0	fe51_mul(t2, t2, t1);
707
708		/* t2 = z (2 200 - 1) */
709	0	fe51_sq(t3, t2);
710	0	for (i = 1; i < 100; ++i)
711	0	fe51_sq(t3, t3);
712
713	0	fe51_mul(t2, t3, t2);
714
715		/* t2 = z ((2 50) * (2 ** 200 - 1) */
716	0	for (i = 0; i < 50; ++i)
717	0	fe51_sq(t2, t2);
718
719		/* t1 = z (2 250 - 1) */
720	0	fe51_mul(t1, t2, t1);
721
722		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
723	0	for (i = 0; i < 5; ++i)
724	0	fe51_sq(t1, t1);
725
726		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
727	0	fe51_mul(out, t1, t0);
728	0	}
729
730		/*
731		* Duplicate of original x25519_scalar_mult_generic, but using
732		* fe51_* subroutines.
733		*/
734		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
735		const uint8_t point[32])
736	0	{
737	0	fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
738	0	uint8_t e[32];
739	0	unsigned swap = 0;
740	0	int pos;
741
742		#ifdef BASE_2_64_IMPLEMENTED
743		if (x25519_fe64_eligible()) {
744		x25519_scalar_mulx(out, scalar, point);
745		return;
746		}
747		#endif
748
749	0	memcpy(e, scalar, 32);
750	0	e[0] &= 0xf8;
751	0	e[31] &= 0x7f;
752	0	e[31] \|= 0x40;
753	0	fe51_frombytes(x1, point);
754	0	fe51_1(x2);
755	0	fe51_0(z2);
756	0	fe51_copy(x3, x1);
757	0	fe51_1(z3);
758
759	0	for (pos = 254; pos >= 0; --pos) {
760	0	unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
761
762	0	swap ^= b;
763	0	fe51_cswap(x2, x3, swap);
764	0	fe51_cswap(z2, z3, swap);
765	0	swap = b;
766	0	fe51_sub(tmp0, x3, z3);
767	0	fe51_sub(tmp1, x2, z2);
768	0	fe51_add(x2, x2, z2);
769	0	fe51_add(z2, x3, z3);
770	0	fe51_mul(z3, tmp0, x2);
771	0	fe51_mul(z2, z2, tmp1);
772	0	fe51_sq(tmp0, tmp1);
773	0	fe51_sq(tmp1, x2);
774	0	fe51_add(x3, z3, z2);
775	0	fe51_sub(z2, z3, z2);
776	0	fe51_mul(x2, tmp1, tmp0);
777	0	fe51_sub(tmp1, tmp1, tmp0);
778	0	fe51_sq(z2, z2);
779	0	fe51_mul121666(z3, tmp1);
780	0	fe51_sq(x3, x3);
781	0	fe51_add(tmp0, tmp0, z3);
782	0	fe51_mul(z3, x1, z2);
783	0	fe51_mul(z2, tmp1, tmp0);
784	0	}
785
786	0	fe51_invert(z2, z2);
787	0	fe51_mul(x2, x2, z2);
788	0	fe51_tobytes(out, x2);
789
790	0	OPENSSL_cleanse(e, sizeof(e));
791	0	}
792		#endif
793
794		/*
795		* Reference base 2^25.5 implementation.
796		*
797		* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
798		* 20141124 (http://bench.cr.yp.to/supercop.html).
799		*
800		* The field functions are shared by Ed25519 and X25519 where possible.
801		*/
802
803		/*
804		* fe means field element. Here the field is \Z/(2^255-19). An element t,
805		* entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
806		* t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
807		* context.
808		*/
809		typedef int32_t fe[10];
810
811		static const int64_t kBottom21Bits = 0x1fffffLL;
812		static const int64_t kBottom25Bits = 0x1ffffffLL;
813		static const int64_t kBottom26Bits = 0x3ffffffLL;
814		static const int64_t kTop39Bits = 0xfffffffffe000000LL;
815		static const int64_t kTop38Bits = 0xfffffffffc000000LL;
816
817		static uint64_t load_3(const uint8_t *in)
818	0	{
819	0	uint64_t result;
820
821	0	result = ((uint64_t)in[0]);
822	0	result \|= ((uint64_t)in[1]) << 8;
823	0	result \|= ((uint64_t)in[2]) << 16;
824	0	return result;
825	0	}
826
827		static uint64_t load_4(const uint8_t *in)
828	0	{
829	0	uint64_t result;
830
831	0	result = ((uint64_t)in[0]);
832	0	result \|= ((uint64_t)in[1]) << 8;
833	0	result \|= ((uint64_t)in[2]) << 16;
834	0	result \|= ((uint64_t)in[3]) << 24;
835	0	return result;
836	0	}
837
838		static void fe_frombytes(fe h, const uint8_t *s)
839	0	{
840		/* Ignores top bit of h. */
841	0	int64_t h0 = load_4(s);
842	0	int64_t h1 = load_3(s + 4) << 6;
843	0	int64_t h2 = load_3(s + 7) << 5;
844	0	int64_t h3 = load_3(s + 10) << 3;
845	0	int64_t h4 = load_3(s + 13) << 2;
846	0	int64_t h5 = load_4(s + 16);
847	0	int64_t h6 = load_3(s + 20) << 7;
848	0	int64_t h7 = load_3(s + 23) << 5;
849	0	int64_t h8 = load_3(s + 26) << 4;
850	0	int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
851	0	int64_t carry0;
852	0	int64_t carry1;
853	0	int64_t carry2;
854	0	int64_t carry3;
855	0	int64_t carry4;
856	0	int64_t carry5;
857	0	int64_t carry6;
858	0	int64_t carry7;
859	0	int64_t carry8;
860	0	int64_t carry9;
861
862	0	carry9 = h9 + (1 << 24);
863	0	h0 += (carry9 >> 25) * 19;
864	0	h9 -= carry9 & kTop39Bits;
865	0	carry1 = h1 + (1 << 24);
866	0	h2 += carry1 >> 25;
867	0	h1 -= carry1 & kTop39Bits;
868	0	carry3 = h3 + (1 << 24);
869	0	h4 += carry3 >> 25;
870	0	h3 -= carry3 & kTop39Bits;
871	0	carry5 = h5 + (1 << 24);
872	0	h6 += carry5 >> 25;
873	0	h5 -= carry5 & kTop39Bits;
874	0	carry7 = h7 + (1 << 24);
875	0	h8 += carry7 >> 25;
876	0	h7 -= carry7 & kTop39Bits;
877
878	0	carry0 = h0 + (1 << 25);
879	0	h1 += carry0 >> 26;
880	0	h0 -= carry0 & kTop38Bits;
881	0	carry2 = h2 + (1 << 25);
882	0	h3 += carry2 >> 26;
883	0	h2 -= carry2 & kTop38Bits;
884	0	carry4 = h4 + (1 << 25);
885	0	h5 += carry4 >> 26;
886	0	h4 -= carry4 & kTop38Bits;
887	0	carry6 = h6 + (1 << 25);
888	0	h7 += carry6 >> 26;
889	0	h6 -= carry6 & kTop38Bits;
890	0	carry8 = h8 + (1 << 25);
891	0	h9 += carry8 >> 26;
892	0	h8 -= carry8 & kTop38Bits;
893
894	0	h[0] = (int32_t)h0;
895	0	h[1] = (int32_t)h1;
896	0	h[2] = (int32_t)h2;
897	0	h[3] = (int32_t)h3;
898	0	h[4] = (int32_t)h4;
899	0	h[5] = (int32_t)h5;
900	0	h[6] = (int32_t)h6;
901	0	h[7] = (int32_t)h7;
902	0	h[8] = (int32_t)h8;
903	0	h[9] = (int32_t)h9;
904	0	}
905
906		/*
907		* Preconditions:
908		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
909		*
910		* Write p=2^255-19; q=floor(h/p).
911		* Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
912		*
913		* Proof:
914		* Have \|h\|<=p so \|q\|<=1 so \|19^2 2^(-255) q\|<1/4.
915		* Also have \|h-2^230 h9\|<2^231 so \|19 2^(-255)(h-2^230 h9)\|<1/4.
916		*
917		* Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
918		* Then 0<y<1.
919		*
920		* Write r=h-pq.
921		* Have 0<=r<=p-1=2^255-20.
922		* Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
923		*
924		* Write x=r+19(2^-255)r+y.
925		* Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
926		*
927		* Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
928		* so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
929		*/
930		static void fe_tobytes(uint8_t *s, const fe h)
931	0	{
932	0	int32_t h0 = h[0];
933	0	int32_t h1 = h[1];
934	0	int32_t h2 = h[2];
935	0	int32_t h3 = h[3];
936	0	int32_t h4 = h[4];
937	0	int32_t h5 = h[5];
938	0	int32_t h6 = h[6];
939	0	int32_t h7 = h[7];
940	0	int32_t h8 = h[8];
941	0	int32_t h9 = h[9];
942	0	int32_t q;
943
944	0	q = (19 * h9 + (((int32_t)1) << 24)) >> 25;
945	0	q = (h0 + q) >> 26;
946	0	q = (h1 + q) >> 25;
947	0	q = (h2 + q) >> 26;
948	0	q = (h3 + q) >> 25;
949	0	q = (h4 + q) >> 26;
950	0	q = (h5 + q) >> 25;
951	0	q = (h6 + q) >> 26;
952	0	q = (h7 + q) >> 25;
953	0	q = (h8 + q) >> 26;
954	0	q = (h9 + q) >> 25;
955
956		/* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
957	0	h0 += 19 * q;
958		/* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
959
960	0	h1 += h0 >> 26;
961	0	h0 &= kBottom26Bits;
962	0	h2 += h1 >> 25;
963	0	h1 &= kBottom25Bits;
964	0	h3 += h2 >> 26;
965	0	h2 &= kBottom26Bits;
966	0	h4 += h3 >> 25;
967	0	h3 &= kBottom25Bits;
968	0	h5 += h4 >> 26;
969	0	h4 &= kBottom26Bits;
970	0	h6 += h5 >> 25;
971	0	h5 &= kBottom25Bits;
972	0	h7 += h6 >> 26;
973	0	h6 &= kBottom26Bits;
974	0	h8 += h7 >> 25;
975	0	h7 &= kBottom25Bits;
976	0	h9 += h8 >> 26;
977	0	h8 &= kBottom26Bits;
978	0	h9 &= kBottom25Bits;
979		/* h10 = carry9 */
980
981		/*
982		* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
983		* Have h0+...+2^230 h9 between 0 and 2^255-1;
984		* evidently 2^255 h10-2^255 q = 0.
985		* Goal: Output h0+...+2^230 h9.
986		*/
987	0	s[0] = (uint8_t)(h0 >> 0);
988	0	s[1] = (uint8_t)(h0 >> 8);
989	0	s[2] = (uint8_t)(h0 >> 16);
990	0	s[3] = (uint8_t)((h0 >> 24) \| ((uint32_t)(h1) << 2));
991	0	s[4] = (uint8_t)(h1 >> 6);
992	0	s[5] = (uint8_t)(h1 >> 14);
993	0	s[6] = (uint8_t)((h1 >> 22) \| ((uint32_t)(h2) << 3));
994	0	s[7] = (uint8_t)(h2 >> 5);
995	0	s[8] = (uint8_t)(h2 >> 13);
996	0	s[9] = (uint8_t)((h2 >> 21) \| ((uint32_t)(h3) << 5));
997	0	s[10] = (uint8_t)(h3 >> 3);
998	0	s[11] = (uint8_t)(h3 >> 11);
999	0	s[12] = (uint8_t)((h3 >> 19) \| ((uint32_t)(h4) << 6));
1000	0	s[13] = (uint8_t)(h4 >> 2);
1001	0	s[14] = (uint8_t)(h4 >> 10);
1002	0	s[15] = (uint8_t)(h4 >> 18);
1003	0	s[16] = (uint8_t)(h5 >> 0);
1004	0	s[17] = (uint8_t)(h5 >> 8);
1005	0	s[18] = (uint8_t)(h5 >> 16);
1006	0	s[19] = (uint8_t)((h5 >> 24) \| ((uint32_t)(h6) << 1));
1007	0	s[20] = (uint8_t)(h6 >> 7);
1008	0	s[21] = (uint8_t)(h6 >> 15);
1009	0	s[22] = (uint8_t)((h6 >> 23) \| ((uint32_t)(h7) << 3));
1010	0	s[23] = (uint8_t)(h7 >> 5);
1011	0	s[24] = (uint8_t)(h7 >> 13);
1012	0	s[25] = (uint8_t)((h7 >> 21) \| ((uint32_t)(h8) << 4));
1013	0	s[26] = (uint8_t)(h8 >> 4);
1014	0	s[27] = (uint8_t)(h8 >> 12);
1015	0	s[28] = (uint8_t)((h8 >> 20) \| ((uint32_t)(h9) << 6));
1016	0	s[29] = (uint8_t)(h9 >> 2);
1017	0	s[30] = (uint8_t)(h9 >> 10);
1018	0	s[31] = (uint8_t)(h9 >> 18);
1019	0	}
1020
1021		/* h = f */
1022		static void fe_copy(fe h, const fe f)
1023	0	{
1024	0	memmove(h, f, sizeof(int32_t) * 10);
1025	0	}
1026
1027		/* h = 0 */
1028		static void fe_0(fe h)
1029	0	{
1030	0	memset(h, 0, sizeof(int32_t) * 10);
1031	0	}
1032
1033		/* h = 1 */
1034		static void fe_1(fe h)
1035	0	{
1036	0	memset(h, 0, sizeof(int32_t) * 10);
1037	0	h[0] = 1;
1038	0	}
1039
1040		/*
1041		* h = f + g
1042		*
1043		* Can overlap h with f or g.
1044		*
1045		* Preconditions:
1046		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1047		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1048		*
1049		* Postconditions:
1050		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1051		*/
1052		static void fe_add(fe h, const fe f, const fe g)
1053	0	{
1054	0	unsigned i;
1055
1056	0	for (i = 0; i < 10; i++) {
1057	0	h[i] = f[i] + g[i];
1058	0	}
1059	0	}
1060
1061		/*
1062		* h = f - g
1063		*
1064		* Can overlap h with f or g.
1065		*
1066		* Preconditions:
1067		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1068		* \|g\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1069		*
1070		* Postconditions:
1071		* \|h\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1072		*/
1073		static void fe_sub(fe h, const fe f, const fe g)
1074	0	{
1075	0	unsigned i;
1076
1077	0	for (i = 0; i < 10; i++) {
1078	0	h[i] = f[i] - g[i];
1079	0	}
1080	0	}
1081
1082		/*
1083		* h = f * g
1084		*
1085		* Can overlap h with f or g.
1086		*
1087		* Preconditions:
1088		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1089		* \|g\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1090		*
1091		* Postconditions:
1092		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1093		*
1094		* Notes on implementation strategy:
1095		*
1096		* Using schoolbook multiplication.
1097		* Karatsuba would save a little in some cost models.
1098		*
1099		* Most multiplications by 2 and 19 are 32-bit precomputations;
1100		* cheaper than 64-bit postcomputations.
1101		*
1102		* There is one remaining multiplication by 19 in the carry chain;
1103		* one *19 precomputation can be merged into this,
1104		* but the resulting data flow is considerably less clean.
1105		*
1106		* There are 12 carries below.
1107		* 10 of them are 2-way parallelizable and vectorizable.
1108		* Can get away with 11 carries, but then data flow is much deeper.
1109		*
1110		* With tighter constraints on inputs can squeeze carries into int32.
1111		*/
1112		static void fe_mul(fe h, const fe f, const fe g)
1113	0	{
1114	0	int32_t f0 = f[0];
1115	0	int32_t f1 = f[1];
1116	0	int32_t f2 = f[2];
1117	0	int32_t f3 = f[3];
1118	0	int32_t f4 = f[4];
1119	0	int32_t f5 = f[5];
1120	0	int32_t f6 = f[6];
1121	0	int32_t f7 = f[7];
1122	0	int32_t f8 = f[8];
1123	0	int32_t f9 = f[9];
1124	0	int32_t g0 = g[0];
1125	0	int32_t g1 = g[1];
1126	0	int32_t g2 = g[2];
1127	0	int32_t g3 = g[3];
1128	0	int32_t g4 = g[4];
1129	0	int32_t g5 = g[5];
1130	0	int32_t g6 = g[6];
1131	0	int32_t g7 = g[7];
1132	0	int32_t g8 = g[8];
1133	0	int32_t g9 = g[9];
1134	0	int32_t g1_19 = 19 * g1; /* 1.9593752^29 /
1135	0	int32_t g2_19 = 19 * g2; /* 1.9593752^30; still ok /
1136	0	int32_t g3_19 = 19 * g3;
1137	0	int32_t g4_19 = 19 * g4;
1138	0	int32_t g5_19 = 19 * g5;
1139	0	int32_t g6_19 = 19 * g6;
1140	0	int32_t g7_19 = 19 * g7;
1141	0	int32_t g8_19 = 19 * g8;
1142	0	int32_t g9_19 = 19 * g9;
1143	0	int32_t f1_2 = 2 * f1;
1144	0	int32_t f3_2 = 2 * f3;
1145	0	int32_t f5_2 = 2 * f5;
1146	0	int32_t f7_2 = 2 * f7;
1147	0	int32_t f9_2 = 2 * f9;
1148	0	int64_t f0g0 = f0 * (int64_t)g0;
1149	0	int64_t f0g1 = f0 * (int64_t)g1;
1150	0	int64_t f0g2 = f0 * (int64_t)g2;
1151	0	int64_t f0g3 = f0 * (int64_t)g3;
1152	0	int64_t f0g4 = f0 * (int64_t)g4;
1153	0	int64_t f0g5 = f0 * (int64_t)g5;
1154	0	int64_t f0g6 = f0 * (int64_t)g6;
1155	0	int64_t f0g7 = f0 * (int64_t)g7;
1156	0	int64_t f0g8 = f0 * (int64_t)g8;
1157	0	int64_t f0g9 = f0 * (int64_t)g9;
1158	0	int64_t f1g0 = f1 * (int64_t)g0;
1159	0	int64_t f1g1_2 = f1_2 * (int64_t)g1;
1160	0	int64_t f1g2 = f1 * (int64_t)g2;
1161	0	int64_t f1g3_2 = f1_2 * (int64_t)g3;
1162	0	int64_t f1g4 = f1 * (int64_t)g4;
1163	0	int64_t f1g5_2 = f1_2 * (int64_t)g5;
1164	0	int64_t f1g6 = f1 * (int64_t)g6;
1165	0	int64_t f1g7_2 = f1_2 * (int64_t)g7;
1166	0	int64_t f1g8 = f1 * (int64_t)g8;
1167	0	int64_t f1g9_38 = f1_2 * (int64_t)g9_19;
1168	0	int64_t f2g0 = f2 * (int64_t)g0;
1169	0	int64_t f2g1 = f2 * (int64_t)g1;
1170	0	int64_t f2g2 = f2 * (int64_t)g2;
1171	0	int64_t f2g3 = f2 * (int64_t)g3;
1172	0	int64_t f2g4 = f2 * (int64_t)g4;
1173	0	int64_t f2g5 = f2 * (int64_t)g5;
1174	0	int64_t f2g6 = f2 * (int64_t)g6;
1175	0	int64_t f2g7 = f2 * (int64_t)g7;
1176	0	int64_t f2g8_19 = f2 * (int64_t)g8_19;
1177	0	int64_t f2g9_19 = f2 * (int64_t)g9_19;
1178	0	int64_t f3g0 = f3 * (int64_t)g0;
1179	0	int64_t f3g1_2 = f3_2 * (int64_t)g1;
1180	0	int64_t f3g2 = f3 * (int64_t)g2;
1181	0	int64_t f3g3_2 = f3_2 * (int64_t)g3;
1182	0	int64_t f3g4 = f3 * (int64_t)g4;
1183	0	int64_t f3g5_2 = f3_2 * (int64_t)g5;
1184	0	int64_t f3g6 = f3 * (int64_t)g6;
1185	0	int64_t f3g7_38 = f3_2 * (int64_t)g7_19;
1186	0	int64_t f3g8_19 = f3 * (int64_t)g8_19;
1187	0	int64_t f3g9_38 = f3_2 * (int64_t)g9_19;
1188	0	int64_t f4g0 = f4 * (int64_t)g0;
1189	0	int64_t f4g1 = f4 * (int64_t)g1;
1190	0	int64_t f4g2 = f4 * (int64_t)g2;
1191	0	int64_t f4g3 = f4 * (int64_t)g3;
1192	0	int64_t f4g4 = f4 * (int64_t)g4;
1193	0	int64_t f4g5 = f4 * (int64_t)g5;
1194	0	int64_t f4g6_19 = f4 * (int64_t)g6_19;
1195	0	int64_t f4g7_19 = f4 * (int64_t)g7_19;
1196	0	int64_t f4g8_19 = f4 * (int64_t)g8_19;
1197	0	int64_t f4g9_19 = f4 * (int64_t)g9_19;
1198	0	int64_t f5g0 = f5 * (int64_t)g0;
1199	0	int64_t f5g1_2 = f5_2 * (int64_t)g1;
1200	0	int64_t f5g2 = f5 * (int64_t)g2;
1201	0	int64_t f5g3_2 = f5_2 * (int64_t)g3;
1202	0	int64_t f5g4 = f5 * (int64_t)g4;
1203	0	int64_t f5g5_38 = f5_2 * (int64_t)g5_19;
1204	0	int64_t f5g6_19 = f5 * (int64_t)g6_19;
1205	0	int64_t f5g7_38 = f5_2 * (int64_t)g7_19;
1206	0	int64_t f5g8_19 = f5 * (int64_t)g8_19;
1207	0	int64_t f5g9_38 = f5_2 * (int64_t)g9_19;
1208	0	int64_t f6g0 = f6 * (int64_t)g0;
1209	0	int64_t f6g1 = f6 * (int64_t)g1;
1210	0	int64_t f6g2 = f6 * (int64_t)g2;
1211	0	int64_t f6g3 = f6 * (int64_t)g3;
1212	0	int64_t f6g4_19 = f6 * (int64_t)g4_19;
1213	0	int64_t f6g5_19 = f6 * (int64_t)g5_19;
1214	0	int64_t f6g6_19 = f6 * (int64_t)g6_19;
1215	0	int64_t f6g7_19 = f6 * (int64_t)g7_19;
1216	0	int64_t f6g8_19 = f6 * (int64_t)g8_19;
1217	0	int64_t f6g9_19 = f6 * (int64_t)g9_19;
1218	0	int64_t f7g0 = f7 * (int64_t)g0;
1219	0	int64_t f7g1_2 = f7_2 * (int64_t)g1;
1220	0	int64_t f7g2 = f7 * (int64_t)g2;
1221	0	int64_t f7g3_38 = f7_2 * (int64_t)g3_19;
1222	0	int64_t f7g4_19 = f7 * (int64_t)g4_19;
1223	0	int64_t f7g5_38 = f7_2 * (int64_t)g5_19;
1224	0	int64_t f7g6_19 = f7 * (int64_t)g6_19;
1225	0	int64_t f7g7_38 = f7_2 * (int64_t)g7_19;
1226	0	int64_t f7g8_19 = f7 * (int64_t)g8_19;
1227	0	int64_t f7g9_38 = f7_2 * (int64_t)g9_19;
1228	0	int64_t f8g0 = f8 * (int64_t)g0;
1229	0	int64_t f8g1 = f8 * (int64_t)g1;
1230	0	int64_t f8g2_19 = f8 * (int64_t)g2_19;
1231	0	int64_t f8g3_19 = f8 * (int64_t)g3_19;
1232	0	int64_t f8g4_19 = f8 * (int64_t)g4_19;
1233	0	int64_t f8g5_19 = f8 * (int64_t)g5_19;
1234	0	int64_t f8g6_19 = f8 * (int64_t)g6_19;
1235	0	int64_t f8g7_19 = f8 * (int64_t)g7_19;
1236	0	int64_t f8g8_19 = f8 * (int64_t)g8_19;
1237	0	int64_t f8g9_19 = f8 * (int64_t)g9_19;
1238	0	int64_t f9g0 = f9 * (int64_t)g0;
1239	0	int64_t f9g1_38 = f9_2 * (int64_t)g1_19;
1240	0	int64_t f9g2_19 = f9 * (int64_t)g2_19;
1241	0	int64_t f9g3_38 = f9_2 * (int64_t)g3_19;
1242	0	int64_t f9g4_19 = f9 * (int64_t)g4_19;
1243	0	int64_t f9g5_38 = f9_2 * (int64_t)g5_19;
1244	0	int64_t f9g6_19 = f9 * (int64_t)g6_19;
1245	0	int64_t f9g7_38 = f9_2 * (int64_t)g7_19;
1246	0	int64_t f9g8_19 = f9 * (int64_t)g8_19;
1247	0	int64_t f9g9_38 = f9_2 * (int64_t)g9_19;
1248	0	int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1249	0	int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1250	0	int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1251	0	int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1252	0	int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1253	0	int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1254	0	int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1255	0	int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1256	0	int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1257	0	int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
1258	0	int64_t carry0;
1259	0	int64_t carry1;
1260	0	int64_t carry2;
1261	0	int64_t carry3;
1262	0	int64_t carry4;
1263	0	int64_t carry5;
1264	0	int64_t carry6;
1265	0	int64_t carry7;
1266	0	int64_t carry8;
1267	0	int64_t carry9;
1268
1269		/* \|h0\| <= (1.651.652^52(1+19+19+19+19)+1.651.652^50(38+38+38+38+38))
1270		* i.e. \|h0\| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1271		* \|h1\| <= (1.651.652^51*(1+1+19+19+19+19+19+19+19+19))
1272		* i.e. \|h1\| <= 1.72^59; narrower ranges for h3, h5, h7, h9 /
1273
1274	0	carry0 = h0 + (1 << 25);
1275	0	h1 += carry0 >> 26;
1276	0	h0 -= carry0 & kTop38Bits;
1277	0	carry4 = h4 + (1 << 25);
1278	0	h5 += carry4 >> 26;
1279	0	h4 -= carry4 & kTop38Bits;
1280		/* \|h0\| <= 2^25 */
1281		/* \|h4\| <= 2^25 */
1282		/* \|h1\| <= 1.712^59 /
1283		/* \|h5\| <= 1.712^59 /
1284
1285	0	carry1 = h1 + (1 << 24);
1286	0	h2 += carry1 >> 25;
1287	0	h1 -= carry1 & kTop39Bits;
1288	0	carry5 = h5 + (1 << 24);
1289	0	h6 += carry5 >> 25;
1290	0	h5 -= carry5 & kTop39Bits;
1291		/* \|h1\| <= 2^24; from now on fits into int32 */
1292		/* \|h5\| <= 2^24; from now on fits into int32 */
1293		/* \|h2\| <= 1.412^60 /
1294		/* \|h6\| <= 1.412^60 /
1295
1296	0	carry2 = h2 + (1 << 25);
1297	0	h3 += carry2 >> 26;
1298	0	h2 -= carry2 & kTop38Bits;
1299	0	carry6 = h6 + (1 << 25);
1300	0	h7 += carry6 >> 26;
1301	0	h6 -= carry6 & kTop38Bits;
1302		/* \|h2\| <= 2^25; from now on fits into int32 unchanged */
1303		/* \|h6\| <= 2^25; from now on fits into int32 unchanged */
1304		/* \|h3\| <= 1.712^59 /
1305		/* \|h7\| <= 1.712^59 /
1306
1307	0	carry3 = h3 + (1 << 24);
1308	0	h4 += carry3 >> 25;
1309	0	h3 -= carry3 & kTop39Bits;
1310	0	carry7 = h7 + (1 << 24);
1311	0	h8 += carry7 >> 25;
1312	0	h7 -= carry7 & kTop39Bits;
1313		/* \|h3\| <= 2^24; from now on fits into int32 unchanged */
1314		/* \|h7\| <= 2^24; from now on fits into int32 unchanged */
1315		/* \|h4\| <= 1.722^34 /
1316		/* \|h8\| <= 1.412^60 /
1317
1318	0	carry4 = h4 + (1 << 25);
1319	0	h5 += carry4 >> 26;
1320	0	h4 -= carry4 & kTop38Bits;
1321	0	carry8 = h8 + (1 << 25);
1322	0	h9 += carry8 >> 26;
1323	0	h8 -= carry8 & kTop38Bits;
1324		/* \|h4\| <= 2^25; from now on fits into int32 unchanged */
1325		/* \|h8\| <= 2^25; from now on fits into int32 unchanged */
1326		/* \|h5\| <= 1.012^24 /
1327		/* \|h9\| <= 1.712^59 /
1328
1329	0	carry9 = h9 + (1 << 24);
1330	0	h0 += (carry9 >> 25) * 19;
1331	0	h9 -= carry9 & kTop39Bits;
1332		/* \|h9\| <= 2^24; from now on fits into int32 unchanged */
1333		/* \|h0\| <= 1.12^39 /
1334
1335	0	carry0 = h0 + (1 << 25);
1336	0	h1 += carry0 >> 26;
1337	0	h0 -= carry0 & kTop38Bits;
1338		/* \|h0\| <= 2^25; from now on fits into int32 unchanged */
1339		/* \|h1\| <= 1.012^24 /
1340
1341	0	h[0] = (int32_t)h0;
1342	0	h[1] = (int32_t)h1;
1343	0	h[2] = (int32_t)h2;
1344	0	h[3] = (int32_t)h3;
1345	0	h[4] = (int32_t)h4;
1346	0	h[5] = (int32_t)h5;
1347	0	h[6] = (int32_t)h6;
1348	0	h[7] = (int32_t)h7;
1349	0	h[8] = (int32_t)h8;
1350	0	h[9] = (int32_t)h9;
1351	0	}
1352
1353		/*
1354		* h = f * f
1355		*
1356		* Can overlap h with f.
1357		*
1358		* Preconditions:
1359		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1360		*
1361		* Postconditions:
1362		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1363		*
1364		* See fe_mul.c for discussion of implementation strategy.
1365		*/
1366		static void fe_sq(fe h, const fe f)
1367	0	{
1368	0	int32_t f0 = f[0];
1369	0	int32_t f1 = f[1];
1370	0	int32_t f2 = f[2];
1371	0	int32_t f3 = f[3];
1372	0	int32_t f4 = f[4];
1373	0	int32_t f5 = f[5];
1374	0	int32_t f6 = f[6];
1375	0	int32_t f7 = f[7];
1376	0	int32_t f8 = f[8];
1377	0	int32_t f9 = f[9];
1378	0	int32_t f0_2 = 2 * f0;
1379	0	int32_t f1_2 = 2 * f1;
1380	0	int32_t f2_2 = 2 * f2;
1381	0	int32_t f3_2 = 2 * f3;
1382	0	int32_t f4_2 = 2 * f4;
1383	0	int32_t f5_2 = 2 * f5;
1384	0	int32_t f6_2 = 2 * f6;
1385	0	int32_t f7_2 = 2 * f7;
1386	0	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1387	0	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1388	0	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1389	0	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1390	0	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1391	0	int64_t f0f0 = f0 * (int64_t)f0;
1392	0	int64_t f0f1_2 = f0_2 * (int64_t)f1;
1393	0	int64_t f0f2_2 = f0_2 * (int64_t)f2;
1394	0	int64_t f0f3_2 = f0_2 * (int64_t)f3;
1395	0	int64_t f0f4_2 = f0_2 * (int64_t)f4;
1396	0	int64_t f0f5_2 = f0_2 * (int64_t)f5;
1397	0	int64_t f0f6_2 = f0_2 * (int64_t)f6;
1398	0	int64_t f0f7_2 = f0_2 * (int64_t)f7;
1399	0	int64_t f0f8_2 = f0_2 * (int64_t)f8;
1400	0	int64_t f0f9_2 = f0_2 * (int64_t)f9;
1401	0	int64_t f1f1_2 = f1_2 * (int64_t)f1;
1402	0	int64_t f1f2_2 = f1_2 * (int64_t)f2;
1403	0	int64_t f1f3_4 = f1_2 * (int64_t)f3_2;
1404	0	int64_t f1f4_2 = f1_2 * (int64_t)f4;
1405	0	int64_t f1f5_4 = f1_2 * (int64_t)f5_2;
1406	0	int64_t f1f6_2 = f1_2 * (int64_t)f6;
1407	0	int64_t f1f7_4 = f1_2 * (int64_t)f7_2;
1408	0	int64_t f1f8_2 = f1_2 * (int64_t)f8;
1409	0	int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
1410	0	int64_t f2f2 = f2 * (int64_t)f2;
1411	0	int64_t f2f3_2 = f2_2 * (int64_t)f3;
1412	0	int64_t f2f4_2 = f2_2 * (int64_t)f4;
1413	0	int64_t f2f5_2 = f2_2 * (int64_t)f5;
1414	0	int64_t f2f6_2 = f2_2 * (int64_t)f6;
1415	0	int64_t f2f7_2 = f2_2 * (int64_t)f7;
1416	0	int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
1417	0	int64_t f2f9_38 = f2 * (int64_t)f9_38;
1418	0	int64_t f3f3_2 = f3_2 * (int64_t)f3;
1419	0	int64_t f3f4_2 = f3_2 * (int64_t)f4;
1420	0	int64_t f3f5_4 = f3_2 * (int64_t)f5_2;
1421	0	int64_t f3f6_2 = f3_2 * (int64_t)f6;
1422	0	int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
1423	0	int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
1424	0	int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
1425	0	int64_t f4f4 = f4 * (int64_t)f4;
1426	0	int64_t f4f5_2 = f4_2 * (int64_t)f5;
1427	0	int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
1428	0	int64_t f4f7_38 = f4 * (int64_t)f7_38;
1429	0	int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
1430	0	int64_t f4f9_38 = f4 * (int64_t)f9_38;
1431	0	int64_t f5f5_38 = f5 * (int64_t)f5_38;
1432	0	int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
1433	0	int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
1434	0	int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
1435	0	int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
1436	0	int64_t f6f6_19 = f6 * (int64_t)f6_19;
1437	0	int64_t f6f7_38 = f6 * (int64_t)f7_38;
1438	0	int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
1439	0	int64_t f6f9_38 = f6 * (int64_t)f9_38;
1440	0	int64_t f7f7_38 = f7 * (int64_t)f7_38;
1441	0	int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
1442	0	int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
1443	0	int64_t f8f8_19 = f8 * (int64_t)f8_19;
1444	0	int64_t f8f9_38 = f8 * (int64_t)f9_38;
1445	0	int64_t f9f9_38 = f9 * (int64_t)f9_38;
1446	0	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1447	0	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1448	0	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1449	0	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1450	0	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1451	0	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1452	0	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1453	0	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1454	0	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1455	0	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1456	0	int64_t carry0;
1457	0	int64_t carry1;
1458	0	int64_t carry2;
1459	0	int64_t carry3;
1460	0	int64_t carry4;
1461	0	int64_t carry5;
1462	0	int64_t carry6;
1463	0	int64_t carry7;
1464	0	int64_t carry8;
1465	0	int64_t carry9;
1466
1467	0	carry0 = h0 + (1 << 25);
1468	0	h1 += carry0 >> 26;
1469	0	h0 -= carry0 & kTop38Bits;
1470	0	carry4 = h4 + (1 << 25);
1471	0	h5 += carry4 >> 26;
1472	0	h4 -= carry4 & kTop38Bits;
1473
1474	0	carry1 = h1 + (1 << 24);
1475	0	h2 += carry1 >> 25;
1476	0	h1 -= carry1 & kTop39Bits;
1477	0	carry5 = h5 + (1 << 24);
1478	0	h6 += carry5 >> 25;
1479	0	h5 -= carry5 & kTop39Bits;
1480
1481	0	carry2 = h2 + (1 << 25);
1482	0	h3 += carry2 >> 26;
1483	0	h2 -= carry2 & kTop38Bits;
1484	0	carry6 = h6 + (1 << 25);
1485	0	h7 += carry6 >> 26;
1486	0	h6 -= carry6 & kTop38Bits;
1487
1488	0	carry3 = h3 + (1 << 24);
1489	0	h4 += carry3 >> 25;
1490	0	h3 -= carry3 & kTop39Bits;
1491	0	carry7 = h7 + (1 << 24);
1492	0	h8 += carry7 >> 25;
1493	0	h7 -= carry7 & kTop39Bits;
1494
1495	0	carry4 = h4 + (1 << 25);
1496	0	h5 += carry4 >> 26;
1497	0	h4 -= carry4 & kTop38Bits;
1498	0	carry8 = h8 + (1 << 25);
1499	0	h9 += carry8 >> 26;
1500	0	h8 -= carry8 & kTop38Bits;
1501
1502	0	carry9 = h9 + (1 << 24);
1503	0	h0 += (carry9 >> 25) * 19;
1504	0	h9 -= carry9 & kTop39Bits;
1505
1506	0	carry0 = h0 + (1 << 25);
1507	0	h1 += carry0 >> 26;
1508	0	h0 -= carry0 & kTop38Bits;
1509
1510	0	h[0] = (int32_t)h0;
1511	0	h[1] = (int32_t)h1;
1512	0	h[2] = (int32_t)h2;
1513	0	h[3] = (int32_t)h3;
1514	0	h[4] = (int32_t)h4;
1515	0	h[5] = (int32_t)h5;
1516	0	h[6] = (int32_t)h6;
1517	0	h[7] = (int32_t)h7;
1518	0	h[8] = (int32_t)h8;
1519	0	h[9] = (int32_t)h9;
1520	0	}
1521
1522		static void fe_invert(fe out, const fe z)
1523	0	{
1524	0	fe t0;
1525	0	fe t1;
1526	0	fe t2;
1527	0	fe t3;
1528	0	int i;
1529
1530		/*
1531		* Compute z -1 = z (2 ** 255 - 19 - 2) with the exponent as
1532		* 2 255 - 21 = (2 5) * (2 ** 250 - 1) + 11.
1533		*/
1534
1535		/* t0 = z ** 2 */
1536	0	fe_sq(t0, z);
1537
1538		/* t1 = t0 (2 2) = z ** 8 */
1539	0	fe_sq(t1, t0);
1540	0	fe_sq(t1, t1);
1541
1542		/* t1 = z * t1 = z ** 9 */
1543	0	fe_mul(t1, z, t1);
1544		/* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1545	0	fe_mul(t0, t0, t1);
1546
1547		/* t2 = t0 2 = z 22 */
1548	0	fe_sq(t2, t0);
1549
1550		/* t1 = t1 * t2 = z (2 5 - 1) */
1551	0	fe_mul(t1, t1, t2);
1552
1553		/* t2 = t1 (2 5) = z ((2 5) * (2 ** 5 - 1)) */
1554	0	fe_sq(t2, t1);
1555	0	for (i = 1; i < 5; ++i) {
1556	0	fe_sq(t2, t2);
1557	0	}
1558
1559		/* t1 = t1 * t2 = z ((2 5 + 1) * (2 5 - 1)) = z (2 ** 10 - 1) */
1560	0	fe_mul(t1, t2, t1);
1561
1562		/* Continuing similarly... */
1563
1564		/* t2 = z (2 20 - 1) */
1565	0	fe_sq(t2, t1);
1566	0	for (i = 1; i < 10; ++i) {
1567	0	fe_sq(t2, t2);
1568	0	}
1569	0	fe_mul(t2, t2, t1);
1570
1571		/* t2 = z (2 40 - 1) */
1572	0	fe_sq(t3, t2);
1573	0	for (i = 1; i < 20; ++i) {
1574	0	fe_sq(t3, t3);
1575	0	}
1576	0	fe_mul(t2, t3, t2);
1577
1578		/* t2 = z (2 10) * (2 ** 40 - 1) */
1579	0	for (i = 0; i < 10; ++i) {
1580	0	fe_sq(t2, t2);
1581	0	}
1582		/* t1 = z (2 50 - 1) */
1583	0	fe_mul(t1, t2, t1);
1584
1585		/* t2 = z (2 100 - 1) */
1586	0	fe_sq(t2, t1);
1587	0	for (i = 1; i < 50; ++i) {
1588	0	fe_sq(t2, t2);
1589	0	}
1590	0	fe_mul(t2, t2, t1);
1591
1592		/* t2 = z (2 200 - 1) */
1593	0	fe_sq(t3, t2);
1594	0	for (i = 1; i < 100; ++i) {
1595	0	fe_sq(t3, t3);
1596	0	}
1597	0	fe_mul(t2, t3, t2);
1598
1599		/* t2 = z ((2 50) * (2 ** 200 - 1) */
1600	0	fe_sq(t2, t2);
1601	0	for (i = 1; i < 50; ++i) {
1602	0	fe_sq(t2, t2);
1603	0	}
1604
1605		/* t1 = z (2 250 - 1) */
1606	0	fe_mul(t1, t2, t1);
1607
1608		/* t1 = z ((2 5) * (2 ** 250 - 1)) */
1609	0	fe_sq(t1, t1);
1610	0	for (i = 1; i < 5; ++i) {
1611	0	fe_sq(t1, t1);
1612	0	}
1613
1614		/* Recall t0 = z 11; out = z (2 ** 255 - 21) */
1615	0	fe_mul(out, t1, t0);
1616	0	}
1617
1618		/*
1619		* h = -f
1620		*
1621		* Preconditions:
1622		* \|f\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1623		*
1624		* Postconditions:
1625		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
1626		*/
1627		static void fe_neg(fe h, const fe f)
1628	0	{
1629	0	unsigned i;
1630
1631	0	for (i = 0; i < 10; i++) {
1632	0	h[i] = -f[i];
1633	0	}
1634	0	}
1635
1636		/*
1637		* Replace (f,g) with (g,g) if b == 1;
1638		* replace (f,g) with (f,g) if b == 0.
1639		*
1640		* Preconditions: b in {0,1}.
1641		*/
1642		static void fe_cmov(fe f, const fe g, unsigned b)
1643	0	{
1644	0	size_t i;
1645
1646	0	b = 0 - b;
1647	0	for (i = 0; i < 10; i++) {
1648	0	int32_t x = f[i] ^ g[i];
1649	0	x &= b;
1650	0	f[i] ^= x;
1651	0	}
1652	0	}
1653
1654		/*
1655		* return 0 if f == 0
1656		* return 1 if f != 0
1657		*
1658		* Preconditions:
1659		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1660		*/
1661		static int fe_isnonzero(const fe f)
1662	0	{
1663	0	uint8_t s[32];
1664	0	static const uint8_t zero[32] = { 0 };
1665
1666	0	fe_tobytes(s, f);
1667
1668	0	return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1669	0	}
1670
1671		/*
1672		* return 1 if f is in {1,3,5,...,q-2}
1673		* return 0 if f is in {0,2,4,...,q-1}
1674		*
1675		* Preconditions:
1676		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
1677		*/
1678		static int fe_isnegative(const fe f)
1679	0	{
1680	0	uint8_t s[32];
1681
1682	0	fe_tobytes(s, f);
1683	0	return s[0] & 1;
1684	0	}
1685
1686		/*
1687		* h = 2 * f * f
1688		*
1689		* Can overlap h with f.
1690		*
1691		* Preconditions:
1692		* \|f\| bounded by 1.652^26,1.652^25,1.652^26,1.652^25,etc.
1693		*
1694		* Postconditions:
1695		* \|h\| bounded by 1.012^25,1.012^24,1.012^25,1.012^24,etc.
1696		*
1697		* See fe_mul.c for discussion of implementation strategy.
1698		*/
1699		static void fe_sq2(fe h, const fe f)
1700	0	{
1701	0	int32_t f0 = f[0];
1702	0	int32_t f1 = f[1];
1703	0	int32_t f2 = f[2];
1704	0	int32_t f3 = f[3];
1705	0	int32_t f4 = f[4];
1706	0	int32_t f5 = f[5];
1707	0	int32_t f6 = f[6];
1708	0	int32_t f7 = f[7];
1709	0	int32_t f8 = f[8];
1710	0	int32_t f9 = f[9];
1711	0	int32_t f0_2 = 2 * f0;
1712	0	int32_t f1_2 = 2 * f1;
1713	0	int32_t f2_2 = 2 * f2;
1714	0	int32_t f3_2 = 2 * f3;
1715	0	int32_t f4_2 = 2 * f4;
1716	0	int32_t f5_2 = 2 * f5;
1717	0	int32_t f6_2 = 2 * f6;
1718	0	int32_t f7_2 = 2 * f7;
1719	0	int32_t f5_38 = 38 * f5; /* 1.9593752^30 /
1720	0	int32_t f6_19 = 19 * f6; /* 1.9593752^30 /
1721	0	int32_t f7_38 = 38 * f7; /* 1.9593752^30 /
1722	0	int32_t f8_19 = 19 * f8; /* 1.9593752^30 /
1723	0	int32_t f9_38 = 38 * f9; /* 1.9593752^30 /
1724	0	int64_t f0f0 = f0 * (int64_t)f0;
1725	0	int64_t f0f1_2 = f0_2 * (int64_t)f1;
1726	0	int64_t f0f2_2 = f0_2 * (int64_t)f2;
1727	0	int64_t f0f3_2 = f0_2 * (int64_t)f3;
1728	0	int64_t f0f4_2 = f0_2 * (int64_t)f4;
1729	0	int64_t f0f5_2 = f0_2 * (int64_t)f5;
1730	0	int64_t f0f6_2 = f0_2 * (int64_t)f6;
1731	0	int64_t f0f7_2 = f0_2 * (int64_t)f7;
1732	0	int64_t f0f8_2 = f0_2 * (int64_t)f8;
1733	0	int64_t f0f9_2 = f0_2 * (int64_t)f9;
1734	0	int64_t f1f1_2 = f1_2 * (int64_t)f1;
1735	0	int64_t f1f2_2 = f1_2 * (int64_t)f2;
1736	0	int64_t f1f3_4 = f1_2 * (int64_t)f3_2;
1737	0	int64_t f1f4_2 = f1_2 * (int64_t)f4;
1738	0	int64_t f1f5_4 = f1_2 * (int64_t)f5_2;
1739	0	int64_t f1f6_2 = f1_2 * (int64_t)f6;
1740	0	int64_t f1f7_4 = f1_2 * (int64_t)f7_2;
1741	0	int64_t f1f8_2 = f1_2 * (int64_t)f8;
1742	0	int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
1743	0	int64_t f2f2 = f2 * (int64_t)f2;
1744	0	int64_t f2f3_2 = f2_2 * (int64_t)f3;
1745	0	int64_t f2f4_2 = f2_2 * (int64_t)f4;
1746	0	int64_t f2f5_2 = f2_2 * (int64_t)f5;
1747	0	int64_t f2f6_2 = f2_2 * (int64_t)f6;
1748	0	int64_t f2f7_2 = f2_2 * (int64_t)f7;
1749	0	int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
1750	0	int64_t f2f9_38 = f2 * (int64_t)f9_38;
1751	0	int64_t f3f3_2 = f3_2 * (int64_t)f3;
1752	0	int64_t f3f4_2 = f3_2 * (int64_t)f4;
1753	0	int64_t f3f5_4 = f3_2 * (int64_t)f5_2;
1754	0	int64_t f3f6_2 = f3_2 * (int64_t)f6;
1755	0	int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
1756	0	int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
1757	0	int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
1758	0	int64_t f4f4 = f4 * (int64_t)f4;
1759	0	int64_t f4f5_2 = f4_2 * (int64_t)f5;
1760	0	int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
1761	0	int64_t f4f7_38 = f4 * (int64_t)f7_38;
1762	0	int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
1763	0	int64_t f4f9_38 = f4 * (int64_t)f9_38;
1764	0	int64_t f5f5_38 = f5 * (int64_t)f5_38;
1765	0	int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
1766	0	int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
1767	0	int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
1768	0	int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
1769	0	int64_t f6f6_19 = f6 * (int64_t)f6_19;
1770	0	int64_t f6f7_38 = f6 * (int64_t)f7_38;
1771	0	int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
1772	0	int64_t f6f9_38 = f6 * (int64_t)f9_38;
1773	0	int64_t f7f7_38 = f7 * (int64_t)f7_38;
1774	0	int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
1775	0	int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
1776	0	int64_t f8f8_19 = f8 * (int64_t)f8_19;
1777	0	int64_t f8f9_38 = f8 * (int64_t)f9_38;
1778	0	int64_t f9f9_38 = f9 * (int64_t)f9_38;
1779	0	int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1780	0	int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1781	0	int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1782	0	int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1783	0	int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1784	0	int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1785	0	int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1786	0	int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1787	0	int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1788	0	int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1789	0	int64_t carry0;
1790	0	int64_t carry1;
1791	0	int64_t carry2;
1792	0	int64_t carry3;
1793	0	int64_t carry4;
1794	0	int64_t carry5;
1795	0	int64_t carry6;
1796	0	int64_t carry7;
1797	0	int64_t carry8;
1798	0	int64_t carry9;
1799
1800	0	h0 += h0;
1801	0	h1 += h1;
1802	0	h2 += h2;
1803	0	h3 += h3;
1804	0	h4 += h4;
1805	0	h5 += h5;
1806	0	h6 += h6;
1807	0	h7 += h7;
1808	0	h8 += h8;
1809	0	h9 += h9;
1810
1811	0	carry0 = h0 + (1 << 25);
1812	0	h1 += carry0 >> 26;
1813	0	h0 -= carry0 & kTop38Bits;
1814	0	carry4 = h4 + (1 << 25);
1815	0	h5 += carry4 >> 26;
1816	0	h4 -= carry4 & kTop38Bits;
1817
1818	0	carry1 = h1 + (1 << 24);
1819	0	h2 += carry1 >> 25;
1820	0	h1 -= carry1 & kTop39Bits;
1821	0	carry5 = h5 + (1 << 24);
1822	0	h6 += carry5 >> 25;
1823	0	h5 -= carry5 & kTop39Bits;
1824
1825	0	carry2 = h2 + (1 << 25);
1826	0	h3 += carry2 >> 26;
1827	0	h2 -= carry2 & kTop38Bits;
1828	0	carry6 = h6 + (1 << 25);
1829	0	h7 += carry6 >> 26;
1830	0	h6 -= carry6 & kTop38Bits;
1831
1832	0	carry3 = h3 + (1 << 24);
1833	0	h4 += carry3 >> 25;
1834	0	h3 -= carry3 & kTop39Bits;
1835	0	carry7 = h7 + (1 << 24);
1836	0	h8 += carry7 >> 25;
1837	0	h7 -= carry7 & kTop39Bits;
1838
1839	0	carry4 = h4 + (1 << 25);
1840	0	h5 += carry4 >> 26;
1841	0	h4 -= carry4 & kTop38Bits;
1842	0	carry8 = h8 + (1 << 25);
1843	0	h9 += carry8 >> 26;
1844	0	h8 -= carry8 & kTop38Bits;
1845
1846	0	carry9 = h9 + (1 << 24);
1847	0	h0 += (carry9 >> 25) * 19;
1848	0	h9 -= carry9 & kTop39Bits;
1849
1850	0	carry0 = h0 + (1 << 25);
1851	0	h1 += carry0 >> 26;
1852	0	h0 -= carry0 & kTop38Bits;
1853
1854	0	h[0] = (int32_t)h0;
1855	0	h[1] = (int32_t)h1;
1856	0	h[2] = (int32_t)h2;
1857	0	h[3] = (int32_t)h3;
1858	0	h[4] = (int32_t)h4;
1859	0	h[5] = (int32_t)h5;
1860	0	h[6] = (int32_t)h6;
1861	0	h[7] = (int32_t)h7;
1862	0	h[8] = (int32_t)h8;
1863	0	h[9] = (int32_t)h9;
1864	0	}
1865
1866		static void fe_pow22523(fe out, const fe z)
1867	0	{
1868	0	fe t0;
1869	0	fe t1;
1870	0	fe t2;
1871	0	int i;
1872
1873	0	fe_sq(t0, z);
1874	0	fe_sq(t1, t0);
1875	0	for (i = 1; i < 2; ++i) {
1876	0	fe_sq(t1, t1);
1877	0	}
1878	0	fe_mul(t1, z, t1);
1879	0	fe_mul(t0, t0, t1);
1880	0	fe_sq(t0, t0);
1881	0	fe_mul(t0, t1, t0);
1882	0	fe_sq(t1, t0);
1883	0	for (i = 1; i < 5; ++i) {
1884	0	fe_sq(t1, t1);
1885	0	}
1886	0	fe_mul(t0, t1, t0);
1887	0	fe_sq(t1, t0);
1888	0	for (i = 1; i < 10; ++i) {
1889	0	fe_sq(t1, t1);
1890	0	}
1891	0	fe_mul(t1, t1, t0);
1892	0	fe_sq(t2, t1);
1893	0	for (i = 1; i < 20; ++i) {
1894	0	fe_sq(t2, t2);
1895	0	}
1896	0	fe_mul(t1, t2, t1);
1897	0	fe_sq(t1, t1);
1898	0	for (i = 1; i < 10; ++i) {
1899	0	fe_sq(t1, t1);
1900	0	}
1901	0	fe_mul(t0, t1, t0);
1902	0	fe_sq(t1, t0);
1903	0	for (i = 1; i < 50; ++i) {
1904	0	fe_sq(t1, t1);
1905	0	}
1906	0	fe_mul(t1, t1, t0);
1907	0	fe_sq(t2, t1);
1908	0	for (i = 1; i < 100; ++i) {
1909	0	fe_sq(t2, t2);
1910	0	}
1911	0	fe_mul(t1, t2, t1);
1912	0	fe_sq(t1, t1);
1913	0	for (i = 1; i < 50; ++i) {
1914	0	fe_sq(t1, t1);
1915	0	}
1916	0	fe_mul(t0, t1, t0);
1917	0	fe_sq(t0, t0);
1918	0	for (i = 1; i < 2; ++i) {
1919	0	fe_sq(t0, t0);
1920	0	}
1921	0	fe_mul(out, t0, z);
1922	0	}
1923
1924		/*
1925		* ge means group element.
1926		*
1927		* Here the group is the set of pairs (x,y) of field elements (see fe.h)
1928		* satisfying -x^2 + y^2 = 1 + d x^2y^2
1929		* where d = -121665/121666.
1930		*
1931		* Representations:
1932		* ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1933		* ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1934		* ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1935		* ge_precomp (Duif): (y+x,y-x,2dxy)
1936		*/
1937		typedef struct {
1938		fe X;
1939		fe Y;
1940		fe Z;
1941		} ge_p2;
1942
1943		typedef struct {
1944		fe X;
1945		fe Y;
1946		fe Z;
1947		fe T;
1948		} ge_p3;
1949
1950		typedef struct {
1951		fe X;
1952		fe Y;
1953		fe Z;
1954		fe T;
1955		} ge_p1p1;
1956
1957		typedef struct {
1958		fe yplusx;
1959		fe yminusx;
1960		fe xy2d;
1961		} ge_precomp;
1962
1963		typedef struct {
1964		fe YplusX;
1965		fe YminusX;
1966		fe Z;
1967		fe T2d;
1968		} ge_cached;
1969
1970		static void ge_tobytes(uint8_t s, const ge_p2 h)
1971	0	{
1972	0	fe recip;
1973	0	fe x;
1974	0	fe y;
1975
1976	0	fe_invert(recip, h->Z);
1977	0	fe_mul(x, h->X, recip);
1978	0	fe_mul(y, h->Y, recip);
1979	0	fe_tobytes(s, y);
1980	0	s[31] ^= fe_isnegative(x) << 7;
1981	0	}
1982
1983		static void ge_p3_tobytes(uint8_t s, const ge_p3 h)
1984	0	{
1985	0	fe recip;
1986	0	fe x;
1987	0	fe y;
1988
1989	0	fe_invert(recip, h->Z);
1990	0	fe_mul(x, h->X, recip);
1991	0	fe_mul(y, h->Y, recip);
1992	0	fe_tobytes(s, y);
1993	0	s[31] ^= fe_isnegative(x) << 7;
1994	0	}
1995
1996		static const fe d = {
1997		-10913610, 13857413, -15372611, 6949391, 114729,
1998		-8787816, -6275908, -3247719, -18696448, -12055116
1999		};
2000
2001		static const fe sqrtm1 = {
2002		-32595792, -7943725, 9377950, 3500415, 12389472,
2003		-272473, -25146209, -2005654, 326686, 11406482
2004		};
2005
2006		static int ge_frombytes_vartime(ge_p3 h, const uint8_t s)
2007	0	{
2008	0	fe u;
2009	0	fe v;
2010	0	fe w;
2011	0	fe vxx;
2012	0	fe check;
2013
2014	0	fe_frombytes(h->Y, s);
2015	0	fe_1(h->Z);
2016	0	fe_sq(u, h->Y);
2017	0	fe_mul(v, u, d);
2018	0	fe_sub(u, u, h->Z); /* u = y^2-1 */
2019	0	fe_add(v, v, h->Z); /* v = dy^2+1 */
2020
2021	0	fe_mul(w, u, v); /* w = uv /
2022
2023	0	fe_pow22523(h->X, w); /* x = w^((q-5)/8) */
2024	0	fe_mul(h->X, h->X, u); /* x = u * w^((q-5)/8) */
2025
2026	0	fe_sq(vxx, h->X);
2027	0	fe_mul(vxx, vxx, v);
2028	0	fe_sub(check, vxx, u); /* vx^2-u */
2029	0	if (fe_isnonzero(check)) {
2030	0	fe_add(check, vxx, u); /* vx^2+u */
2031	0	if (fe_isnonzero(check)) {
2032	0	return -1;
2033	0	}
2034	0	fe_mul(h->X, h->X, sqrtm1);
2035	0	}
2036
2037	0	if (fe_isnegative(h->X) != (s[31] >> 7)) {
2038	0	fe_neg(h->X, h->X);
2039	0	}
2040
2041	0	fe_mul(h->T, h->X, h->Y);
2042	0	return 0;
2043	0	}
2044
2045		static void ge_p2_0(ge_p2 *h)
2046	0	{
2047	0	fe_0(h->X);
2048	0	fe_1(h->Y);
2049	0	fe_1(h->Z);
2050	0	}
2051
2052		static void ge_p3_0(ge_p3 *h)
2053	0	{
2054	0	fe_0(h->X);
2055	0	fe_1(h->Y);
2056	0	fe_1(h->Z);
2057	0	fe_0(h->T);
2058	0	}
2059
2060		static void ge_precomp_0(ge_precomp *h)
2061	0	{
2062	0	fe_1(h->yplusx);
2063	0	fe_1(h->yminusx);
2064	0	fe_0(h->xy2d);
2065	0	}
2066
2067		/* r = p */
2068		static void ge_p3_to_p2(ge_p2 r, const ge_p3 p)
2069	0	{
2070	0	fe_copy(r->X, p->X);
2071	0	fe_copy(r->Y, p->Y);
2072	0	fe_copy(r->Z, p->Z);
2073	0	}
2074
2075		static const fe d2 = {
2076		-21827239, -5839606, -30745221, 13898782, 229458,
2077		15978800, -12551817, -6495438, 29715968, 9444199
2078		};
2079
2080		/* r = p */
2081		static void ge_p3_to_cached(ge_cached r, const ge_p3 p)
2082	0	{
2083	0	fe_add(r->YplusX, p->Y, p->X);
2084	0	fe_sub(r->YminusX, p->Y, p->X);
2085	0	fe_copy(r->Z, p->Z);
2086	0	fe_mul(r->T2d, p->T, d2);
2087	0	}
2088
2089		/* r = p */
2090		static void ge_p1p1_to_p2(ge_p2 r, const ge_p1p1 p)
2091	0	{
2092	0	fe_mul(r->X, p->X, p->T);
2093	0	fe_mul(r->Y, p->Y, p->Z);
2094	0	fe_mul(r->Z, p->Z, p->T);
2095	0	}
2096
2097		/* r = p */
2098		static void ge_p1p1_to_p3(ge_p3 r, const ge_p1p1 p)
2099	0	{
2100	0	fe_mul(r->X, p->X, p->T);
2101	0	fe_mul(r->Y, p->Y, p->Z);
2102	0	fe_mul(r->Z, p->Z, p->T);
2103	0	fe_mul(r->T, p->X, p->Y);
2104	0	}
2105
2106		/* r = 2 * p */
2107		static void ge_p2_dbl(ge_p1p1 r, const ge_p2 p)
2108	0	{
2109	0	fe t0;
2110
2111	0	fe_sq(r->X, p->X);
2112	0	fe_sq(r->Z, p->Y);
2113	0	fe_sq2(r->T, p->Z);
2114	0	fe_add(r->Y, p->X, p->Y);
2115	0	fe_sq(t0, r->Y);
2116	0	fe_add(r->Y, r->Z, r->X);
2117	0	fe_sub(r->Z, r->Z, r->X);
2118	0	fe_sub(r->X, t0, r->Y);
2119	0	fe_sub(r->T, r->T, r->Z);
2120	0	}
2121
2122		/* r = 2 * p */
2123		static void ge_p3_dbl(ge_p1p1 r, const ge_p3 p)
2124	0	{
2125	0	ge_p2 q;
2126	0	ge_p3_to_p2(&q, p);
2127	0	ge_p2_dbl(r, &q);
2128	0	}
2129
2130		/* r = p + q */
2131		static void ge_madd(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2132	0	{
2133	0	fe t0;
2134
2135	0	fe_add(r->X, p->Y, p->X);
2136	0	fe_sub(r->Y, p->Y, p->X);
2137	0	fe_mul(r->Z, r->X, q->yplusx);
2138	0	fe_mul(r->Y, r->Y, q->yminusx);
2139	0	fe_mul(r->T, q->xy2d, p->T);
2140	0	fe_add(t0, p->Z, p->Z);
2141	0	fe_sub(r->X, r->Z, r->Y);
2142	0	fe_add(r->Y, r->Z, r->Y);
2143	0	fe_add(r->Z, t0, r->T);
2144	0	fe_sub(r->T, t0, r->T);
2145	0	}
2146
2147		/* r = p - q */
2148		static void ge_msub(ge_p1p1 r, const ge_p3 p, const ge_precomp *q)
2149	0	{
2150	0	fe t0;
2151
2152	0	fe_add(r->X, p->Y, p->X);
2153	0	fe_sub(r->Y, p->Y, p->X);
2154	0	fe_mul(r->Z, r->X, q->yminusx);
2155	0	fe_mul(r->Y, r->Y, q->yplusx);
2156	0	fe_mul(r->T, q->xy2d, p->T);
2157	0	fe_add(t0, p->Z, p->Z);
2158	0	fe_sub(r->X, r->Z, r->Y);
2159	0	fe_add(r->Y, r->Z, r->Y);
2160	0	fe_sub(r->Z, t0, r->T);
2161	0	fe_add(r->T, t0, r->T);
2162	0	}
2163
2164		/* r = p + q */
2165		static void ge_add(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2166	0	{
2167	0	fe t0;
2168
2169	0	fe_add(r->X, p->Y, p->X);
2170	0	fe_sub(r->Y, p->Y, p->X);
2171	0	fe_mul(r->Z, r->X, q->YplusX);
2172	0	fe_mul(r->Y, r->Y, q->YminusX);
2173	0	fe_mul(r->T, q->T2d, p->T);
2174	0	fe_mul(r->X, p->Z, q->Z);
2175	0	fe_add(t0, r->X, r->X);
2176	0	fe_sub(r->X, r->Z, r->Y);
2177	0	fe_add(r->Y, r->Z, r->Y);
2178	0	fe_add(r->Z, t0, r->T);
2179	0	fe_sub(r->T, t0, r->T);
2180	0	}
2181
2182		/* r = p - q */
2183		static void ge_sub(ge_p1p1 r, const ge_p3 p, const ge_cached *q)
2184	0	{
2185	0	fe t0;
2186
2187	0	fe_add(r->X, p->Y, p->X);
2188	0	fe_sub(r->Y, p->Y, p->X);
2189	0	fe_mul(r->Z, r->X, q->YminusX);
2190	0	fe_mul(r->Y, r->Y, q->YplusX);
2191	0	fe_mul(r->T, q->T2d, p->T);
2192	0	fe_mul(r->X, p->Z, q->Z);
2193	0	fe_add(t0, r->X, r->X);
2194	0	fe_sub(r->X, r->Z, r->Y);
2195	0	fe_add(r->Y, r->Z, r->Y);
2196	0	fe_sub(r->Z, t0, r->T);
2197	0	fe_add(r->T, t0, r->T);
2198	0	}
2199
2200		static uint8_t equal(signed char b, signed char c)
2201	0	{
2202	0	uint8_t ub = b;
2203	0	uint8_t uc = c;
2204	0	uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2205	0	uint32_t y = x; /* 0: yes; 1..255: no */
2206	0	y -= 1; /* 4294967295: yes; 0..254: no */
2207	0	y >>= 31; /* 1: yes; 0: no */
2208	0	return y;
2209	0	}
2210
2211		static void cmov(ge_precomp t, const ge_precomp u, uint8_t b)
2212	0	{
2213	0	fe_cmov(t->yplusx, u->yplusx, b);
2214	0	fe_cmov(t->yminusx, u->yminusx, b);
2215	0	fe_cmov(t->xy2d, u->xy2d, b);
2216	0	}
2217
2218		/* k25519Precomp[i][j] = (j+1)256^iB */
2219		static const ge_precomp k25519Precomp[32][8] = {
2220		{
2221		{
2222		{ 25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2223		27544626, -11754271, -6079156, 2047605 },
2224		{ -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2225		5043384, 19500929, -15469378 },
2226		{ -8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2227		29287919, 11864899, -24514362, -4438546 },
2228		},
2229		{
2230		{ -12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2231		-11717903, -3814571, -358445, -10211303 },
2232		{ -21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2233		-15616551, 11189268, -26829678, -5319081 },
2234		{ 26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2235		-3128826, -9541118, -15472047, -4166697 },
2236		},
2237		{
2238		{ 15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2239		27787600, -14772189, 28944400, -1550024 },
2240		{ 16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2241		16354577, -11775962, 7689662, 11199574 },
2242		{ 30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2243		7512774, 10017326, -17749093, -9920357 },
2244		},
2245		{
2246		{ -17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2247		-28926210, 15006023, 3284568, -6276540 },
2248		{ 23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2249		7464579, 9656445, 13059162, 10374397 },
2250		{ 7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2251		-3839045, -641708, -101325 },
2252		},
2253		{
2254		{ 10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2255		32867885, 14515107, -15438304, 10819380 },
2256		{ 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2257		12483688, -12668491, 5581306 },
2258		{ 19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2259		28542350, 13850243, -23678021, -15815942 },
2260		},
2261		{
2262		{ -15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2263		-19188627, -15224819, -9818940, -12085777 },
2264		{ -8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2265		-15689887, 1762328, 14866737 },
2266		{ -18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2267		-28236412, 3959421, 27914454, 4383652 },
2268		},
2269		{
2270		{ 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2271		5230134, -23952439, -15175766 },
2272		{ -30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2273		20654025, 16520125, 30598449, 7715701 },
2274		{ 28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2275		-31400660, 1370708, 29794553, -1409300 },
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4323		{
4324		{ -22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4325		-1853465, 1367120, 25127874, 6671743 },
4326		{ 29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4327		21382910, 11042292, 25838796, 4642684 },
4328		{ -20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4329		30468147, -13900640, 18423289, 4177476 },
4330		},
4331		},
4332		};
4333
4334		static uint8_t negative(signed char b)
4335	0	{
4336	0	uint32_t x = b;
4337
4338	0	x >>= 31; /* 1: yes; 0: no */
4339	0	return x;
4340	0	}
4341
4342		static void table_select(ge_precomp *t, int pos, signed char b)
4343	0	{
4344	0	ge_precomp minust;
4345	0	uint8_t bnegative = negative(b);
4346	0	uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4347
4348	0	ge_precomp_0(t);
4349	0	cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4350	0	cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4351	0	cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4352	0	cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4353	0	cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4354	0	cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4355	0	cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4356	0	cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4357	0	fe_copy(minust.yplusx, t->yminusx);
4358	0	fe_copy(minust.yminusx, t->yplusx);
4359	0	fe_neg(minust.xy2d, t->xy2d);
4360	0	cmov(t, &minust, bnegative);
4361	0	}
4362
4363		/*
4364		* h = a * B
4365		*
4366		* where a = a[0]+256*a[1]+...+256^31 a[31]
4367		* B is the Ed25519 base point (x,4/5) with x positive.
4368		*
4369		* Preconditions:
4370		* a[31] <= 127
4371		*/
4372		static void ge_scalarmult_base(ge_p3 h, const uint8_t a)
4373	0	{
4374	0	signed char e[64];
4375	0	signed char carry;
4376	0	ge_p1p1 r;
4377	0	ge_p2 s;
4378	0	ge_precomp t;
4379	0	int i;
4380
4381	0	for (i = 0; i < 32; ++i) {
4382	0	e[2 * i + 0] = (a[i] >> 0) & 15;
4383	0	e[2 * i + 1] = (a[i] >> 4) & 15;
4384	0	}
4385		/* each e[i] is between 0 and 15 */
4386		/* e[63] is between 0 and 7 */
4387
4388	0	carry = 0;
4389	0	for (i = 0; i < 63; ++i) {
4390	0	e[i] += carry;
4391	0	carry = e[i] + 8;
4392	0	carry >>= 4;
4393	0	e[i] -= carry << 4;
4394	0	}
4395	0	e[63] += carry;
4396		/* each e[i] is between -8 and 8 */
4397
4398	0	ge_p3_0(h);
4399	0	for (i = 1; i < 64; i += 2) {
4400	0	table_select(&t, i / 2, e[i]);
4401	0	ge_madd(&r, h, &t);
4402	0	ge_p1p1_to_p3(h, &r);
4403	0	}
4404
4405	0	ge_p3_dbl(&r, h);
4406	0	ge_p1p1_to_p2(&s, &r);
4407	0	ge_p2_dbl(&r, &s);
4408	0	ge_p1p1_to_p2(&s, &r);
4409	0	ge_p2_dbl(&r, &s);
4410	0	ge_p1p1_to_p2(&s, &r);
4411	0	ge_p2_dbl(&r, &s);
4412	0	ge_p1p1_to_p3(h, &r);
4413
4414	0	for (i = 0; i < 64; i += 2) {
4415	0	table_select(&t, i / 2, e[i]);
4416	0	ge_madd(&r, h, &t);
4417	0	ge_p1p1_to_p3(h, &r);
4418	0	}
4419
4420	0	OPENSSL_cleanse(e, sizeof(e));
4421	0	}
4422
4423		#if !defined(BASE_2_51_IMPLEMENTED)
4424		/*
4425		* Replace (f,g) with (g,f) if b == 1;
4426		* replace (f,g) with (f,g) if b == 0.
4427		*
4428		* Preconditions: b in {0,1}.
4429		*/
4430		static void fe_cswap(fe f, fe g, unsigned int b)
4431		{
4432		size_t i;
4433
4434		b = 0 - b;
4435		for (i = 0; i < 10; i++) {
4436		int32_t x = f[i] ^ g[i];
4437		x &= b;
4438		f[i] ^= x;
4439		g[i] ^= x;
4440		}
4441		}
4442
4443		/*
4444		* h = f * 121666
4445		*
4446		* Can overlap h with f.
4447		*
4448		* Preconditions:
4449		* \|f\| bounded by 1.12^26,1.12^25,1.12^26,1.12^25,etc.
4450		*
4451		* Postconditions:
4452		* \|h\| bounded by 1.12^25,1.12^24,1.12^25,1.12^24,etc.
4453		*/
4454		static void fe_mul121666(fe h, fe f)
4455		{
4456		int32_t f0 = f[0];
4457		int32_t f1 = f[1];
4458		int32_t f2 = f[2];
4459		int32_t f3 = f[3];
4460		int32_t f4 = f[4];
4461		int32_t f5 = f[5];
4462		int32_t f6 = f[6];
4463		int32_t f7 = f[7];
4464		int32_t f8 = f[8];
4465		int32_t f9 = f[9];
4466		int64_t h0 = f0 * (int64_t)121666;
4467		int64_t h1 = f1 * (int64_t)121666;
4468		int64_t h2 = f2 * (int64_t)121666;
4469		int64_t h3 = f3 * (int64_t)121666;
4470		int64_t h4 = f4 * (int64_t)121666;
4471		int64_t h5 = f5 * (int64_t)121666;
4472		int64_t h6 = f6 * (int64_t)121666;
4473		int64_t h7 = f7 * (int64_t)121666;
4474		int64_t h8 = f8 * (int64_t)121666;
4475		int64_t h9 = f9 * (int64_t)121666;
4476		int64_t carry0;
4477		int64_t carry1;
4478		int64_t carry2;
4479		int64_t carry3;
4480		int64_t carry4;
4481		int64_t carry5;
4482		int64_t carry6;
4483		int64_t carry7;
4484		int64_t carry8;
4485		int64_t carry9;
4486
4487		carry9 = h9 + (1 << 24);
4488		h0 += (carry9 >> 25) * 19;
4489		h9 -= carry9 & kTop39Bits;
4490		carry1 = h1 + (1 << 24);
4491		h2 += carry1 >> 25;
4492		h1 -= carry1 & kTop39Bits;
4493		carry3 = h3 + (1 << 24);
4494		h4 += carry3 >> 25;
4495		h3 -= carry3 & kTop39Bits;
4496		carry5 = h5 + (1 << 24);
4497		h6 += carry5 >> 25;
4498		h5 -= carry5 & kTop39Bits;
4499		carry7 = h7 + (1 << 24);
4500		h8 += carry7 >> 25;
4501		h7 -= carry7 & kTop39Bits;
4502
4503		carry0 = h0 + (1 << 25);
4504		h1 += carry0 >> 26;
4505		h0 -= carry0 & kTop38Bits;
4506		carry2 = h2 + (1 << 25);
4507		h3 += carry2 >> 26;
4508		h2 -= carry2 & kTop38Bits;
4509		carry4 = h4 + (1 << 25);
4510		h5 += carry4 >> 26;
4511		h4 -= carry4 & kTop38Bits;
4512		carry6 = h6 + (1 << 25);
4513		h7 += carry6 >> 26;
4514		h6 -= carry6 & kTop38Bits;
4515		carry8 = h8 + (1 << 25);
4516		h9 += carry8 >> 26;
4517		h8 -= carry8 & kTop38Bits;
4518
4519		h[0] = (int32_t)h0;
4520		h[1] = (int32_t)h1;
4521		h[2] = (int32_t)h2;
4522		h[3] = (int32_t)h3;
4523		h[4] = (int32_t)h4;
4524		h[5] = (int32_t)h5;
4525		h[6] = (int32_t)h6;
4526		h[7] = (int32_t)h7;
4527		h[8] = (int32_t)h8;
4528		h[9] = (int32_t)h9;
4529		}
4530
4531		static void x25519_scalar_mult_generic(uint8_t out[32],
4532		const uint8_t scalar[32],
4533		const uint8_t point[32])
4534		{
4535		fe x1, x2, z2, x3, z3, tmp0, tmp1;
4536		uint8_t e[32];
4537		unsigned swap = 0;
4538		int pos;
4539
4540		memcpy(e, scalar, 32);
4541		e[0] &= 248;
4542		e[31] &= 127;
4543		e[31] \|= 64;
4544		fe_frombytes(x1, point);
4545		fe_1(x2);
4546		fe_0(z2);
4547		fe_copy(x3, x1);
4548		fe_1(z3);
4549
4550		for (pos = 254; pos >= 0; --pos) {
4551		unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4552		swap ^= b;
4553		fe_cswap(x2, x3, swap);
4554		fe_cswap(z2, z3, swap);
4555		swap = b;
4556		fe_sub(tmp0, x3, z3);
4557		fe_sub(tmp1, x2, z2);
4558		fe_add(x2, x2, z2);
4559		fe_add(z2, x3, z3);
4560		fe_mul(z3, tmp0, x2);
4561		fe_mul(z2, z2, tmp1);
4562		fe_sq(tmp0, tmp1);
4563		fe_sq(tmp1, x2);
4564		fe_add(x3, z3, z2);
4565		fe_sub(z2, z3, z2);
4566		fe_mul(x2, tmp1, tmp0);
4567		fe_sub(tmp1, tmp1, tmp0);
4568		fe_sq(z2, z2);
4569		fe_mul121666(z3, tmp1);
4570		fe_sq(x3, x3);
4571		fe_add(tmp0, tmp0, z3);
4572		fe_mul(z3, x1, z2);
4573		fe_mul(z2, tmp1, tmp0);
4574		}
4575
4576		fe_invert(z2, z2);
4577		fe_mul(x2, x2, z2);
4578		fe_tobytes(out, x2);
4579
4580		OPENSSL_cleanse(e, sizeof(e));
4581		}
4582
4583		static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4584		const uint8_t point[32])
4585		{
4586		x25519_scalar_mult_generic(out, scalar, point);
4587		}
4588		#endif
4589
4590		static void slide(signed char r, const uint8_t a)
4591	0	{
4592	0	int i;
4593	0	int b;
4594	0	int k;
4595
4596	0	for (i = 0; i < 256; ++i) {
4597	0	r[i] = 1 & (a[i >> 3] >> (i & 7));
4598	0	}
4599
4600	0	for (i = 0; i < 256; ++i) {
4601	0	if (r[i]) {
4602	0	for (b = 1; b <= 6 && i + b < 256; ++b) {
4603	0	if (r[i + b]) {
4604	0	if (r[i] + (r[i + b] << b) <= 15) {
4605	0	r[i] += r[i + b] << b;
4606	0	r[i + b] = 0;
4607	0	} else if (r[i] - (r[i + b] << b) >= -15) {
4608	0	r[i] -= r[i + b] << b;
4609	0	for (k = i + b; k < 256; ++k) {
4610	0	if (!r[k]) {
4611	0	r[k] = 1;
4612	0	break;
4613	0	}
4614	0	r[k] = 0;
4615	0	}
4616	0	} else {
4617	0	break;
4618	0	}
4619	0	}
4620	0	}
4621	0	}
4622	0	}
4623	0	}
4624
4625		static const ge_precomp Bi[8] = {
4626		{
4627		{ 25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4628		-11754271, -6079156, 2047605 },
4629		{ -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4630		5043384, 19500929, -15469378 },
4631		{ -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4632		11864899, -24514362, -4438546 },
4633		},
4634		{
4635		{ 15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4636		-14772189, 28944400, -1550024 },
4637		{ 16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4638		-11775962, 7689662, 11199574 },
4639		{ 30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4640		10017326, -17749093, -9920357 },
4641		},
4642		{
4643		{ 10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4644		14515107, -15438304, 10819380 },
4645		{ 4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4646		12483688, -12668491, 5581306 },
4647		{ 19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4648		13850243, -23678021, -15815942 },
4649		},
4650		{
4651		{ 5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4652		5230134, -23952439, -15175766 },
4653		{ -30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4654		16520125, 30598449, 7715701 },
4655		{ 28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4656		1370708, 29794553, -1409300 },
4657		},
4658		{
4659		{ -22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4660		-1361450, -13062696, 13821877 },
4661		{ -6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4662		-7212327, 18853322, -14220951 },
4663		{ 4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4664		-10431137, 2207753, -3209784 },
4665		},
4666		{
4667		{ -25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4668		-663000, -31111463, -16132436 },
4669		{ 25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4670		15725684, 171356, 6466918 },
4671		{ 23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4672		-14088058, -30714912, 16193877 },
4673		},
4674		{
4675		{ -33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4676		4729455, -18074513, 9256800 },
4677		{ -25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4678		9761698, -19827198, 630305 },
4679		{ -13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4680		-15960994, -2449256, -14291300 },
4681		},
4682		{
4683		{ -3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4684		15033784, 25105118, -7894876 },
4685		{ -24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4686		1573892, -2625887, 2198790, -15804619 },
4687		{ -3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4688		-16236442, -32461234, -12290683 },
4689		},
4690		};
4691
4692		/*
4693		* r = a * A + b * B
4694		*
4695		* where a = a[0]+256*a[1]+...+256^31 a[31].
4696		* and b = b[0]+256*b[1]+...+256^31 b[31].
4697		* B is the Ed25519 base point (x,4/5) with x positive.
4698		*/
4699		static void ge_double_scalarmult_vartime(ge_p2 r, const uint8_t a,
4700		const ge_p3 A, const uint8_t b)
4701	0	{
4702	0	signed char aslide[256];
4703	0	signed char bslide[256];
4704	0	ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4705	0	ge_p1p1 t;
4706	0	ge_p3 u;
4707	0	ge_p3 A2;
4708	0	int i;
4709
4710	0	slide(aslide, a);
4711	0	slide(bslide, b);
4712
4713	0	ge_p3_to_cached(&Ai[0], A);
4714	0	ge_p3_dbl(&t, A);
4715	0	ge_p1p1_to_p3(&A2, &t);
4716	0	ge_add(&t, &A2, &Ai[0]);
4717	0	ge_p1p1_to_p3(&u, &t);
4718	0	ge_p3_to_cached(&Ai[1], &u);
4719	0	ge_add(&t, &A2, &Ai[1]);
4720	0	ge_p1p1_to_p3(&u, &t);
4721	0	ge_p3_to_cached(&Ai[2], &u);
4722	0	ge_add(&t, &A2, &Ai[2]);
4723	0	ge_p1p1_to_p3(&u, &t);
4724	0	ge_p3_to_cached(&Ai[3], &u);
4725	0	ge_add(&t, &A2, &Ai[3]);
4726	0	ge_p1p1_to_p3(&u, &t);
4727	0	ge_p3_to_cached(&Ai[4], &u);
4728	0	ge_add(&t, &A2, &Ai[4]);
4729	0	ge_p1p1_to_p3(&u, &t);
4730	0	ge_p3_to_cached(&Ai[5], &u);
4731	0	ge_add(&t, &A2, &Ai[5]);
4732	0	ge_p1p1_to_p3(&u, &t);
4733	0	ge_p3_to_cached(&Ai[6], &u);
4734	0	ge_add(&t, &A2, &Ai[6]);
4735	0	ge_p1p1_to_p3(&u, &t);
4736	0	ge_p3_to_cached(&Ai[7], &u);
4737
4738	0	ge_p2_0(r);
4739
4740	0	for (i = 255; i >= 0; --i) {
4741	0	if (aslide[i] \|\| bslide[i]) {
4742	0	break;
4743	0	}
4744	0	}
4745
4746	0	for (; i >= 0; --i) {
4747	0	ge_p2_dbl(&t, r);
4748
4749	0	if (aslide[i] > 0) {
4750	0	ge_p1p1_to_p3(&u, &t);
4751	0	ge_add(&t, &u, &Ai[aslide[i] / 2]);
4752	0	} else if (aslide[i] < 0) {
4753	0	ge_p1p1_to_p3(&u, &t);
4754	0	ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4755	0	}
4756
4757	0	if (bslide[i] > 0) {
4758	0	ge_p1p1_to_p3(&u, &t);
4759	0	ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4760	0	} else if (bslide[i] < 0) {
4761	0	ge_p1p1_to_p3(&u, &t);
4762	0	ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4763	0	}
4764
4765	0	ge_p1p1_to_p2(r, &t);
4766	0	}
4767	0	}
4768
4769		/*
4770		* The set of scalars is \Z/l
4771		* where l = 2^252 + 27742317777372353535851937790883648493.
4772		*
4773		* Input:
4774		* s[0]+256s[1]+...+256^63s[63] = s
4775		*
4776		* Output:
4777		* s[0]+256s[1]+...+256^31s[31] = s mod l
4778		* where l = 2^252 + 27742317777372353535851937790883648493.
4779		* Overwrites s in place.
4780		*/
4781		static void x25519_sc_reduce(uint8_t *s)
4782	0	{
4783	0	int64_t s0 = kBottom21Bits & load_3(s);
4784	0	int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4785	0	int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4786	0	int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4787	0	int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4788	0	int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4789	0	int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4790	0	int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4791	0	int64_t s8 = kBottom21Bits & load_3(s + 21);
4792	0	int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4793	0	int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4794	0	int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4795	0	int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4796	0	int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4797	0	int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4798	0	int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4799	0	int64_t s16 = kBottom21Bits & load_3(s + 42);
4800	0	int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4801	0	int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4802	0	int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4803	0	int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4804	0	int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4805	0	int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4806	0	int64_t s23 = (load_4(s + 60) >> 3);
4807	0	int64_t carry0;
4808	0	int64_t carry1;
4809	0	int64_t carry2;
4810	0	int64_t carry3;
4811	0	int64_t carry4;
4812	0	int64_t carry5;
4813	0	int64_t carry6;
4814	0	int64_t carry7;
4815	0	int64_t carry8;
4816	0	int64_t carry9;
4817	0	int64_t carry10;
4818	0	int64_t carry11;
4819	0	int64_t carry12;
4820	0	int64_t carry13;
4821	0	int64_t carry14;
4822	0	int64_t carry15;
4823	0	int64_t carry16;
4824
4825	0	s11 += s23 * 666643;
4826	0	s12 += s23 * 470296;
4827	0	s13 += s23 * 654183;
4828	0	s14 -= s23 * 997805;
4829	0	s15 += s23 * 136657;
4830	0	s16 -= s23 * 683901;
4831	0	s23 = 0;
4832
4833	0	s10 += s22 * 666643;
4834	0	s11 += s22 * 470296;
4835	0	s12 += s22 * 654183;
4836	0	s13 -= s22 * 997805;
4837	0	s14 += s22 * 136657;
4838	0	s15 -= s22 * 683901;
4839	0	s22 = 0;
4840
4841	0	s9 += s21 * 666643;
4842	0	s10 += s21 * 470296;
4843	0	s11 += s21 * 654183;
4844	0	s12 -= s21 * 997805;
4845	0	s13 += s21 * 136657;
4846	0	s14 -= s21 * 683901;
4847	0	s21 = 0;
4848
4849	0	s8 += s20 * 666643;
4850	0	s9 += s20 * 470296;
4851	0	s10 += s20 * 654183;
4852	0	s11 -= s20 * 997805;
4853	0	s12 += s20 * 136657;
4854	0	s13 -= s20 * 683901;
4855	0	s20 = 0;
4856
4857	0	s7 += s19 * 666643;
4858	0	s8 += s19 * 470296;
4859	0	s9 += s19 * 654183;
4860	0	s10 -= s19 * 997805;
4861	0	s11 += s19 * 136657;
4862	0	s12 -= s19 * 683901;
4863	0	s19 = 0;
4864
4865	0	s6 += s18 * 666643;
4866	0	s7 += s18 * 470296;
4867	0	s8 += s18 * 654183;
4868	0	s9 -= s18 * 997805;
4869	0	s10 += s18 * 136657;
4870	0	s11 -= s18 * 683901;
4871	0	s18 = 0;
4872
4873	0	carry6 = (s6 + (1 << 20)) >> 21;
4874	0	s7 += carry6;
4875	0	s6 -= carry6 * (1 << 21);
4876	0	carry8 = (s8 + (1 << 20)) >> 21;
4877	0	s9 += carry8;
4878	0	s8 -= carry8 * (1 << 21);
4879	0	carry10 = (s10 + (1 << 20)) >> 21;
4880	0	s11 += carry10;
4881	0	s10 -= carry10 * (1 << 21);
4882	0	carry12 = (s12 + (1 << 20)) >> 21;
4883	0	s13 += carry12;
4884	0	s12 -= carry12 * (1 << 21);
4885	0	carry14 = (s14 + (1 << 20)) >> 21;
4886	0	s15 += carry14;
4887	0	s14 -= carry14 * (1 << 21);
4888	0	carry16 = (s16 + (1 << 20)) >> 21;
4889	0	s17 += carry16;
4890	0	s16 -= carry16 * (1 << 21);
4891
4892	0	carry7 = (s7 + (1 << 20)) >> 21;
4893	0	s8 += carry7;
4894	0	s7 -= carry7 * (1 << 21);
4895	0	carry9 = (s9 + (1 << 20)) >> 21;
4896	0	s10 += carry9;
4897	0	s9 -= carry9 * (1 << 21);
4898	0	carry11 = (s11 + (1 << 20)) >> 21;
4899	0	s12 += carry11;
4900	0	s11 -= carry11 * (1 << 21);
4901	0	carry13 = (s13 + (1 << 20)) >> 21;
4902	0	s14 += carry13;
4903	0	s13 -= carry13 * (1 << 21);
4904	0	carry15 = (s15 + (1 << 20)) >> 21;
4905	0	s16 += carry15;
4906	0	s15 -= carry15 * (1 << 21);
4907
4908	0	s5 += s17 * 666643;
4909	0	s6 += s17 * 470296;
4910	0	s7 += s17 * 654183;
4911	0	s8 -= s17 * 997805;
4912	0	s9 += s17 * 136657;
4913	0	s10 -= s17 * 683901;
4914	0	s17 = 0;
4915
4916	0	s4 += s16 * 666643;
4917	0	s5 += s16 * 470296;
4918	0	s6 += s16 * 654183;
4919	0	s7 -= s16 * 997805;
4920	0	s8 += s16 * 136657;
4921	0	s9 -= s16 * 683901;
4922	0	s16 = 0;
4923
4924	0	s3 += s15 * 666643;
4925	0	s4 += s15 * 470296;
4926	0	s5 += s15 * 654183;
4927	0	s6 -= s15 * 997805;
4928	0	s7 += s15 * 136657;
4929	0	s8 -= s15 * 683901;
4930	0	s15 = 0;
4931
4932	0	s2 += s14 * 666643;
4933	0	s3 += s14 * 470296;
4934	0	s4 += s14 * 654183;
4935	0	s5 -= s14 * 997805;
4936	0	s6 += s14 * 136657;
4937	0	s7 -= s14 * 683901;
4938	0	s14 = 0;
4939
4940	0	s1 += s13 * 666643;
4941	0	s2 += s13 * 470296;
4942	0	s3 += s13 * 654183;
4943	0	s4 -= s13 * 997805;
4944	0	s5 += s13 * 136657;
4945	0	s6 -= s13 * 683901;
4946	0	s13 = 0;
4947
4948	0	s0 += s12 * 666643;
4949	0	s1 += s12 * 470296;
4950	0	s2 += s12 * 654183;
4951	0	s3 -= s12 * 997805;
4952	0	s4 += s12 * 136657;
4953	0	s5 -= s12 * 683901;
4954	0	s12 = 0;
4955
4956	0	carry0 = (s0 + (1 << 20)) >> 21;
4957	0	s1 += carry0;
4958	0	s0 -= carry0 * (1 << 21);
4959	0	carry2 = (s2 + (1 << 20)) >> 21;
4960	0	s3 += carry2;
4961	0	s2 -= carry2 * (1 << 21);
4962	0	carry4 = (s4 + (1 << 20)) >> 21;
4963	0	s5 += carry4;
4964	0	s4 -= carry4 * (1 << 21);
4965	0	carry6 = (s6 + (1 << 20)) >> 21;
4966	0	s7 += carry6;
4967	0	s6 -= carry6 * (1 << 21);
4968	0	carry8 = (s8 + (1 << 20)) >> 21;
4969	0	s9 += carry8;
4970	0	s8 -= carry8 * (1 << 21);
4971	0	carry10 = (s10 + (1 << 20)) >> 21;
4972	0	s11 += carry10;
4973	0	s10 -= carry10 * (1 << 21);
4974
4975	0	carry1 = (s1 + (1 << 20)) >> 21;
4976	0	s2 += carry1;
4977	0	s1 -= carry1 * (1 << 21);
4978	0	carry3 = (s3 + (1 << 20)) >> 21;
4979	0	s4 += carry3;
4980	0	s3 -= carry3 * (1 << 21);
4981	0	carry5 = (s5 + (1 << 20)) >> 21;
4982	0	s6 += carry5;
4983	0	s5 -= carry5 * (1 << 21);
4984	0	carry7 = (s7 + (1 << 20)) >> 21;
4985	0	s8 += carry7;
4986	0	s7 -= carry7 * (1 << 21);
4987	0	carry9 = (s9 + (1 << 20)) >> 21;
4988	0	s10 += carry9;
4989	0	s9 -= carry9 * (1 << 21);
4990	0	carry11 = (s11 + (1 << 20)) >> 21;
4991	0	s12 += carry11;
4992	0	s11 -= carry11 * (1 << 21);
4993
4994	0	s0 += s12 * 666643;
4995	0	s1 += s12 * 470296;
4996	0	s2 += s12 * 654183;
4997	0	s3 -= s12 * 997805;
4998	0	s4 += s12 * 136657;
4999	0	s5 -= s12 * 683901;
5000	0	s12 = 0;
5001
5002	0	carry0 = s0 >> 21;
5003	0	s1 += carry0;
5004	0	s0 -= carry0 * (1 << 21);
5005	0	carry1 = s1 >> 21;
5006	0	s2 += carry1;
5007	0	s1 -= carry1 * (1 << 21);
5008	0	carry2 = s2 >> 21;
5009	0	s3 += carry2;
5010	0	s2 -= carry2 * (1 << 21);
5011	0	carry3 = s3 >> 21;
5012	0	s4 += carry3;
5013	0	s3 -= carry3 * (1 << 21);
5014	0	carry4 = s4 >> 21;
5015	0	s5 += carry4;
5016	0	s4 -= carry4 * (1 << 21);
5017	0	carry5 = s5 >> 21;
5018	0	s6 += carry5;
5019	0	s5 -= carry5 * (1 << 21);
5020	0	carry6 = s6 >> 21;
5021	0	s7 += carry6;
5022	0	s6 -= carry6 * (1 << 21);
5023	0	carry7 = s7 >> 21;
5024	0	s8 += carry7;
5025	0	s7 -= carry7 * (1 << 21);
5026	0	carry8 = s8 >> 21;
5027	0	s9 += carry8;
5028	0	s8 -= carry8 * (1 << 21);
5029	0	carry9 = s9 >> 21;
5030	0	s10 += carry9;
5031	0	s9 -= carry9 * (1 << 21);
5032	0	carry10 = s10 >> 21;
5033	0	s11 += carry10;
5034	0	s10 -= carry10 * (1 << 21);
5035	0	carry11 = s11 >> 21;
5036	0	s12 += carry11;
5037	0	s11 -= carry11 * (1 << 21);
5038
5039	0	s0 += s12 * 666643;
5040	0	s1 += s12 * 470296;
5041	0	s2 += s12 * 654183;
5042	0	s3 -= s12 * 997805;
5043	0	s4 += s12 * 136657;
5044	0	s5 -= s12 * 683901;
5045	0	s12 = 0;
5046
5047	0	carry0 = s0 >> 21;
5048	0	s1 += carry0;
5049	0	s0 -= carry0 * (1 << 21);
5050	0	carry1 = s1 >> 21;
5051	0	s2 += carry1;
5052	0	s1 -= carry1 * (1 << 21);
5053	0	carry2 = s2 >> 21;
5054	0	s3 += carry2;
5055	0	s2 -= carry2 * (1 << 21);
5056	0	carry3 = s3 >> 21;
5057	0	s4 += carry3;
5058	0	s3 -= carry3 * (1 << 21);
5059	0	carry4 = s4 >> 21;
5060	0	s5 += carry4;
5061	0	s4 -= carry4 * (1 << 21);
5062	0	carry5 = s5 >> 21;
5063	0	s6 += carry5;
5064	0	s5 -= carry5 * (1 << 21);
5065	0	carry6 = s6 >> 21;
5066	0	s7 += carry6;
5067	0	s6 -= carry6 * (1 << 21);
5068	0	carry7 = s7 >> 21;
5069	0	s8 += carry7;
5070	0	s7 -= carry7 * (1 << 21);
5071	0	carry8 = s8 >> 21;
5072	0	s9 += carry8;
5073	0	s8 -= carry8 * (1 << 21);
5074	0	carry9 = s9 >> 21;
5075	0	s10 += carry9;
5076	0	s9 -= carry9 * (1 << 21);
5077	0	carry10 = s10 >> 21;
5078	0	s11 += carry10;
5079	0	s10 -= carry10 * (1 << 21);
5080
5081	0	s[0] = (uint8_t)(s0 >> 0);
5082	0	s[1] = (uint8_t)(s0 >> 8);
5083	0	s[2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5084	0	s[3] = (uint8_t)(s1 >> 3);
5085	0	s[4] = (uint8_t)(s1 >> 11);
5086	0	s[5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5087	0	s[6] = (uint8_t)(s2 >> 6);
5088	0	s[7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5089	0	s[8] = (uint8_t)(s3 >> 1);
5090	0	s[9] = (uint8_t)(s3 >> 9);
5091	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5092	0	s[11] = (uint8_t)(s4 >> 4);
5093	0	s[12] = (uint8_t)(s4 >> 12);
5094	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5095	0	s[14] = (uint8_t)(s5 >> 7);
5096	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5097	0	s[16] = (uint8_t)(s6 >> 2);
5098	0	s[17] = (uint8_t)(s6 >> 10);
5099	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5100	0	s[19] = (uint8_t)(s7 >> 5);
5101	0	s[20] = (uint8_t)(s7 >> 13);
5102	0	s[21] = (uint8_t)(s8 >> 0);
5103	0	s[22] = (uint8_t)(s8 >> 8);
5104	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5105	0	s[24] = (uint8_t)(s9 >> 3);
5106	0	s[25] = (uint8_t)(s9 >> 11);
5107	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5108	0	s[27] = (uint8_t)(s10 >> 6);
5109	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5110	0	s[29] = (uint8_t)(s11 >> 1);
5111	0	s[30] = (uint8_t)(s11 >> 9);
5112	0	s[31] = (uint8_t)(s11 >> 17);
5113	0	}
5114
5115		/*
5116		* Input:
5117		* a[0]+256a[1]+...+256^31a[31] = a
5118		* b[0]+256b[1]+...+256^31b[31] = b
5119		* c[0]+256c[1]+...+256^31c[31] = c
5120		*
5121		* Output:
5122		* s[0]+256s[1]+...+256^31s[31] = (ab+c) mod l
5123		* where l = 2^252 + 27742317777372353535851937790883648493.
5124		*/
5125		static void sc_muladd(uint8_t s, const uint8_t a, const uint8_t *b,
5126		const uint8_t *c)
5127	0	{
5128	0	int64_t a0 = kBottom21Bits & load_3(a);
5129	0	int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
5130	0	int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
5131	0	int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
5132	0	int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
5133	0	int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
5134	0	int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
5135	0	int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
5136	0	int64_t a8 = kBottom21Bits & load_3(a + 21);
5137	0	int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
5138	0	int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
5139	0	int64_t a11 = (load_4(a + 28) >> 7);
5140	0	int64_t b0 = kBottom21Bits & load_3(b);
5141	0	int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
5142	0	int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
5143	0	int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
5144	0	int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
5145	0	int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
5146	0	int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
5147	0	int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
5148	0	int64_t b8 = kBottom21Bits & load_3(b + 21);
5149	0	int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
5150	0	int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
5151	0	int64_t b11 = (load_4(b + 28) >> 7);
5152	0	int64_t c0 = kBottom21Bits & load_3(c);
5153	0	int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
5154	0	int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
5155	0	int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
5156	0	int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
5157	0	int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
5158	0	int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
5159	0	int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
5160	0	int64_t c8 = kBottom21Bits & load_3(c + 21);
5161	0	int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
5162	0	int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5163	0	int64_t c11 = (load_4(c + 28) >> 7);
5164	0	int64_t s0;
5165	0	int64_t s1;
5166	0	int64_t s2;
5167	0	int64_t s3;
5168	0	int64_t s4;
5169	0	int64_t s5;
5170	0	int64_t s6;
5171	0	int64_t s7;
5172	0	int64_t s8;
5173	0	int64_t s9;
5174	0	int64_t s10;
5175	0	int64_t s11;
5176	0	int64_t s12;
5177	0	int64_t s13;
5178	0	int64_t s14;
5179	0	int64_t s15;
5180	0	int64_t s16;
5181	0	int64_t s17;
5182	0	int64_t s18;
5183	0	int64_t s19;
5184	0	int64_t s20;
5185	0	int64_t s21;
5186	0	int64_t s22;
5187	0	int64_t s23;
5188	0	int64_t carry0;
5189	0	int64_t carry1;
5190	0	int64_t carry2;
5191	0	int64_t carry3;
5192	0	int64_t carry4;
5193	0	int64_t carry5;
5194	0	int64_t carry6;
5195	0	int64_t carry7;
5196	0	int64_t carry8;
5197	0	int64_t carry9;
5198	0	int64_t carry10;
5199	0	int64_t carry11;
5200	0	int64_t carry12;
5201	0	int64_t carry13;
5202	0	int64_t carry14;
5203	0	int64_t carry15;
5204	0	int64_t carry16;
5205	0	int64_t carry17;
5206	0	int64_t carry18;
5207	0	int64_t carry19;
5208	0	int64_t carry20;
5209	0	int64_t carry21;
5210	0	int64_t carry22;
5211
5212	0	s0 = c0 + a0 * b0;
5213	0	s1 = c1 + a0 * b1 + a1 * b0;
5214	0	s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5215	0	s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5216	0	s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5217	0	s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5218	0	s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5219	0	s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5220	0	s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5221	0	s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5222	0	s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
5223	0	s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0;
5224	0	s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5225	0	s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5226	0	s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5227	0	s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5228	0	s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5229	0	s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5230	0	s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5231	0	s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5232	0	s20 = a9 * b11 + a10 * b10 + a11 * b9;
5233	0	s21 = a10 * b11 + a11 * b10;
5234	0	s22 = a11 * b11;
5235	0	s23 = 0;
5236
5237	0	carry0 = (s0 + (1 << 20)) >> 21;
5238	0	s1 += carry0;
5239	0	s0 -= carry0 * (1 << 21);
5240	0	carry2 = (s2 + (1 << 20)) >> 21;
5241	0	s3 += carry2;
5242	0	s2 -= carry2 * (1 << 21);
5243	0	carry4 = (s4 + (1 << 20)) >> 21;
5244	0	s5 += carry4;
5245	0	s4 -= carry4 * (1 << 21);
5246	0	carry6 = (s6 + (1 << 20)) >> 21;
5247	0	s7 += carry6;
5248	0	s6 -= carry6 * (1 << 21);
5249	0	carry8 = (s8 + (1 << 20)) >> 21;
5250	0	s9 += carry8;
5251	0	s8 -= carry8 * (1 << 21);
5252	0	carry10 = (s10 + (1 << 20)) >> 21;
5253	0	s11 += carry10;
5254	0	s10 -= carry10 * (1 << 21);
5255	0	carry12 = (s12 + (1 << 20)) >> 21;
5256	0	s13 += carry12;
5257	0	s12 -= carry12 * (1 << 21);
5258	0	carry14 = (s14 + (1 << 20)) >> 21;
5259	0	s15 += carry14;
5260	0	s14 -= carry14 * (1 << 21);
5261	0	carry16 = (s16 + (1 << 20)) >> 21;
5262	0	s17 += carry16;
5263	0	s16 -= carry16 * (1 << 21);
5264	0	carry18 = (s18 + (1 << 20)) >> 21;
5265	0	s19 += carry18;
5266	0	s18 -= carry18 * (1 << 21);
5267	0	carry20 = (s20 + (1 << 20)) >> 21;
5268	0	s21 += carry20;
5269	0	s20 -= carry20 * (1 << 21);
5270	0	carry22 = (s22 + (1 << 20)) >> 21;
5271	0	s23 += carry22;
5272	0	s22 -= carry22 * (1 << 21);
5273
5274	0	carry1 = (s1 + (1 << 20)) >> 21;
5275	0	s2 += carry1;
5276	0	s1 -= carry1 * (1 << 21);
5277	0	carry3 = (s3 + (1 << 20)) >> 21;
5278	0	s4 += carry3;
5279	0	s3 -= carry3 * (1 << 21);
5280	0	carry5 = (s5 + (1 << 20)) >> 21;
5281	0	s6 += carry5;
5282	0	s5 -= carry5 * (1 << 21);
5283	0	carry7 = (s7 + (1 << 20)) >> 21;
5284	0	s8 += carry7;
5285	0	s7 -= carry7 * (1 << 21);
5286	0	carry9 = (s9 + (1 << 20)) >> 21;
5287	0	s10 += carry9;
5288	0	s9 -= carry9 * (1 << 21);
5289	0	carry11 = (s11 + (1 << 20)) >> 21;
5290	0	s12 += carry11;
5291	0	s11 -= carry11 * (1 << 21);
5292	0	carry13 = (s13 + (1 << 20)) >> 21;
5293	0	s14 += carry13;
5294	0	s13 -= carry13 * (1 << 21);
5295	0	carry15 = (s15 + (1 << 20)) >> 21;
5296	0	s16 += carry15;
5297	0	s15 -= carry15 * (1 << 21);
5298	0	carry17 = (s17 + (1 << 20)) >> 21;
5299	0	s18 += carry17;
5300	0	s17 -= carry17 * (1 << 21);
5301	0	carry19 = (s19 + (1 << 20)) >> 21;
5302	0	s20 += carry19;
5303	0	s19 -= carry19 * (1 << 21);
5304	0	carry21 = (s21 + (1 << 20)) >> 21;
5305	0	s22 += carry21;
5306	0	s21 -= carry21 * (1 << 21);
5307
5308	0	s11 += s23 * 666643;
5309	0	s12 += s23 * 470296;
5310	0	s13 += s23 * 654183;
5311	0	s14 -= s23 * 997805;
5312	0	s15 += s23 * 136657;
5313	0	s16 -= s23 * 683901;
5314	0	s23 = 0;
5315
5316	0	s10 += s22 * 666643;
5317	0	s11 += s22 * 470296;
5318	0	s12 += s22 * 654183;
5319	0	s13 -= s22 * 997805;
5320	0	s14 += s22 * 136657;
5321	0	s15 -= s22 * 683901;
5322	0	s22 = 0;
5323
5324	0	s9 += s21 * 666643;
5325	0	s10 += s21 * 470296;
5326	0	s11 += s21 * 654183;
5327	0	s12 -= s21 * 997805;
5328	0	s13 += s21 * 136657;
5329	0	s14 -= s21 * 683901;
5330	0	s21 = 0;
5331
5332	0	s8 += s20 * 666643;
5333	0	s9 += s20 * 470296;
5334	0	s10 += s20 * 654183;
5335	0	s11 -= s20 * 997805;
5336	0	s12 += s20 * 136657;
5337	0	s13 -= s20 * 683901;
5338	0	s20 = 0;
5339
5340	0	s7 += s19 * 666643;
5341	0	s8 += s19 * 470296;
5342	0	s9 += s19 * 654183;
5343	0	s10 -= s19 * 997805;
5344	0	s11 += s19 * 136657;
5345	0	s12 -= s19 * 683901;
5346	0	s19 = 0;
5347
5348	0	s6 += s18 * 666643;
5349	0	s7 += s18 * 470296;
5350	0	s8 += s18 * 654183;
5351	0	s9 -= s18 * 997805;
5352	0	s10 += s18 * 136657;
5353	0	s11 -= s18 * 683901;
5354	0	s18 = 0;
5355
5356	0	carry6 = (s6 + (1 << 20)) >> 21;
5357	0	s7 += carry6;
5358	0	s6 -= carry6 * (1 << 21);
5359	0	carry8 = (s8 + (1 << 20)) >> 21;
5360	0	s9 += carry8;
5361	0	s8 -= carry8 * (1 << 21);
5362	0	carry10 = (s10 + (1 << 20)) >> 21;
5363	0	s11 += carry10;
5364	0	s10 -= carry10 * (1 << 21);
5365	0	carry12 = (s12 + (1 << 20)) >> 21;
5366	0	s13 += carry12;
5367	0	s12 -= carry12 * (1 << 21);
5368	0	carry14 = (s14 + (1 << 20)) >> 21;
5369	0	s15 += carry14;
5370	0	s14 -= carry14 * (1 << 21);
5371	0	carry16 = (s16 + (1 << 20)) >> 21;
5372	0	s17 += carry16;
5373	0	s16 -= carry16 * (1 << 21);
5374
5375	0	carry7 = (s7 + (1 << 20)) >> 21;
5376	0	s8 += carry7;
5377	0	s7 -= carry7 * (1 << 21);
5378	0	carry9 = (s9 + (1 << 20)) >> 21;
5379	0	s10 += carry9;
5380	0	s9 -= carry9 * (1 << 21);
5381	0	carry11 = (s11 + (1 << 20)) >> 21;
5382	0	s12 += carry11;
5383	0	s11 -= carry11 * (1 << 21);
5384	0	carry13 = (s13 + (1 << 20)) >> 21;
5385	0	s14 += carry13;
5386	0	s13 -= carry13 * (1 << 21);
5387	0	carry15 = (s15 + (1 << 20)) >> 21;
5388	0	s16 += carry15;
5389	0	s15 -= carry15 * (1 << 21);
5390
5391	0	s5 += s17 * 666643;
5392	0	s6 += s17 * 470296;
5393	0	s7 += s17 * 654183;
5394	0	s8 -= s17 * 997805;
5395	0	s9 += s17 * 136657;
5396	0	s10 -= s17 * 683901;
5397	0	s17 = 0;
5398
5399	0	s4 += s16 * 666643;
5400	0	s5 += s16 * 470296;
5401	0	s6 += s16 * 654183;
5402	0	s7 -= s16 * 997805;
5403	0	s8 += s16 * 136657;
5404	0	s9 -= s16 * 683901;
5405	0	s16 = 0;
5406
5407	0	s3 += s15 * 666643;
5408	0	s4 += s15 * 470296;
5409	0	s5 += s15 * 654183;
5410	0	s6 -= s15 * 997805;
5411	0	s7 += s15 * 136657;
5412	0	s8 -= s15 * 683901;
5413	0	s15 = 0;
5414
5415	0	s2 += s14 * 666643;
5416	0	s3 += s14 * 470296;
5417	0	s4 += s14 * 654183;
5418	0	s5 -= s14 * 997805;
5419	0	s6 += s14 * 136657;
5420	0	s7 -= s14 * 683901;
5421	0	s14 = 0;
5422
5423	0	s1 += s13 * 666643;
5424	0	s2 += s13 * 470296;
5425	0	s3 += s13 * 654183;
5426	0	s4 -= s13 * 997805;
5427	0	s5 += s13 * 136657;
5428	0	s6 -= s13 * 683901;
5429	0	s13 = 0;
5430
5431	0	s0 += s12 * 666643;
5432	0	s1 += s12 * 470296;
5433	0	s2 += s12 * 654183;
5434	0	s3 -= s12 * 997805;
5435	0	s4 += s12 * 136657;
5436	0	s5 -= s12 * 683901;
5437	0	s12 = 0;
5438
5439	0	carry0 = (s0 + (1 << 20)) >> 21;
5440	0	s1 += carry0;
5441	0	s0 -= carry0 * (1 << 21);
5442	0	carry2 = (s2 + (1 << 20)) >> 21;
5443	0	s3 += carry2;
5444	0	s2 -= carry2 * (1 << 21);
5445	0	carry4 = (s4 + (1 << 20)) >> 21;
5446	0	s5 += carry4;
5447	0	s4 -= carry4 * (1 << 21);
5448	0	carry6 = (s6 + (1 << 20)) >> 21;
5449	0	s7 += carry6;
5450	0	s6 -= carry6 * (1 << 21);
5451	0	carry8 = (s8 + (1 << 20)) >> 21;
5452	0	s9 += carry8;
5453	0	s8 -= carry8 * (1 << 21);
5454	0	carry10 = (s10 + (1 << 20)) >> 21;
5455	0	s11 += carry10;
5456	0	s10 -= carry10 * (1 << 21);
5457
5458	0	carry1 = (s1 + (1 << 20)) >> 21;
5459	0	s2 += carry1;
5460	0	s1 -= carry1 * (1 << 21);
5461	0	carry3 = (s3 + (1 << 20)) >> 21;
5462	0	s4 += carry3;
5463	0	s3 -= carry3 * (1 << 21);
5464	0	carry5 = (s5 + (1 << 20)) >> 21;
5465	0	s6 += carry5;
5466	0	s5 -= carry5 * (1 << 21);
5467	0	carry7 = (s7 + (1 << 20)) >> 21;
5468	0	s8 += carry7;
5469	0	s7 -= carry7 * (1 << 21);
5470	0	carry9 = (s9 + (1 << 20)) >> 21;
5471	0	s10 += carry9;
5472	0	s9 -= carry9 * (1 << 21);
5473	0	carry11 = (s11 + (1 << 20)) >> 21;
5474	0	s12 += carry11;
5475	0	s11 -= carry11 * (1 << 21);
5476
5477	0	s0 += s12 * 666643;
5478	0	s1 += s12 * 470296;
5479	0	s2 += s12 * 654183;
5480	0	s3 -= s12 * 997805;
5481	0	s4 += s12 * 136657;
5482	0	s5 -= s12 * 683901;
5483	0	s12 = 0;
5484
5485	0	carry0 = s0 >> 21;
5486	0	s1 += carry0;
5487	0	s0 -= carry0 * (1 << 21);
5488	0	carry1 = s1 >> 21;
5489	0	s2 += carry1;
5490	0	s1 -= carry1 * (1 << 21);
5491	0	carry2 = s2 >> 21;
5492	0	s3 += carry2;
5493	0	s2 -= carry2 * (1 << 21);
5494	0	carry3 = s3 >> 21;
5495	0	s4 += carry3;
5496	0	s3 -= carry3 * (1 << 21);
5497	0	carry4 = s4 >> 21;
5498	0	s5 += carry4;
5499	0	s4 -= carry4 * (1 << 21);
5500	0	carry5 = s5 >> 21;
5501	0	s6 += carry5;
5502	0	s5 -= carry5 * (1 << 21);
5503	0	carry6 = s6 >> 21;
5504	0	s7 += carry6;
5505	0	s6 -= carry6 * (1 << 21);
5506	0	carry7 = s7 >> 21;
5507	0	s8 += carry7;
5508	0	s7 -= carry7 * (1 << 21);
5509	0	carry8 = s8 >> 21;
5510	0	s9 += carry8;
5511	0	s8 -= carry8 * (1 << 21);
5512	0	carry9 = s9 >> 21;
5513	0	s10 += carry9;
5514	0	s9 -= carry9 * (1 << 21);
5515	0	carry10 = s10 >> 21;
5516	0	s11 += carry10;
5517	0	s10 -= carry10 * (1 << 21);
5518	0	carry11 = s11 >> 21;
5519	0	s12 += carry11;
5520	0	s11 -= carry11 * (1 << 21);
5521
5522	0	s0 += s12 * 666643;
5523	0	s1 += s12 * 470296;
5524	0	s2 += s12 * 654183;
5525	0	s3 -= s12 * 997805;
5526	0	s4 += s12 * 136657;
5527	0	s5 -= s12 * 683901;
5528	0	s12 = 0;
5529
5530	0	carry0 = s0 >> 21;
5531	0	s1 += carry0;
5532	0	s0 -= carry0 * (1 << 21);
5533	0	carry1 = s1 >> 21;
5534	0	s2 += carry1;
5535	0	s1 -= carry1 * (1 << 21);
5536	0	carry2 = s2 >> 21;
5537	0	s3 += carry2;
5538	0	s2 -= carry2 * (1 << 21);
5539	0	carry3 = s3 >> 21;
5540	0	s4 += carry3;
5541	0	s3 -= carry3 * (1 << 21);
5542	0	carry4 = s4 >> 21;
5543	0	s5 += carry4;
5544	0	s4 -= carry4 * (1 << 21);
5545	0	carry5 = s5 >> 21;
5546	0	s6 += carry5;
5547	0	s5 -= carry5 * (1 << 21);
5548	0	carry6 = s6 >> 21;
5549	0	s7 += carry6;
5550	0	s6 -= carry6 * (1 << 21);
5551	0	carry7 = s7 >> 21;
5552	0	s8 += carry7;
5553	0	s7 -= carry7 * (1 << 21);
5554	0	carry8 = s8 >> 21;
5555	0	s9 += carry8;
5556	0	s8 -= carry8 * (1 << 21);
5557	0	carry9 = s9 >> 21;
5558	0	s10 += carry9;
5559	0	s9 -= carry9 * (1 << 21);
5560	0	carry10 = s10 >> 21;
5561	0	s11 += carry10;
5562	0	s10 -= carry10 * (1 << 21);
5563
5564	0	s[0] = (uint8_t)(s0 >> 0);
5565	0	s[1] = (uint8_t)(s0 >> 8);
5566	0	s[2] = (uint8_t)((s0 >> 16) \| (s1 << 5));
5567	0	s[3] = (uint8_t)(s1 >> 3);
5568	0	s[4] = (uint8_t)(s1 >> 11);
5569	0	s[5] = (uint8_t)((s1 >> 19) \| (s2 << 2));
5570	0	s[6] = (uint8_t)(s2 >> 6);
5571	0	s[7] = (uint8_t)((s2 >> 14) \| (s3 << 7));
5572	0	s[8] = (uint8_t)(s3 >> 1);
5573	0	s[9] = (uint8_t)(s3 >> 9);
5574	0	s[10] = (uint8_t)((s3 >> 17) \| (s4 << 4));
5575	0	s[11] = (uint8_t)(s4 >> 4);
5576	0	s[12] = (uint8_t)(s4 >> 12);
5577	0	s[13] = (uint8_t)((s4 >> 20) \| (s5 << 1));
5578	0	s[14] = (uint8_t)(s5 >> 7);
5579	0	s[15] = (uint8_t)((s5 >> 15) \| (s6 << 6));
5580	0	s[16] = (uint8_t)(s6 >> 2);
5581	0	s[17] = (uint8_t)(s6 >> 10);
5582	0	s[18] = (uint8_t)((s6 >> 18) \| (s7 << 3));
5583	0	s[19] = (uint8_t)(s7 >> 5);
5584	0	s[20] = (uint8_t)(s7 >> 13);
5585	0	s[21] = (uint8_t)(s8 >> 0);
5586	0	s[22] = (uint8_t)(s8 >> 8);
5587	0	s[23] = (uint8_t)((s8 >> 16) \| (s9 << 5));
5588	0	s[24] = (uint8_t)(s9 >> 3);
5589	0	s[25] = (uint8_t)(s9 >> 11);
5590	0	s[26] = (uint8_t)((s9 >> 19) \| (s10 << 2));
5591	0	s[27] = (uint8_t)(s10 >> 6);
5592	0	s[28] = (uint8_t)((s10 >> 14) \| (s11 << 7));
5593	0	s[29] = (uint8_t)(s11 >> 1);
5594	0	s[30] = (uint8_t)(s11 >> 9);
5595	0	s[31] = (uint8_t)(s11 >> 17);
5596	0	}
5597
5598		static int hash_init_with_dom(EVP_MD_CTX *hash_ctx,
5599		EVP_MD *sha512,
5600		const uint8_t dom2flag,
5601		const uint8_t phflag,
5602		const uint8_t *context,
5603		const size_t context_len)
5604	0	{
5605		/* ASCII: "SigEd25519 no Ed25519 collisions", in hex for EBCDIC compatibility */
5606	0	const char dom_s[] = "\x53\x69\x67\x45\x64\x32\x35\x35\x31\x39\x20\x6e"
5607	0	"\x6f\x20\x45\x64\x32\x35\x35\x31\x39\x20\x63\x6f"
5608	0	"\x6c\x6c\x69\x73\x69\x6f\x6e\x73";
5609	0	uint8_t dom[2];
5610
5611	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL))
5612	0	return 0;
5613
5614		/* return early if dom2flag is not set */
5615	0	if (!dom2flag)
5616	0	return 1;
5617
5618	0	if (context_len > UINT8_MAX)
5619	0	return 0;
5620
5621	0	dom[0] = (uint8_t)(phflag >= 1 ? 1 : 0);
5622	0	dom[1] = (uint8_t)context_len;
5623
5624	0	if (!EVP_DigestUpdate(hash_ctx, dom_s, sizeof(dom_s) - 1)
5625	0	\|\| !EVP_DigestUpdate(hash_ctx, dom, sizeof(dom))
5626	0	\|\| !EVP_DigestUpdate(hash_ctx, context, context_len)) {
5627	0	return 0;
5628	0	}
5629
5630	0	return 1;
5631	0	}
5632
5633		int ossl_ed25519_sign(uint8_t out_sig, const uint8_t tbs, size_t tbs_len,
5634		const uint8_t public_key[32], const uint8_t private_key[32],
5635		const uint8_t dom2flag, const uint8_t phflag, const uint8_t csflag,
5636		const uint8_t *context, size_t context_len,
5637		OSSL_LIB_CTX libctx, const char propq)
5638	0	{
5639	0	uint8_t az[SHA512_DIGEST_LENGTH];
5640	0	uint8_t nonce[SHA512_DIGEST_LENGTH];
5641	0	ge_p3 R;
5642	0	uint8_t hram[SHA512_DIGEST_LENGTH];
5643	0	EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5644	0	EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5645	0	unsigned int sz;
5646	0	int res = 0;
5647
5648	0	if (context == NULL)
5649	0	context_len = 0;
5650
5651		/* if csflag is set, then a non-empty context-string is required */
5652	0	if (csflag && context_len == 0)
5653	0	goto err;
5654
5655		/* if dom2flag is not set, then an empty context-string is required */
5656	0	if (!dom2flag && context_len > 0)
5657	0	goto err;
5658
5659	0	if (sha512 == NULL \|\| hash_ctx == NULL)
5660	0	goto err;
5661
5662	0	if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL)
5663	0	\|\| !EVP_DigestUpdate(hash_ctx, private_key, 32)
5664	0	\|\| !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5665	0	goto err;
5666
5667	0	az[0] &= 248;
5668	0	az[31] &= 63;
5669	0	az[31] \|= 64;
5670
5671	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5672	0	\|\| !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5673	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5674	0	\|\| !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5675	0	goto err;
5676
5677	0	x25519_sc_reduce(nonce);
5678	0	ge_scalarmult_base(&R, nonce);
5679	0	ge_p3_tobytes(out_sig, &R);
5680
5681	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5682	0	\|\| !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5683	0	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5684	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5685	0	\|\| !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5686	0	goto err;
5687
5688	0	x25519_sc_reduce(hram);
5689	0	sc_muladd(out_sig + 32, hram, az, nonce);
5690
5691	0	res = 1;
5692	0	err:
5693	0	OPENSSL_cleanse(nonce, sizeof(nonce));
5694	0	OPENSSL_cleanse(az, sizeof(az));
5695	0	EVP_MD_free(sha512);
5696	0	EVP_MD_CTX_free(hash_ctx);
5697	0	return res;
5698	0	}
5699
5700		/*
5701		* This function should not be necessary since ossl_ed25519_verify() already
5702		* does this check internally.
5703		* For some reason the FIPS ACVP requires a EDDSA KeyVer test.
5704		*/
5705		int ossl_ed25519_pubkey_verify(const uint8_t *pub, size_t pub_len)
5706	0	{
5707	0	ge_p3 A;
5708
5709	0	if (pub_len != ED25519_KEYLEN)
5710	0	return 0;
5711	0	return (ge_frombytes_vartime(&A, pub) == 0);
5712	0	}
5713
5714		static const char allzeroes[15];
5715
5716		int ossl_ed25519_verify(const uint8_t *tbs, size_t tbs_len,
5717		const uint8_t signature[64], const uint8_t public_key[32],
5718		const uint8_t dom2flag, const uint8_t phflag, const uint8_t csflag,
5719		const uint8_t *context, size_t context_len,
5720		OSSL_LIB_CTX libctx, const char propq)
5721	0	{
5722	0	int i;
5723	0	ge_p3 A;
5724	0	const uint8_t r, s;
5725	0	EVP_MD *sha512;
5726	0	EVP_MD_CTX *hash_ctx = NULL;
5727	0	unsigned int sz;
5728	0	int res = 0;
5729	0	ge_p2 R;
5730	0	uint8_t rcheck[32];
5731	0	uint8_t h[SHA512_DIGEST_LENGTH];
5732		/* 27742317777372353535851937790883648493 in little endian format */
5733	0	const uint8_t l_low[16] = {
5734	0	0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5735	0	0xDE, 0xF9, 0xDE, 0x14
5736	0	};
5737
5738	0	if (context == NULL)
5739	0	context_len = 0;
5740
5741		/* if csflag is set, then a non-empty context-string is required */
5742	0	if (csflag && context_len == 0)
5743	0	return 0;
5744
5745		/* if dom2flag is not set, then an empty context-string is required */
5746	0	if (!dom2flag && context_len > 0)
5747	0	return 0;
5748
5749	0	r = signature;
5750	0	s = signature + 32;
5751
5752		/*
5753		* Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5754		*
5755		* If not the signature is publicly invalid. Since it's public we can do the
5756		* check in variable time.
5757		*
5758		* First check the most significant byte
5759		*/
5760	0	if (s[31] > 0x10)
5761	0	return 0;
5762	0	if (s[31] == 0x10) {
5763		/*
5764		* Most significant byte indicates a value close to 2^252 so check the
5765		* rest
5766		*/
5767	0	if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5768	0	return 0;
5769	0	for (i = 15; i >= 0; i--) {
5770	0	if (s[i] < l_low[i])
5771	0	break;
5772	0	if (s[i] > l_low[i])
5773	0	return 0;
5774	0	}
5775	0	if (i < 0)
5776	0	return 0;
5777	0	}
5778
5779	0	if (ge_frombytes_vartime(&A, public_key) != 0) {
5780	0	return 0;
5781	0	}
5782
5783	0	fe_neg(A.X, A.X);
5784	0	fe_neg(A.T, A.T);
5785
5786	0	sha512 = EVP_MD_fetch(libctx, SN_sha512, propq);
5787	0	if (sha512 == NULL)
5788	0	return 0;
5789	0	hash_ctx = EVP_MD_CTX_new();
5790	0	if (hash_ctx == NULL)
5791	0	goto err;
5792
5793	0	if (!hash_init_with_dom(hash_ctx, sha512, dom2flag, phflag, context, context_len)
5794	0	\|\| !EVP_DigestUpdate(hash_ctx, r, 32)
5795	0	\|\| !EVP_DigestUpdate(hash_ctx, public_key, 32)
5796	0	\|\| !EVP_DigestUpdate(hash_ctx, tbs, tbs_len)
5797	0	\|\| !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5798	0	goto err;
5799
5800	0	x25519_sc_reduce(h);
5801
5802	0	ge_double_scalarmult_vartime(&R, h, &A, s);
5803
5804	0	ge_tobytes(rcheck, &R);
5805
5806	0	res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5807
5808		/* note that we have used the strict verification equation here.
5809		* we checked that ENC( [h](-A) + [s]B ) == r
5810		* B is the base point.
5811		*
5812		* the less strict verification equation uses the curve cofactor:
5813		* [h8](-A) + [s8]B == [8]R
5814		*/
5815	0	err:
5816	0	EVP_MD_free(sha512);
5817	0	EVP_MD_CTX_free(hash_ctx);
5818	0	return res;
5819	0	}
5820
5821		int ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32],
5822		const uint8_t private_key[32],
5823		const char *propq)
5824	0	{
5825	0	uint8_t az[SHA512_DIGEST_LENGTH];
5826	0	ge_p3 A;
5827	0	int r;
5828	0	EVP_MD *sha512 = NULL;
5829
5830	0	sha512 = EVP_MD_fetch(ctx, SN_sha512, propq);
5831	0	if (sha512 == NULL)
5832	0	return 0;
5833	0	r = EVP_Digest(private_key, 32, az, NULL, sha512, NULL);
5834	0	EVP_MD_free(sha512);
5835	0	if (!r) {
5836	0	OPENSSL_cleanse(az, sizeof(az));
5837	0	return 0;
5838	0	}
5839
5840	0	az[0] &= 248;
5841	0	az[31] &= 63;
5842	0	az[31] \|= 64;
5843
5844	0	ge_scalarmult_base(&A, az);
5845	0	ge_p3_tobytes(out_public_key, &A);
5846
5847	0	OPENSSL_cleanse(az, sizeof(az));
5848	0	return 1;
5849	0	}
5850
5851		int ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5852		const uint8_t peer_public_value[32])
5853	0	{
5854	0	static const uint8_t kZeros[32] = { 0 };
5855	0	x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5856		/* The all-zero output results when the input is a point of small order. */
5857	0	return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5858	0	}
5859
5860		void ossl_x25519_public_from_private(uint8_t out_public_value[32],
5861		const uint8_t private_key[32])
5862	0	{
5863	0	uint8_t e[32];
5864	0	ge_p3 A;
5865	0	fe zplusy, zminusy, zminusy_inv;
5866
5867	0	memcpy(e, private_key, 32);
5868	0	e[0] &= 248;
5869	0	e[31] &= 127;
5870	0	e[31] \|= 64;
5871
5872	0	ge_scalarmult_base(&A, e);
5873
5874		/*
5875		* We only need the u-coordinate of the curve25519 point.
5876		* The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5877		* u=(Z+Y)/(Z-Y).
5878		*/
5879	0	fe_add(zplusy, A.Z, A.Y);
5880	0	fe_sub(zminusy, A.Z, A.Y);
5881	0	fe_invert(zminusy_inv, zminusy);
5882	0	fe_mul(zplusy, zplusy, zminusy_inv);
5883	0	fe_tobytes(out_public_value, zplusy);
5884
5885	0	OPENSSL_cleanse(e, sizeof(e));
5886	0	}

Coverage Report

Created: 2026-07-16 06:59