Bug Summary

File:out/../deps/openssl/openssl/crypto/ec/curve25519.c
Warning:line 5372, column 5
Value stored to 's12' is never read

Annotated Source Code

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clang -cc1 -cc1 -triple x86_64-unknown-linux-gnu -analyze -disable-free -clear-ast-before-backend -disable-llvm-verifier -discard-value-names -main-file-name curve25519.c -analyzer-checker=core -analyzer-checker=apiModeling -analyzer-checker=unix -analyzer-checker=deadcode -analyzer-checker=security.insecureAPI.UncheckedReturn -analyzer-checker=security.insecureAPI.getpw -analyzer-checker=security.insecureAPI.gets -analyzer-checker=security.insecureAPI.mktemp -analyzer-checker=security.insecureAPI.mkstemp -analyzer-checker=security.insecureAPI.vfork -analyzer-checker=nullability.NullPassedToNonnull -analyzer-checker=nullability.NullReturnedFromNonnull -analyzer-output plist -w -setup-static-analyzer -mrelocation-model pic -pic-level 2 -pic-is-pie -mframe-pointer=all -fmath-errno -ffp-contract=on -fno-rounding-math -mconstructor-aliases -funwind-tables=2 -target-cpu x86-64 -tune-cpu generic -debugger-tuning=gdb -fcoverage-compilation-dir=/home/maurizio/node-v18.6.0/out -resource-dir /usr/local/lib/clang/16.0.0 -D V8_DEPRECATION_WARNINGS -D V8_IMMINENT_DEPRECATION_WARNINGS -D _GLIBCXX_USE_CXX11_ABI=1 -D NODE_OPENSSL_CONF_NAME=nodejs_conf -D NODE_OPENSSL_HAS_QUIC -D __STDC_FORMAT_MACROS -D OPENSSL_NO_PINSHARED -D OPENSSL_THREADS -D OPENSSL_NO_HW -D OPENSSL_API_COMPAT=0x10100001L -D STATIC_LEGACY -D NDEBUG -D OPENSSL_USE_NODELETE -D L_ENDIAN -D OPENSSL_BUILDING_OPENSSL -D AES_ASM -D BSAES_ASM -D CMLL_ASM -D ECP_NISTZ256_ASM -D GHASH_ASM -D KECCAK1600_ASM -D MD5_ASM -D OPENSSL_BN_ASM_GF2m -D OPENSSL_BN_ASM_MONT -D OPENSSL_BN_ASM_MONT5 -D OPENSSL_CPUID_OBJ -D OPENSSL_IA32_SSE2 -D PADLOCK_ASM -D POLY1305_ASM -D SHA1_ASM -D SHA256_ASM -D SHA512_ASM -D VPAES_ASM -D WHIRLPOOL_ASM -D X25519_ASM -D OPENSSL_PIC -D MODULESDIR="/home/maurizio/node-v18.6.0/out/Release/obj.target/deps/openssl/lib/openssl-modules" -D OPENSSLDIR="/home/maurizio/node-v18.6.0/out/Release/obj.target/deps/openssl" -D OPENSSLDIR="/etc/ssl" -D ENGINESDIR="/dev/null" -D TERMIOS -I ../deps/openssl/openssl -I ../deps/openssl/openssl/include -I ../deps/openssl/openssl/crypto -I ../deps/openssl/openssl/crypto/include -I ../deps/openssl/openssl/crypto/modes -I ../deps/openssl/openssl/crypto/ec/curve448 -I ../deps/openssl/openssl/crypto/ec/curve448/arch_32 -I ../deps/openssl/openssl/providers/common/include -I ../deps/openssl/openssl/providers/implementations/include -I ../deps/openssl/config -I ../deps/openssl/config/archs/linux-x86_64/asm -I ../deps/openssl/config/archs/linux-x86_64/asm/include -I ../deps/openssl/config/archs/linux-x86_64/asm/crypto -I ../deps/openssl/config/archs/linux-x86_64/asm/crypto/include/internal -I ../deps/openssl/config/archs/linux-x86_64/asm/providers/common/include -internal-isystem /usr/local/lib/clang/16.0.0/include -internal-isystem /usr/local/include -internal-isystem /usr/lib/gcc/x86_64-redhat-linux/8/../../../../x86_64-redhat-linux/include -internal-externc-isystem /include -internal-externc-isystem /usr/include -O3 -Wno-unused-parameter -Wno-missing-field-initializers -Wno-old-style-declaration -fdebug-compilation-dir=/home/maurizio/node-v18.6.0/out -ferror-limit 19 -fgnuc-version=4.2.1 -vectorize-loops -vectorize-slp -analyzer-output=html -faddrsig -D__GCC_HAVE_DWARF2_CFI_ASM=1 -o /tmp/scan-build-2022-08-22-142216-507842-1 -x c ../deps/openssl/openssl/crypto/ec/curve25519.c
1/*
2 * Copyright 2016-2021 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_ASM1) && (defined(__x86_641) || defined(__x86_64__1) || \
25 defined(_M_AMD64) || defined(_M_X64))
26
27# define BASE_2_64_IMPLEMENTED
28
29typedef uint64_t fe64[4];
30
31int x25519_fe64_eligible(void);
32
33/*
34 * Following subroutines perform corresponding operations modulo
35 * 2^256-38, i.e. double the curve modulus. However, inputs and
36 * outputs are permitted to be partially reduced, i.e. to remain
37 * in [0..2^256) range. It's all tied up in final fe64_tobytes
38 * that performs full reduction modulo 2^255-19.
39 *
40 * There are no reference C implementations for these.
41 */
42void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g);
43void x25519_fe64_sqr(fe64 h, const fe64 f);
44void x25519_fe64_mul121666(fe64 h, fe64 f);
45void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g);
46void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g);
47void x25519_fe64_tobytes(uint8_t *s, const fe64 f);
48# define fe64_mulx25519_fe64_mul x25519_fe64_mul
49# define fe64_sqrx25519_fe64_sqr x25519_fe64_sqr
50# define fe64_mul121666x25519_fe64_mul121666 x25519_fe64_mul121666
51# define fe64_addx25519_fe64_add x25519_fe64_add
52# define fe64_subx25519_fe64_sub x25519_fe64_sub
53# define fe64_tobytesx25519_fe64_tobytes x25519_fe64_tobytes
54
55static uint64_t load_8(const uint8_t *in)
56{
57 uint64_t result;
58
59 result = in[0];
60 result |= ((uint64_t)in[1]) << 8;
61 result |= ((uint64_t)in[2]) << 16;
62 result |= ((uint64_t)in[3]) << 24;
63 result |= ((uint64_t)in[4]) << 32;
64 result |= ((uint64_t)in[5]) << 40;
65 result |= ((uint64_t)in[6]) << 48;
66 result |= ((uint64_t)in[7]) << 56;
67
68 return result;
69}
70
71static void fe64_frombytes(fe64 h, const uint8_t *s)
72{
73 h[0] = load_8(s);
74 h[1] = load_8(s + 8);
75 h[2] = load_8(s + 16);
76 h[3] = load_8(s + 24) & 0x7fffffffffffffff;
77}
78
79static void fe64_0(fe64 h)
80{
81 h[0] = 0;
82 h[1] = 0;
83 h[2] = 0;
84 h[3] = 0;
85}
86
87static void fe64_1(fe64 h)
88{
89 h[0] = 1;
90 h[1] = 0;
91 h[2] = 0;
92 h[3] = 0;
93}
94
95static void fe64_copy(fe64 h, const fe64 f)
96{
97 h[0] = f[0];
98 h[1] = f[1];
99 h[2] = f[2];
100 h[3] = f[3];
101}
102
103static void fe64_cswap(fe64 f, fe64 g, unsigned int b)
104{
105 int i;
106 uint64_t mask = 0 - (uint64_t)b;
107
108 for (i = 0; i < 4; i++) {
109 uint64_t x = f[i] ^ g[i];
110 x &= mask;
111 f[i] ^= x;
112 g[i] ^= x;
113 }
114}
115
116static void fe64_invert(fe64 out, const fe64 z)
117{
118 fe64 t0;
119 fe64 t1;
120 fe64 t2;
121 fe64 t3;
122 int i;
123
124 /*
125 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
126 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
127 */
128
129 /* t0 = z ** 2 */
130 fe64_sqrx25519_fe64_sqr(t0, z);
131
132 /* t1 = t0 ** (2 ** 2) = z ** 8 */
133 fe64_sqrx25519_fe64_sqr(t1, t0);
134 fe64_sqrx25519_fe64_sqr(t1, t1);
135
136 /* t1 = z * t1 = z ** 9 */
137 fe64_mulx25519_fe64_mul(t1, z, t1);
138 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
139 fe64_mulx25519_fe64_mul(t0, t0, t1);
140
141 /* t2 = t0 ** 2 = z ** 22 */
142 fe64_sqrx25519_fe64_sqr(t2, t0);
143
144 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
145 fe64_mulx25519_fe64_mul(t1, t1, t2);
146
147 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
148 fe64_sqrx25519_fe64_sqr(t2, t1);
149 for (i = 1; i < 5; ++i)
150 fe64_sqrx25519_fe64_sqr(t2, t2);
151
152 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
153 fe64_mulx25519_fe64_mul(t1, t2, t1);
154
155 /* Continuing similarly... */
156
157 /* t2 = z ** (2 ** 20 - 1) */
158 fe64_sqrx25519_fe64_sqr(t2, t1);
159 for (i = 1; i < 10; ++i)
160 fe64_sqrx25519_fe64_sqr(t2, t2);
161
162 fe64_mulx25519_fe64_mul(t2, t2, t1);
163
164 /* t2 = z ** (2 ** 40 - 1) */
165 fe64_sqrx25519_fe64_sqr(t3, t2);
166 for (i = 1; i < 20; ++i)
167 fe64_sqrx25519_fe64_sqr(t3, t3);
168
169 fe64_mulx25519_fe64_mul(t2, t3, t2);
170
171 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
172 for (i = 0; i < 10; ++i)
173 fe64_sqrx25519_fe64_sqr(t2, t2);
174
175 /* t1 = z ** (2 ** 50 - 1) */
176 fe64_mulx25519_fe64_mul(t1, t2, t1);
177
178 /* t2 = z ** (2 ** 100 - 1) */
179 fe64_sqrx25519_fe64_sqr(t2, t1);
180 for (i = 1; i < 50; ++i)
181 fe64_sqrx25519_fe64_sqr(t2, t2);
182
183 fe64_mulx25519_fe64_mul(t2, t2, t1);
184
185 /* t2 = z ** (2 ** 200 - 1) */
186 fe64_sqrx25519_fe64_sqr(t3, t2);
187 for (i = 1; i < 100; ++i)
188 fe64_sqrx25519_fe64_sqr(t3, t3);
189
190 fe64_mulx25519_fe64_mul(t2, t3, t2);
191
192 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
193 for (i = 0; i < 50; ++i)
194 fe64_sqrx25519_fe64_sqr(t2, t2);
195
196 /* t1 = z ** (2 ** 250 - 1) */
197 fe64_mulx25519_fe64_mul(t1, t2, t1);
198
199 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
200 for (i = 0; i < 5; ++i)
201 fe64_sqrx25519_fe64_sqr(t1, t1);
202
203 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
204 fe64_mulx25519_fe64_mul(out, t1, t0);
205}
206
207/*
208 * Duplicate of original x25519_scalar_mult_generic, but using
209 * fe64_* subroutines.
210 */
211static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32],
212 const uint8_t point[32])
213{
214 fe64 x1, x2, z2, x3, z3, tmp0, tmp1;
215 uint8_t e[32];
216 unsigned swap = 0;
217 int pos;
218
219 memcpy(e, scalar, 32);
220 e[0] &= 0xf8;
221 e[31] &= 0x7f;
222 e[31] |= 0x40;
223 fe64_frombytes(x1, point);
224 fe64_1(x2);
225 fe64_0(z2);
226 fe64_copy(x3, x1);
227 fe64_1(z3);
228
229 for (pos = 254; pos >= 0; --pos) {
230 unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
231
232 swap ^= b;
233 fe64_cswap(x2, x3, swap);
234 fe64_cswap(z2, z3, swap);
235 swap = b;
236 fe64_subx25519_fe64_sub(tmp0, x3, z3);
237 fe64_subx25519_fe64_sub(tmp1, x2, z2);
238 fe64_addx25519_fe64_add(x2, x2, z2);
239 fe64_addx25519_fe64_add(z2, x3, z3);
240 fe64_mulx25519_fe64_mul(z3, x2, tmp0);
241 fe64_mulx25519_fe64_mul(z2, z2, tmp1);
242 fe64_sqrx25519_fe64_sqr(tmp0, tmp1);
243 fe64_sqrx25519_fe64_sqr(tmp1, x2);
244 fe64_addx25519_fe64_add(x3, z3, z2);
245 fe64_subx25519_fe64_sub(z2, z3, z2);
246 fe64_mulx25519_fe64_mul(x2, tmp1, tmp0);
247 fe64_subx25519_fe64_sub(tmp1, tmp1, tmp0);
248 fe64_sqrx25519_fe64_sqr(z2, z2);
249 fe64_mul121666x25519_fe64_mul121666(z3, tmp1);
250 fe64_sqrx25519_fe64_sqr(x3, x3);
251 fe64_addx25519_fe64_add(tmp0, tmp0, z3);
252 fe64_mulx25519_fe64_mul(z3, x1, z2);
253 fe64_mulx25519_fe64_mul(z2, tmp1, tmp0);
254 }
255
256 fe64_invert(z2, z2);
257 fe64_mulx25519_fe64_mul(x2, x2, z2);
258 fe64_tobytesx25519_fe64_tobytes(out, x2);
259
260 OPENSSL_cleanse(e, sizeof(e));
261}
262#endif
263
264#if defined(X25519_ASM1) \
265 || ( defined(INT128_MAX((int128_t) ((((int128_t) 1) << ((sizeof(int128_t) * 8)
- 1)) ^ ((int128_t) -1)))
) \
266 && !defined(__sparc__) \
267 && (!defined(__SIZEOF_LONG__8) || (__SIZEOF_LONG__8 == 8)) \
268 && !(defined(__ANDROID__) && !defined(__clang__1)) )
269/*
270 * Base 2^51 implementation. It's virtually no different from reference
271 * base 2^25.5 implementation in respect to lax boundary conditions for
272 * intermediate values and even individual limbs. So that whatever you
273 * know about the reference, applies even here...
274 */
275# define BASE_2_51_IMPLEMENTED
276
277typedef uint64_t fe51[5];
278
279static const uint64_t MASK51 = 0x7ffffffffffff;
280
281static uint64_t load_7(const uint8_t *in)
282{
283 uint64_t result;
284
285 result = in[0];
286 result |= ((uint64_t)in[1]) << 8;
287 result |= ((uint64_t)in[2]) << 16;
288 result |= ((uint64_t)in[3]) << 24;
289 result |= ((uint64_t)in[4]) << 32;
290 result |= ((uint64_t)in[5]) << 40;
291 result |= ((uint64_t)in[6]) << 48;
292
293 return result;
294}
295
296static uint64_t load_6(const uint8_t *in)
297{
298 uint64_t result;
299
300 result = in[0];
301 result |= ((uint64_t)in[1]) << 8;
302 result |= ((uint64_t)in[2]) << 16;
303 result |= ((uint64_t)in[3]) << 24;
304 result |= ((uint64_t)in[4]) << 32;
305 result |= ((uint64_t)in[5]) << 40;
306
307 return result;
308}
309
310static void fe51_frombytes(fe51 h, const uint8_t *s)
311{
312 uint64_t h0 = load_7(s); /* 56 bits */
313 uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */
314 uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */
315 uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */
316 uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */
317
318 h1 |= h0 >> 51; h0 &= MASK51;
319 h2 |= h1 >> 51; h1 &= MASK51;
320 h3 |= h2 >> 51; h2 &= MASK51;
321 h4 |= h3 >> 51; h3 &= MASK51;
322
323 h[0] = h0;
324 h[1] = h1;
325 h[2] = h2;
326 h[3] = h3;
327 h[4] = h4;
328}
329
330static void fe51_tobytes(uint8_t *s, const fe51 h)
331{
332 uint64_t h0 = h[0];
333 uint64_t h1 = h[1];
334 uint64_t h2 = h[2];
335 uint64_t h3 = h[3];
336 uint64_t h4 = h[4];
337 uint64_t q;
338
339 /* compare to modulus */
340 q = (h0 + 19) >> 51;
341 q = (h1 + q) >> 51;
342 q = (h2 + q) >> 51;
343 q = (h3 + q) >> 51;
344 q = (h4 + q) >> 51;
345
346 /* full reduce */
347 h0 += 19 * q;
348 h1 += h0 >> 51; h0 &= MASK51;
349 h2 += h1 >> 51; h1 &= MASK51;
350 h3 += h2 >> 51; h2 &= MASK51;
351 h4 += h3 >> 51; h3 &= MASK51;
352 h4 &= MASK51;
353
354 /* smash */
355 s[0] = (uint8_t)(h0 >> 0);
356 s[1] = (uint8_t)(h0 >> 8);
357 s[2] = (uint8_t)(h0 >> 16);
358 s[3] = (uint8_t)(h0 >> 24);
359 s[4] = (uint8_t)(h0 >> 32);
360 s[5] = (uint8_t)(h0 >> 40);
361 s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3));
362 s[7] = (uint8_t)(h1 >> 5);
363 s[8] = (uint8_t)(h1 >> 13);
364 s[9] = (uint8_t)(h1 >> 21);
365 s[10] = (uint8_t)(h1 >> 29);
366 s[11] = (uint8_t)(h1 >> 37);
367 s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6));
368 s[13] = (uint8_t)(h2 >> 2);
369 s[14] = (uint8_t)(h2 >> 10);
370 s[15] = (uint8_t)(h2 >> 18);
371 s[16] = (uint8_t)(h2 >> 26);
372 s[17] = (uint8_t)(h2 >> 34);
373 s[18] = (uint8_t)(h2 >> 42);
374 s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1));
375 s[20] = (uint8_t)(h3 >> 7);
376 s[21] = (uint8_t)(h3 >> 15);
377 s[22] = (uint8_t)(h3 >> 23);
378 s[23] = (uint8_t)(h3 >> 31);
379 s[24] = (uint8_t)(h3 >> 39);
380 s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4));
381 s[26] = (uint8_t)(h4 >> 4);
382 s[27] = (uint8_t)(h4 >> 12);
383 s[28] = (uint8_t)(h4 >> 20);
384 s[29] = (uint8_t)(h4 >> 28);
385 s[30] = (uint8_t)(h4 >> 36);
386 s[31] = (uint8_t)(h4 >> 44);
387}
388
389# if defined(X25519_ASM1)
390void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g);
391void x25519_fe51_sqr(fe51 h, const fe51 f);
392void x25519_fe51_mul121666(fe51 h, fe51 f);
393# define fe51_mulx25519_fe51_mul x25519_fe51_mul
394# define fe51_sqx25519_fe51_sqr x25519_fe51_sqr
395# define fe51_mul121666x25519_fe51_mul121666 x25519_fe51_mul121666
396# else
397
398typedef uint128_t u128;
399
400static void fe51_mulx25519_fe51_mul(fe51 h, const fe51 f, const fe51 g)
401{
402 u128 h0, h1, h2, h3, h4;
403 uint64_t f_i, g0, g1, g2, g3, g4;
404
405 f_i = f[0];
406 h0 = (u128)f_i * (g0 = g[0]);
407 h1 = (u128)f_i * (g1 = g[1]);
408 h2 = (u128)f_i * (g2 = g[2]);
409 h3 = (u128)f_i * (g3 = g[3]);
410 h4 = (u128)f_i * (g4 = g[4]);
411
412 f_i = f[1];
413 h0 += (u128)f_i * (g4 *= 19);
414 h1 += (u128)f_i * g0;
415 h2 += (u128)f_i * g1;
416 h3 += (u128)f_i * g2;
417 h4 += (u128)f_i * g3;
418
419 f_i = f[2];
420 h0 += (u128)f_i * (g3 *= 19);
421 h1 += (u128)f_i * g4;
422 h2 += (u128)f_i * g0;
423 h3 += (u128)f_i * g1;
424 h4 += (u128)f_i * g2;
425
426 f_i = f[3];
427 h0 += (u128)f_i * (g2 *= 19);
428 h1 += (u128)f_i * g3;
429 h2 += (u128)f_i * g4;
430 h3 += (u128)f_i * g0;
431 h4 += (u128)f_i * g1;
432
433 f_i = f[4];
434 h0 += (u128)f_i * (g1 *= 19);
435 h1 += (u128)f_i * g2;
436 h2 += (u128)f_i * g3;
437 h3 += (u128)f_i * g4;
438 h4 += (u128)f_i * g0;
439
440 /* partial [lazy] reduction */
441 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
442 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
443
444 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
445 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
446
447 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
448 g3 += g2 >> 51; g2 &= MASK51;
449 g1 += g0 >> 51; g0 &= MASK51;
450
451 h[0] = g0;
452 h[1] = g1;
453 h[2] = g2;
454 h[3] = g3;
455 h[4] = g4;
456}
457
458static void fe51_sqx25519_fe51_sqr(fe51 h, const fe51 f)
459{
460# if defined(OPENSSL_SMALL_FOOTPRINT)
461 fe51_mulx25519_fe51_mul(h, f, f);
462# else
463 /* dedicated squaring gives 16-25% overall improvement */
464 uint64_t g0 = f[0];
465 uint64_t g1 = f[1];
466 uint64_t g2 = f[2];
467 uint64_t g3 = f[3];
468 uint64_t g4 = f[4];
469 u128 h0, h1, h2, h3, h4;
470
471 h0 = (u128)g0 * g0; g0 *= 2;
472 h1 = (u128)g0 * g1;
473 h2 = (u128)g0 * g2;
474 h3 = (u128)g0 * g3;
475 h4 = (u128)g0 * g4;
476
477 g0 = g4; /* borrow g0 */
478 h3 += (u128)g0 * (g4 *= 19);
479
480 h2 += (u128)g1 * g1; g1 *= 2;
481 h3 += (u128)g1 * g2;
482 h4 += (u128)g1 * g3;
483 h0 += (u128)g1 * g4;
484
485 g0 = g3; /* borrow g0 */
486 h1 += (u128)g0 * (g3 *= 19);
487 h2 += (u128)(g0 * 2) * g4;
488
489 h4 += (u128)g2 * g2; g2 *= 2;
490 h0 += (u128)g2 * g3;
491 h1 += (u128)g2 * g4;
492
493 /* partial [lazy] reduction */
494 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
495 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
496
497 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
498 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
499
500 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
501 g3 += g2 >> 51; g2 &= MASK51;
502 g1 += g0 >> 51; g0 &= MASK51;
503
504 h[0] = g0;
505 h[1] = g1;
506 h[2] = g2;
507 h[3] = g3;
508 h[4] = g4;
509# endif
510}
511
512static void fe51_mul121666x25519_fe51_mul121666(fe51 h, fe51 f)
513{
514 u128 h0 = f[0] * (u128)121666;
515 u128 h1 = f[1] * (u128)121666;
516 u128 h2 = f[2] * (u128)121666;
517 u128 h3 = f[3] * (u128)121666;
518 u128 h4 = f[4] * (u128)121666;
519 uint64_t g0, g1, g2, g3, g4;
520
521 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51;
522 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51;
523
524 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51;
525 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51;
526
527 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51;
528 g3 += g2 >> 51; g2 &= MASK51;
529 g1 += g0 >> 51; g0 &= MASK51;
530
531 h[0] = g0;
532 h[1] = g1;
533 h[2] = g2;
534 h[3] = g3;
535 h[4] = g4;
536}
537# endif
538
539static void fe51_add(fe51 h, const fe51 f, const fe51 g)
540{
541 h[0] = f[0] + g[0];
542 h[1] = f[1] + g[1];
543 h[2] = f[2] + g[2];
544 h[3] = f[3] + g[3];
545 h[4] = f[4] + g[4];
546}
547
548static void fe51_sub(fe51 h, const fe51 f, const fe51 g)
549{
550 /*
551 * Add 2*modulus to ensure that result remains positive
552 * even if subtrahend is partially reduced.
553 */
554 h[0] = (f[0] + 0xfffffffffffda) - g[0];
555 h[1] = (f[1] + 0xffffffffffffe) - g[1];
556 h[2] = (f[2] + 0xffffffffffffe) - g[2];
557 h[3] = (f[3] + 0xffffffffffffe) - g[3];
558 h[4] = (f[4] + 0xffffffffffffe) - g[4];
559}
560
561static void fe51_0(fe51 h)
562{
563 h[0] = 0;
564 h[1] = 0;
565 h[2] = 0;
566 h[3] = 0;
567 h[4] = 0;
568}
569
570static void fe51_1(fe51 h)
571{
572 h[0] = 1;
573 h[1] = 0;
574 h[2] = 0;
575 h[3] = 0;
576 h[4] = 0;
577}
578
579static void fe51_copy(fe51 h, const fe51 f)
580{
581 h[0] = f[0];
582 h[1] = f[1];
583 h[2] = f[2];
584 h[3] = f[3];
585 h[4] = f[4];
586}
587
588static void fe51_cswap(fe51 f, fe51 g, unsigned int b)
589{
590 int i;
591 uint64_t mask = 0 - (uint64_t)b;
592
593 for (i = 0; i < 5; i++) {
594 int64_t x = f[i] ^ g[i];
595 x &= mask;
596 f[i] ^= x;
597 g[i] ^= x;
598 }
599}
600
601static void fe51_invert(fe51 out, const fe51 z)
602{
603 fe51 t0;
604 fe51 t1;
605 fe51 t2;
606 fe51 t3;
607 int i;
608
609 /*
610 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
611 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
612 */
613
614 /* t0 = z ** 2 */
615 fe51_sqx25519_fe51_sqr(t0, z);
616
617 /* t1 = t0 ** (2 ** 2) = z ** 8 */
618 fe51_sqx25519_fe51_sqr(t1, t0);
619 fe51_sqx25519_fe51_sqr(t1, t1);
620
621 /* t1 = z * t1 = z ** 9 */
622 fe51_mulx25519_fe51_mul(t1, z, t1);
623 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
624 fe51_mulx25519_fe51_mul(t0, t0, t1);
625
626 /* t2 = t0 ** 2 = z ** 22 */
627 fe51_sqx25519_fe51_sqr(t2, t0);
628
629 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
630 fe51_mulx25519_fe51_mul(t1, t1, t2);
631
632 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
633 fe51_sqx25519_fe51_sqr(t2, t1);
634 for (i = 1; i < 5; ++i)
635 fe51_sqx25519_fe51_sqr(t2, t2);
636
637 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
638 fe51_mulx25519_fe51_mul(t1, t2, t1);
639
640 /* Continuing similarly... */
641
642 /* t2 = z ** (2 ** 20 - 1) */
643 fe51_sqx25519_fe51_sqr(t2, t1);
644 for (i = 1; i < 10; ++i)
645 fe51_sqx25519_fe51_sqr(t2, t2);
646
647 fe51_mulx25519_fe51_mul(t2, t2, t1);
648
649 /* t2 = z ** (2 ** 40 - 1) */
650 fe51_sqx25519_fe51_sqr(t3, t2);
651 for (i = 1; i < 20; ++i)
652 fe51_sqx25519_fe51_sqr(t3, t3);
653
654 fe51_mulx25519_fe51_mul(t2, t3, t2);
655
656 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
657 for (i = 0; i < 10; ++i)
658 fe51_sqx25519_fe51_sqr(t2, t2);
659
660 /* t1 = z ** (2 ** 50 - 1) */
661 fe51_mulx25519_fe51_mul(t1, t2, t1);
662
663 /* t2 = z ** (2 ** 100 - 1) */
664 fe51_sqx25519_fe51_sqr(t2, t1);
665 for (i = 1; i < 50; ++i)
666 fe51_sqx25519_fe51_sqr(t2, t2);
667
668 fe51_mulx25519_fe51_mul(t2, t2, t1);
669
670 /* t2 = z ** (2 ** 200 - 1) */
671 fe51_sqx25519_fe51_sqr(t3, t2);
672 for (i = 1; i < 100; ++i)
673 fe51_sqx25519_fe51_sqr(t3, t3);
674
675 fe51_mulx25519_fe51_mul(t2, t3, t2);
676
677 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
678 for (i = 0; i < 50; ++i)
679 fe51_sqx25519_fe51_sqr(t2, t2);
680
681 /* t1 = z ** (2 ** 250 - 1) */
682 fe51_mulx25519_fe51_mul(t1, t2, t1);
683
684 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
685 for (i = 0; i < 5; ++i)
686 fe51_sqx25519_fe51_sqr(t1, t1);
687
688 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
689 fe51_mulx25519_fe51_mul(out, t1, t0);
690}
691
692/*
693 * Duplicate of original x25519_scalar_mult_generic, but using
694 * fe51_* subroutines.
695 */
696static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
697 const uint8_t point[32])
698{
699 fe51 x1, x2, z2, x3, z3, tmp0, tmp1;
700 uint8_t e[32];
701 unsigned swap = 0;
702 int pos;
703
704# ifdef BASE_2_64_IMPLEMENTED
705 if (x25519_fe64_eligible()) {
706 x25519_scalar_mulx(out, scalar, point);
707 return;
708 }
709# endif
710
711 memcpy(e, scalar, 32);
712 e[0] &= 0xf8;
713 e[31] &= 0x7f;
714 e[31] |= 0x40;
715 fe51_frombytes(x1, point);
716 fe51_1(x2);
717 fe51_0(z2);
718 fe51_copy(x3, x1);
719 fe51_1(z3);
720
721 for (pos = 254; pos >= 0; --pos) {
722 unsigned int b = 1 & (e[pos / 8] >> (pos & 7));
723
724 swap ^= b;
725 fe51_cswap(x2, x3, swap);
726 fe51_cswap(z2, z3, swap);
727 swap = b;
728 fe51_sub(tmp0, x3, z3);
729 fe51_sub(tmp1, x2, z2);
730 fe51_add(x2, x2, z2);
731 fe51_add(z2, x3, z3);
732 fe51_mulx25519_fe51_mul(z3, tmp0, x2);
733 fe51_mulx25519_fe51_mul(z2, z2, tmp1);
734 fe51_sqx25519_fe51_sqr(tmp0, tmp1);
735 fe51_sqx25519_fe51_sqr(tmp1, x2);
736 fe51_add(x3, z3, z2);
737 fe51_sub(z2, z3, z2);
738 fe51_mulx25519_fe51_mul(x2, tmp1, tmp0);
739 fe51_sub(tmp1, tmp1, tmp0);
740 fe51_sqx25519_fe51_sqr(z2, z2);
741 fe51_mul121666x25519_fe51_mul121666(z3, tmp1);
742 fe51_sqx25519_fe51_sqr(x3, x3);
743 fe51_add(tmp0, tmp0, z3);
744 fe51_mulx25519_fe51_mul(z3, x1, z2);
745 fe51_mulx25519_fe51_mul(z2, tmp1, tmp0);
746 }
747
748 fe51_invert(z2, z2);
749 fe51_mulx25519_fe51_mul(x2, x2, z2);
750 fe51_tobytes(out, x2);
751
752 OPENSSL_cleanse(e, sizeof(e));
753}
754#endif
755
756/*
757 * Reference base 2^25.5 implementation.
758 *
759 * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP
760 * 20141124 (http://bench.cr.yp.to/supercop.html).
761 *
762 * The field functions are shared by Ed25519 and X25519 where possible.
763 */
764
765/*
766 * fe means field element. Here the field is \Z/(2^255-19). An element t,
767 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77
768 * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on
769 * context.
770 */
771typedef int32_t fe[10];
772
773static const int64_t kBottom21Bits = 0x1fffffLL;
774static const int64_t kBottom25Bits = 0x1ffffffLL;
775static const int64_t kBottom26Bits = 0x3ffffffLL;
776static const int64_t kTop39Bits = 0xfffffffffe000000LL;
777static const int64_t kTop38Bits = 0xfffffffffc000000LL;
778
779static uint64_t load_3(const uint8_t *in)
780{
781 uint64_t result;
782
783 result = ((uint64_t)in[0]);
784 result |= ((uint64_t)in[1]) << 8;
785 result |= ((uint64_t)in[2]) << 16;
786 return result;
787}
788
789static uint64_t load_4(const uint8_t *in)
790{
791 uint64_t result;
792
793 result = ((uint64_t)in[0]);
794 result |= ((uint64_t)in[1]) << 8;
795 result |= ((uint64_t)in[2]) << 16;
796 result |= ((uint64_t)in[3]) << 24;
797 return result;
798}
799
800static void fe_frombytes(fe h, const uint8_t *s)
801{
802 /* Ignores top bit of h. */
803 int64_t h0 = load_4(s);
804 int64_t h1 = load_3(s + 4) << 6;
805 int64_t h2 = load_3(s + 7) << 5;
806 int64_t h3 = load_3(s + 10) << 3;
807 int64_t h4 = load_3(s + 13) << 2;
808 int64_t h5 = load_4(s + 16);
809 int64_t h6 = load_3(s + 20) << 7;
810 int64_t h7 = load_3(s + 23) << 5;
811 int64_t h8 = load_3(s + 26) << 4;
812 int64_t h9 = (load_3(s + 29) & 0x7fffff) << 2;
813 int64_t carry0;
814 int64_t carry1;
815 int64_t carry2;
816 int64_t carry3;
817 int64_t carry4;
818 int64_t carry5;
819 int64_t carry6;
820 int64_t carry7;
821 int64_t carry8;
822 int64_t carry9;
823
824 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
825 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
826 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
827 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
828 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
829
830 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
831 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
832 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
833 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
834 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
835
836 h[0] = (int32_t)h0;
837 h[1] = (int32_t)h1;
838 h[2] = (int32_t)h2;
839 h[3] = (int32_t)h3;
840 h[4] = (int32_t)h4;
841 h[5] = (int32_t)h5;
842 h[6] = (int32_t)h6;
843 h[7] = (int32_t)h7;
844 h[8] = (int32_t)h8;
845 h[9] = (int32_t)h9;
846}
847
848/*
849 * Preconditions:
850 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
851 *
852 * Write p=2^255-19; q=floor(h/p).
853 * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
854 *
855 * Proof:
856 * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
857 * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
858 *
859 * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
860 * Then 0<y<1.
861 *
862 * Write r=h-pq.
863 * Have 0<=r<=p-1=2^255-20.
864 * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
865 *
866 * Write x=r+19(2^-255)r+y.
867 * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
868 *
869 * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
870 * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
871 */
872static void fe_tobytes(uint8_t *s, const fe h)
873{
874 int32_t h0 = h[0];
875 int32_t h1 = h[1];
876 int32_t h2 = h[2];
877 int32_t h3 = h[3];
878 int32_t h4 = h[4];
879 int32_t h5 = h[5];
880 int32_t h6 = h[6];
881 int32_t h7 = h[7];
882 int32_t h8 = h[8];
883 int32_t h9 = h[9];
884 int32_t q;
885
886 q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
887 q = (h0 + q) >> 26;
888 q = (h1 + q) >> 25;
889 q = (h2 + q) >> 26;
890 q = (h3 + q) >> 25;
891 q = (h4 + q) >> 26;
892 q = (h5 + q) >> 25;
893 q = (h6 + q) >> 26;
894 q = (h7 + q) >> 25;
895 q = (h8 + q) >> 26;
896 q = (h9 + q) >> 25;
897
898 /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
899 h0 += 19 * q;
900 /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
901
902 h1 += h0 >> 26; h0 &= kBottom26Bits;
903 h2 += h1 >> 25; h1 &= kBottom25Bits;
904 h3 += h2 >> 26; h2 &= kBottom26Bits;
905 h4 += h3 >> 25; h3 &= kBottom25Bits;
906 h5 += h4 >> 26; h4 &= kBottom26Bits;
907 h6 += h5 >> 25; h5 &= kBottom25Bits;
908 h7 += h6 >> 26; h6 &= kBottom26Bits;
909 h8 += h7 >> 25; h7 &= kBottom25Bits;
910 h9 += h8 >> 26; h8 &= kBottom26Bits;
911 h9 &= kBottom25Bits;
912 /* h10 = carry9 */
913
914 /*
915 * Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
916 * Have h0+...+2^230 h9 between 0 and 2^255-1;
917 * evidently 2^255 h10-2^255 q = 0.
918 * Goal: Output h0+...+2^230 h9.
919 */
920 s[ 0] = (uint8_t) (h0 >> 0);
921 s[ 1] = (uint8_t) (h0 >> 8);
922 s[ 2] = (uint8_t) (h0 >> 16);
923 s[ 3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2));
924 s[ 4] = (uint8_t) (h1 >> 6);
925 s[ 5] = (uint8_t) (h1 >> 14);
926 s[ 6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3));
927 s[ 7] = (uint8_t) (h2 >> 5);
928 s[ 8] = (uint8_t) (h2 >> 13);
929 s[ 9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5));
930 s[10] = (uint8_t) (h3 >> 3);
931 s[11] = (uint8_t) (h3 >> 11);
932 s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6));
933 s[13] = (uint8_t) (h4 >> 2);
934 s[14] = (uint8_t) (h4 >> 10);
935 s[15] = (uint8_t) (h4 >> 18);
936 s[16] = (uint8_t) (h5 >> 0);
937 s[17] = (uint8_t) (h5 >> 8);
938 s[18] = (uint8_t) (h5 >> 16);
939 s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1));
940 s[20] = (uint8_t) (h6 >> 7);
941 s[21] = (uint8_t) (h6 >> 15);
942 s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3));
943 s[23] = (uint8_t) (h7 >> 5);
944 s[24] = (uint8_t) (h7 >> 13);
945 s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4));
946 s[26] = (uint8_t) (h8 >> 4);
947 s[27] = (uint8_t) (h8 >> 12);
948 s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6));
949 s[29] = (uint8_t) (h9 >> 2);
950 s[30] = (uint8_t) (h9 >> 10);
951 s[31] = (uint8_t) (h9 >> 18);
952}
953
954/* h = f */
955static void fe_copy(fe h, const fe f)
956{
957 memmove(h, f, sizeof(int32_t) * 10);
958}
959
960/* h = 0 */
961static void fe_0(fe h)
962{
963 memset(h, 0, sizeof(int32_t) * 10);
964}
965
966/* h = 1 */
967static void fe_1(fe h)
968{
969 memset(h, 0, sizeof(int32_t) * 10);
970 h[0] = 1;
971}
972
973/*
974 * h = f + g
975 *
976 * Can overlap h with f or g.
977 *
978 * Preconditions:
979 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
980 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
981 *
982 * Postconditions:
983 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
984 */
985static void fe_add(fe h, const fe f, const fe g)
986{
987 unsigned i;
988
989 for (i = 0; i < 10; i++) {
990 h[i] = f[i] + g[i];
991 }
992}
993
994/*
995 * h = f - g
996 *
997 * Can overlap h with f or g.
998 *
999 * Preconditions:
1000 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1001 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1002 *
1003 * Postconditions:
1004 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1005 */
1006static void fe_sub(fe h, const fe f, const fe g)
1007{
1008 unsigned i;
1009
1010 for (i = 0; i < 10; i++) {
1011 h[i] = f[i] - g[i];
1012 }
1013}
1014
1015/*
1016 * h = f * g
1017 *
1018 * Can overlap h with f or g.
1019 *
1020 * Preconditions:
1021 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1022 * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1023 *
1024 * Postconditions:
1025 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1026 *
1027 * Notes on implementation strategy:
1028 *
1029 * Using schoolbook multiplication.
1030 * Karatsuba would save a little in some cost models.
1031 *
1032 * Most multiplications by 2 and 19 are 32-bit precomputations;
1033 * cheaper than 64-bit postcomputations.
1034 *
1035 * There is one remaining multiplication by 19 in the carry chain;
1036 * one *19 precomputation can be merged into this,
1037 * but the resulting data flow is considerably less clean.
1038 *
1039 * There are 12 carries below.
1040 * 10 of them are 2-way parallelizable and vectorizable.
1041 * Can get away with 11 carries, but then data flow is much deeper.
1042 *
1043 * With tighter constraints on inputs can squeeze carries into int32.
1044 */
1045static void fe_mul(fe h, const fe f, const fe g)
1046{
1047 int32_t f0 = f[0];
1048 int32_t f1 = f[1];
1049 int32_t f2 = f[2];
1050 int32_t f3 = f[3];
1051 int32_t f4 = f[4];
1052 int32_t f5 = f[5];
1053 int32_t f6 = f[6];
1054 int32_t f7 = f[7];
1055 int32_t f8 = f[8];
1056 int32_t f9 = f[9];
1057 int32_t g0 = g[0];
1058 int32_t g1 = g[1];
1059 int32_t g2 = g[2];
1060 int32_t g3 = g[3];
1061 int32_t g4 = g[4];
1062 int32_t g5 = g[5];
1063 int32_t g6 = g[6];
1064 int32_t g7 = g[7];
1065 int32_t g8 = g[8];
1066 int32_t g9 = g[9];
1067 int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */
1068 int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
1069 int32_t g3_19 = 19 * g3;
1070 int32_t g4_19 = 19 * g4;
1071 int32_t g5_19 = 19 * g5;
1072 int32_t g6_19 = 19 * g6;
1073 int32_t g7_19 = 19 * g7;
1074 int32_t g8_19 = 19 * g8;
1075 int32_t g9_19 = 19 * g9;
1076 int32_t f1_2 = 2 * f1;
1077 int32_t f3_2 = 2 * f3;
1078 int32_t f5_2 = 2 * f5;
1079 int32_t f7_2 = 2 * f7;
1080 int32_t f9_2 = 2 * f9;
1081 int64_t f0g0 = f0 * (int64_t) g0;
1082 int64_t f0g1 = f0 * (int64_t) g1;
1083 int64_t f0g2 = f0 * (int64_t) g2;
1084 int64_t f0g3 = f0 * (int64_t) g3;
1085 int64_t f0g4 = f0 * (int64_t) g4;
1086 int64_t f0g5 = f0 * (int64_t) g5;
1087 int64_t f0g6 = f0 * (int64_t) g6;
1088 int64_t f0g7 = f0 * (int64_t) g7;
1089 int64_t f0g8 = f0 * (int64_t) g8;
1090 int64_t f0g9 = f0 * (int64_t) g9;
1091 int64_t f1g0 = f1 * (int64_t) g0;
1092 int64_t f1g1_2 = f1_2 * (int64_t) g1;
1093 int64_t f1g2 = f1 * (int64_t) g2;
1094 int64_t f1g3_2 = f1_2 * (int64_t) g3;
1095 int64_t f1g4 = f1 * (int64_t) g4;
1096 int64_t f1g5_2 = f1_2 * (int64_t) g5;
1097 int64_t f1g6 = f1 * (int64_t) g6;
1098 int64_t f1g7_2 = f1_2 * (int64_t) g7;
1099 int64_t f1g8 = f1 * (int64_t) g8;
1100 int64_t f1g9_38 = f1_2 * (int64_t) g9_19;
1101 int64_t f2g0 = f2 * (int64_t) g0;
1102 int64_t f2g1 = f2 * (int64_t) g1;
1103 int64_t f2g2 = f2 * (int64_t) g2;
1104 int64_t f2g3 = f2 * (int64_t) g3;
1105 int64_t f2g4 = f2 * (int64_t) g4;
1106 int64_t f2g5 = f2 * (int64_t) g5;
1107 int64_t f2g6 = f2 * (int64_t) g6;
1108 int64_t f2g7 = f2 * (int64_t) g7;
1109 int64_t f2g8_19 = f2 * (int64_t) g8_19;
1110 int64_t f2g9_19 = f2 * (int64_t) g9_19;
1111 int64_t f3g0 = f3 * (int64_t) g0;
1112 int64_t f3g1_2 = f3_2 * (int64_t) g1;
1113 int64_t f3g2 = f3 * (int64_t) g2;
1114 int64_t f3g3_2 = f3_2 * (int64_t) g3;
1115 int64_t f3g4 = f3 * (int64_t) g4;
1116 int64_t f3g5_2 = f3_2 * (int64_t) g5;
1117 int64_t f3g6 = f3 * (int64_t) g6;
1118 int64_t f3g7_38 = f3_2 * (int64_t) g7_19;
1119 int64_t f3g8_19 = f3 * (int64_t) g8_19;
1120 int64_t f3g9_38 = f3_2 * (int64_t) g9_19;
1121 int64_t f4g0 = f4 * (int64_t) g0;
1122 int64_t f4g1 = f4 * (int64_t) g1;
1123 int64_t f4g2 = f4 * (int64_t) g2;
1124 int64_t f4g3 = f4 * (int64_t) g3;
1125 int64_t f4g4 = f4 * (int64_t) g4;
1126 int64_t f4g5 = f4 * (int64_t) g5;
1127 int64_t f4g6_19 = f4 * (int64_t) g6_19;
1128 int64_t f4g7_19 = f4 * (int64_t) g7_19;
1129 int64_t f4g8_19 = f4 * (int64_t) g8_19;
1130 int64_t f4g9_19 = f4 * (int64_t) g9_19;
1131 int64_t f5g0 = f5 * (int64_t) g0;
1132 int64_t f5g1_2 = f5_2 * (int64_t) g1;
1133 int64_t f5g2 = f5 * (int64_t) g2;
1134 int64_t f5g3_2 = f5_2 * (int64_t) g3;
1135 int64_t f5g4 = f5 * (int64_t) g4;
1136 int64_t f5g5_38 = f5_2 * (int64_t) g5_19;
1137 int64_t f5g6_19 = f5 * (int64_t) g6_19;
1138 int64_t f5g7_38 = f5_2 * (int64_t) g7_19;
1139 int64_t f5g8_19 = f5 * (int64_t) g8_19;
1140 int64_t f5g9_38 = f5_2 * (int64_t) g9_19;
1141 int64_t f6g0 = f6 * (int64_t) g0;
1142 int64_t f6g1 = f6 * (int64_t) g1;
1143 int64_t f6g2 = f6 * (int64_t) g2;
1144 int64_t f6g3 = f6 * (int64_t) g3;
1145 int64_t f6g4_19 = f6 * (int64_t) g4_19;
1146 int64_t f6g5_19 = f6 * (int64_t) g5_19;
1147 int64_t f6g6_19 = f6 * (int64_t) g6_19;
1148 int64_t f6g7_19 = f6 * (int64_t) g7_19;
1149 int64_t f6g8_19 = f6 * (int64_t) g8_19;
1150 int64_t f6g9_19 = f6 * (int64_t) g9_19;
1151 int64_t f7g0 = f7 * (int64_t) g0;
1152 int64_t f7g1_2 = f7_2 * (int64_t) g1;
1153 int64_t f7g2 = f7 * (int64_t) g2;
1154 int64_t f7g3_38 = f7_2 * (int64_t) g3_19;
1155 int64_t f7g4_19 = f7 * (int64_t) g4_19;
1156 int64_t f7g5_38 = f7_2 * (int64_t) g5_19;
1157 int64_t f7g6_19 = f7 * (int64_t) g6_19;
1158 int64_t f7g7_38 = f7_2 * (int64_t) g7_19;
1159 int64_t f7g8_19 = f7 * (int64_t) g8_19;
1160 int64_t f7g9_38 = f7_2 * (int64_t) g9_19;
1161 int64_t f8g0 = f8 * (int64_t) g0;
1162 int64_t f8g1 = f8 * (int64_t) g1;
1163 int64_t f8g2_19 = f8 * (int64_t) g2_19;
1164 int64_t f8g3_19 = f8 * (int64_t) g3_19;
1165 int64_t f8g4_19 = f8 * (int64_t) g4_19;
1166 int64_t f8g5_19 = f8 * (int64_t) g5_19;
1167 int64_t f8g6_19 = f8 * (int64_t) g6_19;
1168 int64_t f8g7_19 = f8 * (int64_t) g7_19;
1169 int64_t f8g8_19 = f8 * (int64_t) g8_19;
1170 int64_t f8g9_19 = f8 * (int64_t) g9_19;
1171 int64_t f9g0 = f9 * (int64_t) g0;
1172 int64_t f9g1_38 = f9_2 * (int64_t) g1_19;
1173 int64_t f9g2_19 = f9 * (int64_t) g2_19;
1174 int64_t f9g3_38 = f9_2 * (int64_t) g3_19;
1175 int64_t f9g4_19 = f9 * (int64_t) g4_19;
1176 int64_t f9g5_38 = f9_2 * (int64_t) g5_19;
1177 int64_t f9g6_19 = f9 * (int64_t) g6_19;
1178 int64_t f9g7_38 = f9_2 * (int64_t) g7_19;
1179 int64_t f9g8_19 = f9 * (int64_t) g8_19;
1180 int64_t f9g9_38 = f9_2 * (int64_t) g9_19;
1181 int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
1182 int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + f7g4_19 + f8g3_19 + f9g2_19;
1183 int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + f7g5_38 + f8g4_19 + f9g3_38;
1184 int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + f7g6_19 + f8g5_19 + f9g4_19;
1185 int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + f7g7_38 + f8g6_19 + f9g5_38;
1186 int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + f8g7_19 + f9g6_19;
1187 int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 + f8g8_19 + f9g7_38;
1188 int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
1189 int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + f8g0 + f9g9_38;
1190 int64_t h9 = f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0 ;
1191 int64_t carry0;
1192 int64_t carry1;
1193 int64_t carry2;
1194 int64_t carry3;
1195 int64_t carry4;
1196 int64_t carry5;
1197 int64_t carry6;
1198 int64_t carry7;
1199 int64_t carry8;
1200 int64_t carry9;
1201
1202 /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
1203 * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
1204 * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
1205 * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */
1206
1207 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1208 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1209 /* |h0| <= 2^25 */
1210 /* |h4| <= 2^25 */
1211 /* |h1| <= 1.71*2^59 */
1212 /* |h5| <= 1.71*2^59 */
1213
1214 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1215 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1216 /* |h1| <= 2^24; from now on fits into int32 */
1217 /* |h5| <= 2^24; from now on fits into int32 */
1218 /* |h2| <= 1.41*2^60 */
1219 /* |h6| <= 1.41*2^60 */
1220
1221 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1222 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1223 /* |h2| <= 2^25; from now on fits into int32 unchanged */
1224 /* |h6| <= 2^25; from now on fits into int32 unchanged */
1225 /* |h3| <= 1.71*2^59 */
1226 /* |h7| <= 1.71*2^59 */
1227
1228 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1229 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1230 /* |h3| <= 2^24; from now on fits into int32 unchanged */
1231 /* |h7| <= 2^24; from now on fits into int32 unchanged */
1232 /* |h4| <= 1.72*2^34 */
1233 /* |h8| <= 1.41*2^60 */
1234
1235 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1236 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1237 /* |h4| <= 2^25; from now on fits into int32 unchanged */
1238 /* |h8| <= 2^25; from now on fits into int32 unchanged */
1239 /* |h5| <= 1.01*2^24 */
1240 /* |h9| <= 1.71*2^59 */
1241
1242 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1243 /* |h9| <= 2^24; from now on fits into int32 unchanged */
1244 /* |h0| <= 1.1*2^39 */
1245
1246 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1247 /* |h0| <= 2^25; from now on fits into int32 unchanged */
1248 /* |h1| <= 1.01*2^24 */
1249
1250 h[0] = (int32_t)h0;
1251 h[1] = (int32_t)h1;
1252 h[2] = (int32_t)h2;
1253 h[3] = (int32_t)h3;
1254 h[4] = (int32_t)h4;
1255 h[5] = (int32_t)h5;
1256 h[6] = (int32_t)h6;
1257 h[7] = (int32_t)h7;
1258 h[8] = (int32_t)h8;
1259 h[9] = (int32_t)h9;
1260}
1261
1262/*
1263 * h = f * f
1264 *
1265 * Can overlap h with f.
1266 *
1267 * Preconditions:
1268 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1269 *
1270 * Postconditions:
1271 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1272 *
1273 * See fe_mul.c for discussion of implementation strategy.
1274 */
1275static void fe_sq(fe h, const fe f)
1276{
1277 int32_t f0 = f[0];
1278 int32_t f1 = f[1];
1279 int32_t f2 = f[2];
1280 int32_t f3 = f[3];
1281 int32_t f4 = f[4];
1282 int32_t f5 = f[5];
1283 int32_t f6 = f[6];
1284 int32_t f7 = f[7];
1285 int32_t f8 = f[8];
1286 int32_t f9 = f[9];
1287 int32_t f0_2 = 2 * f0;
1288 int32_t f1_2 = 2 * f1;
1289 int32_t f2_2 = 2 * f2;
1290 int32_t f3_2 = 2 * f3;
1291 int32_t f4_2 = 2 * f4;
1292 int32_t f5_2 = 2 * f5;
1293 int32_t f6_2 = 2 * f6;
1294 int32_t f7_2 = 2 * f7;
1295 int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1296 int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1297 int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1298 int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1299 int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1300 int64_t f0f0 = f0 * (int64_t) f0;
1301 int64_t f0f1_2 = f0_2 * (int64_t) f1;
1302 int64_t f0f2_2 = f0_2 * (int64_t) f2;
1303 int64_t f0f3_2 = f0_2 * (int64_t) f3;
1304 int64_t f0f4_2 = f0_2 * (int64_t) f4;
1305 int64_t f0f5_2 = f0_2 * (int64_t) f5;
1306 int64_t f0f6_2 = f0_2 * (int64_t) f6;
1307 int64_t f0f7_2 = f0_2 * (int64_t) f7;
1308 int64_t f0f8_2 = f0_2 * (int64_t) f8;
1309 int64_t f0f9_2 = f0_2 * (int64_t) f9;
1310 int64_t f1f1_2 = f1_2 * (int64_t) f1;
1311 int64_t f1f2_2 = f1_2 * (int64_t) f2;
1312 int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1313 int64_t f1f4_2 = f1_2 * (int64_t) f4;
1314 int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1315 int64_t f1f6_2 = f1_2 * (int64_t) f6;
1316 int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1317 int64_t f1f8_2 = f1_2 * (int64_t) f8;
1318 int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1319 int64_t f2f2 = f2 * (int64_t) f2;
1320 int64_t f2f3_2 = f2_2 * (int64_t) f3;
1321 int64_t f2f4_2 = f2_2 * (int64_t) f4;
1322 int64_t f2f5_2 = f2_2 * (int64_t) f5;
1323 int64_t f2f6_2 = f2_2 * (int64_t) f6;
1324 int64_t f2f7_2 = f2_2 * (int64_t) f7;
1325 int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1326 int64_t f2f9_38 = f2 * (int64_t) f9_38;
1327 int64_t f3f3_2 = f3_2 * (int64_t) f3;
1328 int64_t f3f4_2 = f3_2 * (int64_t) f4;
1329 int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1330 int64_t f3f6_2 = f3_2 * (int64_t) f6;
1331 int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1332 int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1333 int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1334 int64_t f4f4 = f4 * (int64_t) f4;
1335 int64_t f4f5_2 = f4_2 * (int64_t) f5;
1336 int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1337 int64_t f4f7_38 = f4 * (int64_t) f7_38;
1338 int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1339 int64_t f4f9_38 = f4 * (int64_t) f9_38;
1340 int64_t f5f5_38 = f5 * (int64_t) f5_38;
1341 int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1342 int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1343 int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1344 int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1345 int64_t f6f6_19 = f6 * (int64_t) f6_19;
1346 int64_t f6f7_38 = f6 * (int64_t) f7_38;
1347 int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1348 int64_t f6f9_38 = f6 * (int64_t) f9_38;
1349 int64_t f7f7_38 = f7 * (int64_t) f7_38;
1350 int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1351 int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1352 int64_t f8f8_19 = f8 * (int64_t) f8_19;
1353 int64_t f8f9_38 = f8 * (int64_t) f9_38;
1354 int64_t f9f9_38 = f9 * (int64_t) f9_38;
1355 int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1356 int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1357 int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1358 int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1359 int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1360 int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1361 int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1362 int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1363 int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1364 int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1365 int64_t carry0;
1366 int64_t carry1;
1367 int64_t carry2;
1368 int64_t carry3;
1369 int64_t carry4;
1370 int64_t carry5;
1371 int64_t carry6;
1372 int64_t carry7;
1373 int64_t carry8;
1374 int64_t carry9;
1375
1376 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1377 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1378
1379 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1380 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1381
1382 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1383 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1384
1385 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1386 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1387
1388 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1389 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1390
1391 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1392
1393 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1394
1395 h[0] = (int32_t)h0;
1396 h[1] = (int32_t)h1;
1397 h[2] = (int32_t)h2;
1398 h[3] = (int32_t)h3;
1399 h[4] = (int32_t)h4;
1400 h[5] = (int32_t)h5;
1401 h[6] = (int32_t)h6;
1402 h[7] = (int32_t)h7;
1403 h[8] = (int32_t)h8;
1404 h[9] = (int32_t)h9;
1405}
1406
1407static void fe_invert(fe out, const fe z)
1408{
1409 fe t0;
1410 fe t1;
1411 fe t2;
1412 fe t3;
1413 int i;
1414
1415 /*
1416 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as
1417 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11.
1418 */
1419
1420 /* t0 = z ** 2 */
1421 fe_sq(t0, z);
1422
1423 /* t1 = t0 ** (2 ** 2) = z ** 8 */
1424 fe_sq(t1, t0);
1425 fe_sq(t1, t1);
1426
1427 /* t1 = z * t1 = z ** 9 */
1428 fe_mul(t1, z, t1);
1429 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */
1430 fe_mul(t0, t0, t1);
1431
1432 /* t2 = t0 ** 2 = z ** 22 */
1433 fe_sq(t2, t0);
1434
1435 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */
1436 fe_mul(t1, t1, t2);
1437
1438 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */
1439 fe_sq(t2, t1);
1440 for (i = 1; i < 5; ++i) {
1441 fe_sq(t2, t2);
1442 }
1443
1444 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */
1445 fe_mul(t1, t2, t1);
1446
1447 /* Continuing similarly... */
1448
1449 /* t2 = z ** (2 ** 20 - 1) */
1450 fe_sq(t2, t1);
1451 for (i = 1; i < 10; ++i) {
1452 fe_sq(t2, t2);
1453 }
1454 fe_mul(t2, t2, t1);
1455
1456 /* t2 = z ** (2 ** 40 - 1) */
1457 fe_sq(t3, t2);
1458 for (i = 1; i < 20; ++i) {
1459 fe_sq(t3, t3);
1460 }
1461 fe_mul(t2, t3, t2);
1462
1463 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */
1464 for (i = 0; i < 10; ++i) {
1465 fe_sq(t2, t2);
1466 }
1467 /* t1 = z ** (2 ** 50 - 1) */
1468 fe_mul(t1, t2, t1);
1469
1470 /* t2 = z ** (2 ** 100 - 1) */
1471 fe_sq(t2, t1);
1472 for (i = 1; i < 50; ++i) {
1473 fe_sq(t2, t2);
1474 }
1475 fe_mul(t2, t2, t1);
1476
1477 /* t2 = z ** (2 ** 200 - 1) */
1478 fe_sq(t3, t2);
1479 for (i = 1; i < 100; ++i) {
1480 fe_sq(t3, t3);
1481 }
1482 fe_mul(t2, t3, t2);
1483
1484 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */
1485 fe_sq(t2, t2);
1486 for (i = 1; i < 50; ++i) {
1487 fe_sq(t2, t2);
1488 }
1489
1490 /* t1 = z ** (2 ** 250 - 1) */
1491 fe_mul(t1, t2, t1);
1492
1493 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */
1494 fe_sq(t1, t1);
1495 for (i = 1; i < 5; ++i) {
1496 fe_sq(t1, t1);
1497 }
1498
1499 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */
1500 fe_mul(out, t1, t0);
1501}
1502
1503/*
1504 * h = -f
1505 *
1506 * Preconditions:
1507 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1508 *
1509 * Postconditions:
1510 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
1511 */
1512static void fe_neg(fe h, const fe f)
1513{
1514 unsigned i;
1515
1516 for (i = 0; i < 10; i++) {
1517 h[i] = -f[i];
1518 }
1519}
1520
1521/*
1522 * Replace (f,g) with (g,g) if b == 1;
1523 * replace (f,g) with (f,g) if b == 0.
1524 *
1525 * Preconditions: b in {0,1}.
1526 */
1527static void fe_cmov(fe f, const fe g, unsigned b)
1528{
1529 size_t i;
1530
1531 b = 0-b;
1532 for (i = 0; i < 10; i++) {
1533 int32_t x = f[i] ^ g[i];
1534 x &= b;
1535 f[i] ^= x;
1536 }
1537}
1538
1539/*
1540 * return 0 if f == 0
1541 * return 1 if f != 0
1542 *
1543 * Preconditions:
1544 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1545 */
1546static int fe_isnonzero(const fe f)
1547{
1548 uint8_t s[32];
1549 static const uint8_t zero[32] = {0};
1550
1551 fe_tobytes(s, f);
1552
1553 return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;
1554}
1555
1556/*
1557 * return 1 if f is in {1,3,5,...,q-2}
1558 * return 0 if f is in {0,2,4,...,q-1}
1559 *
1560 * Preconditions:
1561 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
1562 */
1563static int fe_isnegative(const fe f)
1564{
1565 uint8_t s[32];
1566
1567 fe_tobytes(s, f);
1568 return s[0] & 1;
1569}
1570
1571/*
1572 * h = 2 * f * f
1573 *
1574 * Can overlap h with f.
1575 *
1576 * Preconditions:
1577 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
1578 *
1579 * Postconditions:
1580 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
1581 *
1582 * See fe_mul.c for discussion of implementation strategy.
1583 */
1584static void fe_sq2(fe h, const fe f)
1585{
1586 int32_t f0 = f[0];
1587 int32_t f1 = f[1];
1588 int32_t f2 = f[2];
1589 int32_t f3 = f[3];
1590 int32_t f4 = f[4];
1591 int32_t f5 = f[5];
1592 int32_t f6 = f[6];
1593 int32_t f7 = f[7];
1594 int32_t f8 = f[8];
1595 int32_t f9 = f[9];
1596 int32_t f0_2 = 2 * f0;
1597 int32_t f1_2 = 2 * f1;
1598 int32_t f2_2 = 2 * f2;
1599 int32_t f3_2 = 2 * f3;
1600 int32_t f4_2 = 2 * f4;
1601 int32_t f5_2 = 2 * f5;
1602 int32_t f6_2 = 2 * f6;
1603 int32_t f7_2 = 2 * f7;
1604 int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */
1605 int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */
1606 int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */
1607 int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */
1608 int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */
1609 int64_t f0f0 = f0 * (int64_t) f0;
1610 int64_t f0f1_2 = f0_2 * (int64_t) f1;
1611 int64_t f0f2_2 = f0_2 * (int64_t) f2;
1612 int64_t f0f3_2 = f0_2 * (int64_t) f3;
1613 int64_t f0f4_2 = f0_2 * (int64_t) f4;
1614 int64_t f0f5_2 = f0_2 * (int64_t) f5;
1615 int64_t f0f6_2 = f0_2 * (int64_t) f6;
1616 int64_t f0f7_2 = f0_2 * (int64_t) f7;
1617 int64_t f0f8_2 = f0_2 * (int64_t) f8;
1618 int64_t f0f9_2 = f0_2 * (int64_t) f9;
1619 int64_t f1f1_2 = f1_2 * (int64_t) f1;
1620 int64_t f1f2_2 = f1_2 * (int64_t) f2;
1621 int64_t f1f3_4 = f1_2 * (int64_t) f3_2;
1622 int64_t f1f4_2 = f1_2 * (int64_t) f4;
1623 int64_t f1f5_4 = f1_2 * (int64_t) f5_2;
1624 int64_t f1f6_2 = f1_2 * (int64_t) f6;
1625 int64_t f1f7_4 = f1_2 * (int64_t) f7_2;
1626 int64_t f1f8_2 = f1_2 * (int64_t) f8;
1627 int64_t f1f9_76 = f1_2 * (int64_t) f9_38;
1628 int64_t f2f2 = f2 * (int64_t) f2;
1629 int64_t f2f3_2 = f2_2 * (int64_t) f3;
1630 int64_t f2f4_2 = f2_2 * (int64_t) f4;
1631 int64_t f2f5_2 = f2_2 * (int64_t) f5;
1632 int64_t f2f6_2 = f2_2 * (int64_t) f6;
1633 int64_t f2f7_2 = f2_2 * (int64_t) f7;
1634 int64_t f2f8_38 = f2_2 * (int64_t) f8_19;
1635 int64_t f2f9_38 = f2 * (int64_t) f9_38;
1636 int64_t f3f3_2 = f3_2 * (int64_t) f3;
1637 int64_t f3f4_2 = f3_2 * (int64_t) f4;
1638 int64_t f3f5_4 = f3_2 * (int64_t) f5_2;
1639 int64_t f3f6_2 = f3_2 * (int64_t) f6;
1640 int64_t f3f7_76 = f3_2 * (int64_t) f7_38;
1641 int64_t f3f8_38 = f3_2 * (int64_t) f8_19;
1642 int64_t f3f9_76 = f3_2 * (int64_t) f9_38;
1643 int64_t f4f4 = f4 * (int64_t) f4;
1644 int64_t f4f5_2 = f4_2 * (int64_t) f5;
1645 int64_t f4f6_38 = f4_2 * (int64_t) f6_19;
1646 int64_t f4f7_38 = f4 * (int64_t) f7_38;
1647 int64_t f4f8_38 = f4_2 * (int64_t) f8_19;
1648 int64_t f4f9_38 = f4 * (int64_t) f9_38;
1649 int64_t f5f5_38 = f5 * (int64_t) f5_38;
1650 int64_t f5f6_38 = f5_2 * (int64_t) f6_19;
1651 int64_t f5f7_76 = f5_2 * (int64_t) f7_38;
1652 int64_t f5f8_38 = f5_2 * (int64_t) f8_19;
1653 int64_t f5f9_76 = f5_2 * (int64_t) f9_38;
1654 int64_t f6f6_19 = f6 * (int64_t) f6_19;
1655 int64_t f6f7_38 = f6 * (int64_t) f7_38;
1656 int64_t f6f8_38 = f6_2 * (int64_t) f8_19;
1657 int64_t f6f9_38 = f6 * (int64_t) f9_38;
1658 int64_t f7f7_38 = f7 * (int64_t) f7_38;
1659 int64_t f7f8_38 = f7_2 * (int64_t) f8_19;
1660 int64_t f7f9_76 = f7_2 * (int64_t) f9_38;
1661 int64_t f8f8_19 = f8 * (int64_t) f8_19;
1662 int64_t f8f9_38 = f8 * (int64_t) f9_38;
1663 int64_t f9f9_38 = f9 * (int64_t) f9_38;
1664 int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
1665 int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
1666 int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
1667 int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
1668 int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
1669 int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
1670 int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
1671 int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
1672 int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
1673 int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
1674 int64_t carry0;
1675 int64_t carry1;
1676 int64_t carry2;
1677 int64_t carry3;
1678 int64_t carry4;
1679 int64_t carry5;
1680 int64_t carry6;
1681 int64_t carry7;
1682 int64_t carry8;
1683 int64_t carry9;
1684
1685 h0 += h0;
1686 h1 += h1;
1687 h2 += h2;
1688 h3 += h3;
1689 h4 += h4;
1690 h5 += h5;
1691 h6 += h6;
1692 h7 += h7;
1693 h8 += h8;
1694 h9 += h9;
1695
1696 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1697 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1698
1699 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
1700 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
1701
1702 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
1703 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
1704
1705 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
1706 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
1707
1708 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
1709 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
1710
1711 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
1712
1713 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
1714
1715 h[0] = (int32_t)h0;
1716 h[1] = (int32_t)h1;
1717 h[2] = (int32_t)h2;
1718 h[3] = (int32_t)h3;
1719 h[4] = (int32_t)h4;
1720 h[5] = (int32_t)h5;
1721 h[6] = (int32_t)h6;
1722 h[7] = (int32_t)h7;
1723 h[8] = (int32_t)h8;
1724 h[9] = (int32_t)h9;
1725}
1726
1727static void fe_pow22523(fe out, const fe z)
1728{
1729 fe t0;
1730 fe t1;
1731 fe t2;
1732 int i;
1733
1734 fe_sq(t0, z);
1735 fe_sq(t1, t0);
1736 for (i = 1; i < 2; ++i) {
1737 fe_sq(t1, t1);
1738 }
1739 fe_mul(t1, z, t1);
1740 fe_mul(t0, t0, t1);
1741 fe_sq(t0, t0);
1742 fe_mul(t0, t1, t0);
1743 fe_sq(t1, t0);
1744 for (i = 1; i < 5; ++i) {
1745 fe_sq(t1, t1);
1746 }
1747 fe_mul(t0, t1, t0);
1748 fe_sq(t1, t0);
1749 for (i = 1; i < 10; ++i) {
1750 fe_sq(t1, t1);
1751 }
1752 fe_mul(t1, t1, t0);
1753 fe_sq(t2, t1);
1754 for (i = 1; i < 20; ++i) {
1755 fe_sq(t2, t2);
1756 }
1757 fe_mul(t1, t2, t1);
1758 fe_sq(t1, t1);
1759 for (i = 1; i < 10; ++i) {
1760 fe_sq(t1, t1);
1761 }
1762 fe_mul(t0, t1, t0);
1763 fe_sq(t1, t0);
1764 for (i = 1; i < 50; ++i) {
1765 fe_sq(t1, t1);
1766 }
1767 fe_mul(t1, t1, t0);
1768 fe_sq(t2, t1);
1769 for (i = 1; i < 100; ++i) {
1770 fe_sq(t2, t2);
1771 }
1772 fe_mul(t1, t2, t1);
1773 fe_sq(t1, t1);
1774 for (i = 1; i < 50; ++i) {
1775 fe_sq(t1, t1);
1776 }
1777 fe_mul(t0, t1, t0);
1778 fe_sq(t0, t0);
1779 for (i = 1; i < 2; ++i) {
1780 fe_sq(t0, t0);
1781 }
1782 fe_mul(out, t0, z);
1783}
1784
1785/*
1786 * ge means group element.
1787 *
1788 * Here the group is the set of pairs (x,y) of field elements (see fe.h)
1789 * satisfying -x^2 + y^2 = 1 + d x^2y^2
1790 * where d = -121665/121666.
1791 *
1792 * Representations:
1793 * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
1794 * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
1795 * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
1796 * ge_precomp (Duif): (y+x,y-x,2dxy)
1797 */
1798typedef struct {
1799 fe X;
1800 fe Y;
1801 fe Z;
1802} ge_p2;
1803
1804typedef struct {
1805 fe X;
1806 fe Y;
1807 fe Z;
1808 fe T;
1809} ge_p3;
1810
1811typedef struct {
1812 fe X;
1813 fe Y;
1814 fe Z;
1815 fe T;
1816} ge_p1p1;
1817
1818typedef struct {
1819 fe yplusx;
1820 fe yminusx;
1821 fe xy2d;
1822} ge_precomp;
1823
1824typedef struct {
1825 fe YplusX;
1826 fe YminusX;
1827 fe Z;
1828 fe T2d;
1829} ge_cached;
1830
1831static void ge_tobytes(uint8_t *s, const ge_p2 *h)
1832{
1833 fe recip;
1834 fe x;
1835 fe y;
1836
1837 fe_invert(recip, h->Z);
1838 fe_mul(x, h->X, recip);
1839 fe_mul(y, h->Y, recip);
1840 fe_tobytes(s, y);
1841 s[31] ^= fe_isnegative(x) << 7;
1842}
1843
1844static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h)
1845{
1846 fe recip;
1847 fe x;
1848 fe y;
1849
1850 fe_invert(recip, h->Z);
1851 fe_mul(x, h->X, recip);
1852 fe_mul(y, h->Y, recip);
1853 fe_tobytes(s, y);
1854 s[31] ^= fe_isnegative(x) << 7;
1855}
1856
1857static const fe d = {
1858 -10913610, 13857413, -15372611, 6949391, 114729,
1859 -8787816, -6275908, -3247719, -18696448, -12055116
1860};
1861
1862static const fe sqrtm1 = {
1863 -32595792, -7943725, 9377950, 3500415, 12389472,
1864 -272473, -25146209, -2005654, 326686, 11406482
1865};
1866
1867static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s)
1868{
1869 fe u;
1870 fe v;
1871 fe v3;
1872 fe vxx;
1873 fe check;
1874
1875 fe_frombytes(h->Y, s);
1876 fe_1(h->Z);
1877 fe_sq(u, h->Y);
1878 fe_mul(v, u, d);
1879 fe_sub(u, u, h->Z); /* u = y^2-1 */
1880 fe_add(v, v, h->Z); /* v = dy^2+1 */
1881
1882 fe_sq(v3, v);
1883 fe_mul(v3, v3, v); /* v3 = v^3 */
1884 fe_sq(h->X, v3);
1885 fe_mul(h->X, h->X, v);
1886 fe_mul(h->X, h->X, u); /* x = uv^7 */
1887
1888 fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */
1889 fe_mul(h->X, h->X, v3);
1890 fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */
1891
1892 fe_sq(vxx, h->X);
1893 fe_mul(vxx, vxx, v);
1894 fe_sub(check, vxx, u); /* vx^2-u */
1895 if (fe_isnonzero(check)) {
1896 fe_add(check, vxx, u); /* vx^2+u */
1897 if (fe_isnonzero(check)) {
1898 return -1;
1899 }
1900 fe_mul(h->X, h->X, sqrtm1);
1901 }
1902
1903 if (fe_isnegative(h->X) != (s[31] >> 7)) {
1904 fe_neg(h->X, h->X);
1905 }
1906
1907 fe_mul(h->T, h->X, h->Y);
1908 return 0;
1909}
1910
1911static void ge_p2_0(ge_p2 *h)
1912{
1913 fe_0(h->X);
1914 fe_1(h->Y);
1915 fe_1(h->Z);
1916}
1917
1918static void ge_p3_0(ge_p3 *h)
1919{
1920 fe_0(h->X);
1921 fe_1(h->Y);
1922 fe_1(h->Z);
1923 fe_0(h->T);
1924}
1925
1926static void ge_precomp_0(ge_precomp *h)
1927{
1928 fe_1(h->yplusx);
1929 fe_1(h->yminusx);
1930 fe_0(h->xy2d);
1931}
1932
1933/* r = p */
1934static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p)
1935{
1936 fe_copy(r->X, p->X);
1937 fe_copy(r->Y, p->Y);
1938 fe_copy(r->Z, p->Z);
1939}
1940
1941static const fe d2 = {
1942 -21827239, -5839606, -30745221, 13898782, 229458,
1943 15978800, -12551817, -6495438, 29715968, 9444199
1944};
1945
1946/* r = p */
1947static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p)
1948{
1949 fe_add(r->YplusX, p->Y, p->X);
1950 fe_sub(r->YminusX, p->Y, p->X);
1951 fe_copy(r->Z, p->Z);
1952 fe_mul(r->T2d, p->T, d2);
1953}
1954
1955/* r = p */
1956static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p)
1957{
1958 fe_mul(r->X, p->X, p->T);
1959 fe_mul(r->Y, p->Y, p->Z);
1960 fe_mul(r->Z, p->Z, p->T);
1961}
1962
1963/* r = p */
1964static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p)
1965{
1966 fe_mul(r->X, p->X, p->T);
1967 fe_mul(r->Y, p->Y, p->Z);
1968 fe_mul(r->Z, p->Z, p->T);
1969 fe_mul(r->T, p->X, p->Y);
1970}
1971
1972/* r = 2 * p */
1973static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p)
1974{
1975 fe t0;
1976
1977 fe_sq(r->X, p->X);
1978 fe_sq(r->Z, p->Y);
1979 fe_sq2(r->T, p->Z);
1980 fe_add(r->Y, p->X, p->Y);
1981 fe_sq(t0, r->Y);
1982 fe_add(r->Y, r->Z, r->X);
1983 fe_sub(r->Z, r->Z, r->X);
1984 fe_sub(r->X, t0, r->Y);
1985 fe_sub(r->T, r->T, r->Z);
1986}
1987
1988/* r = 2 * p */
1989static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p)
1990{
1991 ge_p2 q;
1992 ge_p3_to_p2(&q, p);
1993 ge_p2_dbl(r, &q);
1994}
1995
1996/* r = p + q */
1997static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
1998{
1999 fe t0;
2000
2001 fe_add(r->X, p->Y, p->X);
2002 fe_sub(r->Y, p->Y, p->X);
2003 fe_mul(r->Z, r->X, q->yplusx);
2004 fe_mul(r->Y, r->Y, q->yminusx);
2005 fe_mul(r->T, q->xy2d, p->T);
2006 fe_add(t0, p->Z, p->Z);
2007 fe_sub(r->X, r->Z, r->Y);
2008 fe_add(r->Y, r->Z, r->Y);
2009 fe_add(r->Z, t0, r->T);
2010 fe_sub(r->T, t0, r->T);
2011}
2012
2013/* r = p - q */
2014static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q)
2015{
2016 fe t0;
2017
2018 fe_add(r->X, p->Y, p->X);
2019 fe_sub(r->Y, p->Y, p->X);
2020 fe_mul(r->Z, r->X, q->yminusx);
2021 fe_mul(r->Y, r->Y, q->yplusx);
2022 fe_mul(r->T, q->xy2d, p->T);
2023 fe_add(t0, p->Z, p->Z);
2024 fe_sub(r->X, r->Z, r->Y);
2025 fe_add(r->Y, r->Z, r->Y);
2026 fe_sub(r->Z, t0, r->T);
2027 fe_add(r->T, t0, r->T);
2028}
2029
2030/* r = p + q */
2031static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
2032{
2033 fe t0;
2034
2035 fe_add(r->X, p->Y, p->X);
2036 fe_sub(r->Y, p->Y, p->X);
2037 fe_mul(r->Z, r->X, q->YplusX);
2038 fe_mul(r->Y, r->Y, q->YminusX);
2039 fe_mul(r->T, q->T2d, p->T);
2040 fe_mul(r->X, p->Z, q->Z);
2041 fe_add(t0, r->X, r->X);
2042 fe_sub(r->X, r->Z, r->Y);
2043 fe_add(r->Y, r->Z, r->Y);
2044 fe_add(r->Z, t0, r->T);
2045 fe_sub(r->T, t0, r->T);
2046}
2047
2048/* r = p - q */
2049static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q)
2050{
2051 fe t0;
2052
2053 fe_add(r->X, p->Y, p->X);
2054 fe_sub(r->Y, p->Y, p->X);
2055 fe_mul(r->Z, r->X, q->YminusX);
2056 fe_mul(r->Y, r->Y, q->YplusX);
2057 fe_mul(r->T, q->T2d, p->T);
2058 fe_mul(r->X, p->Z, q->Z);
2059 fe_add(t0, r->X, r->X);
2060 fe_sub(r->X, r->Z, r->Y);
2061 fe_add(r->Y, r->Z, r->Y);
2062 fe_sub(r->Z, t0, r->T);
2063 fe_add(r->T, t0, r->T);
2064}
2065
2066static uint8_t equal(signed char b, signed char c)
2067{
2068 uint8_t ub = b;
2069 uint8_t uc = c;
2070 uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */
2071 uint32_t y = x; /* 0: yes; 1..255: no */
2072 y -= 1; /* 4294967295: yes; 0..254: no */
2073 y >>= 31; /* 1: yes; 0: no */
2074 return y;
2075}
2076
2077static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b)
2078{
2079 fe_cmov(t->yplusx, u->yplusx, b);
2080 fe_cmov(t->yminusx, u->yminusx, b);
2081 fe_cmov(t->xy2d, u->xy2d, b);
2082}
2083
2084/* k25519Precomp[i][j] = (j+1)*256^i*B */
2085static const ge_precomp k25519Precomp[32][8] = {
2086 {
2087 {
2088 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787,
2089 27544626, -11754271, -6079156, 2047605},
2090 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
2091 5043384, 19500929, -15469378},
2092 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380,
2093 29287919, 11864899, -24514362, -4438546},
2094 },
2095 {
2096 {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717,
2097 -11717903, -3814571, -358445, -10211303},
2098 {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005,
2099 -15616551, 11189268, -26829678, -5319081},
2100 {26966642, 11152617, 32442495, 15396054, 14353839, -12752335,
2101 -3128826, -9541118, -15472047, -4166697},
2102 },
2103 {
2104 {15636291, -9688557, 24204773, -7912398, 616977, -16685262,
2105 27787600, -14772189, 28944400, -1550024},
2106 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043,
2107 16354577, -11775962, 7689662, 11199574},
2108 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852,
2109 7512774, 10017326, -17749093, -9920357},
2110 },
2111 {
2112 {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379,
2113 -28926210, 15006023, 3284568, -6276540},
2114 {23599295, -8306047, -11193664, -7687416, 13236774, 10506355,
2115 7464579, 9656445, 13059162, 10374397},
2116 {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
2117 -3839045, -641708, -101325},
2118 },
2119 {
2120 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861,
2121 32867885, 14515107, -15438304, 10819380},
2122 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
2123 12483688, -12668491, 5581306},
2124 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115,
2125 28542350, 13850243, -23678021, -15815942},
2126 },
2127 {
2128 {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511,
2129 -19188627, -15224819, -9818940, -12085777},
2130 {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
2131 -15689887, 1762328, 14866737},
2132 {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101,
2133 -28236412, 3959421, 27914454, 4383652},
2134 },
2135 {
2136 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
2137 5230134, -23952439, -15175766},
2138 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722,
2139 20654025, 16520125, 30598449, 7715701},
2140 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316,
2141 -31400660, 1370708, 29794553, -1409300},
2142 },
2143 {
2144 {14499471, -2729599, -33191113, -4254652, 28494862, 14271267,
2145 30290735, 10876454, -33154098, 2381726},
2146 {-7195431, -2655363, -14730155, 462251, -27724326, 3941372,
2147 -6236617, 3696005, -32300832, 15351955},
2148 {27431194, 8222322, 16448760, -3907995, -18707002, 11938355,
2149 -32961401, -2970515, 29551813, 10109425},
2150 },
2151 },
2152 {
2153 {
2154 {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384,
2155 -2378284, -1627556, 10092783, -4764171},
2156 {27939166, 14210322, 4677035, 16277044, -22964462, -12398139,
2157 -32508754, 12005538, -17810127, 12803510},
2158 {17228999, -15661624, -1233527, 300140, -1224870, -11714777,
2159 30364213, -9038194, 18016357, 4397660},
2160 },
2161 {
2162 {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212,
2163 -26619106, 14544525, -17477504, 982639},
2164 {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
2165 -4120128, -21047696, 9934963},
2166 {5793303, 16271923, -24131614, -10116404, 29188560, 1206517,
2167 -14747930, 4559895, -30123922, -10897950},
2168 },
2169 {
2170 {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264,
2171 24191034, 4541697, -13338309, 5500568},
2172 {12650548, -1497113, 9052871, 11355358, -17680037, -8400164,
2173 -17430592, 12264343, 10874051, 13524335},
2174 {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
2175 5080568, -22528059, 5376628},
2176 },
2177 {
2178 {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897,
2179 -22321305, -9447443, 4535768, 1569007},
2180 {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819,
2181 -30494562, 3044290, 31848280, 12543772},
2182 {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203,
2183 -27377195, -2062731, 7718482, 14474653},
2184 },
2185 {
2186 {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965,
2187 -7236665, 24316168, -5253567},
2188 {13741529, 10911568, -33233417, -8603737, -20177830, -1033297,
2189 33040651, -13424532, -20729456, 8321686},
2190 {21060490, -2212744, 15712757, -4336099, 1639040, 10656336,
2191 23845965, -11874838, -9984458, 608372},
2192 },
2193 {
2194 {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547,
2195 1123968, -6780577, 27229399, 23887},
2196 {-23244140, -294205, -11744728, 14712571, -29465699, -2029617,
2197 12797024, -6440308, -1633405, 16678954},
2198 {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805,
2199 -1508144, -4795045, -17169265, 4904953},
2200 },
2201 {
2202 {24059557, 14617003, 19037157, -15039908, 19766093, -14906429,
2203 5169211, 16191880, 2128236, -4326833},
2204 {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247,
2205 -29806336, 916033, -6882542, -2986532},
2206 {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175,
2207 285431, 2763829, 15736322, 4143876},
2208 },
2209 {
2210 {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
2211 -14594663, 23527084, -16458268},
2212 {33431127, -11130478, -17838966, -15626900, 8909499, 8376530,
2213 -32625340, 4087881, -15188911, -14416214},
2214 {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
2215 4357868, -4774191, -16323038},
2216 },
2217 },
2218 {
2219 {
2220 {6721966, 13833823, -23523388, -1551314, 26354293, -11863321,
2221 23365147, -3949732, 7390890, 2759800},
2222 {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
2223 -4264057, 1244380, -12919645},
2224 {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
2225 9208236, 15886429, 16489664},
2226 },
2227 {
2228 {1996075, 10375649, 14346367, 13311202, -6874135, -16438411,
2229 -13693198, 398369, -30606455, -712933},
2230 {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363,
2231 13348553, 12076947, -30836462, 5113182},
2232 {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344,
2233 -30341101, -7336386, 13847711, 5387222},
2234 },
2235 {
2236 {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611,
2237 8763061, 3617786, -19600662, 10370991},
2238 {20246567, -14369378, 22358229, -543712, 18507283, -10413996,
2239 14554437, -8746092, 32232924, 16763880},
2240 {9648505, 10094563, 26416693, 14745928, -30374318, -6472621,
2241 11094161, 15689506, 3140038, -16510092},
2242 },
2243 {
2244 {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685,
2245 -27224800, 9448613, -28774454, 366295},
2246 {19153450, 11523972, -11096490, -6503142, -24647631, 5420647,
2247 28344573, 8041113, 719605, 11671788},
2248 {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
2249 -15266516, 27000813, -10195553},
2250 },
2251 {
2252 {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
2253 5336097, 6750977, -14521026},
2254 {11836410, -3979488, 26297894, 16080799, 23455045, 15735944,
2255 1695823, -8819122, 8169720, 16220347},
2256 {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763,
2257 -11144307, -2627664, -5990708, -14166033},
2258 },
2259 {
2260 {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004,
2261 27884329, 2847284, 2655861, 1738395},
2262 {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821,
2263 21651608, -3239336, -19087449, -11005278},
2264 {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
2265 5821408, 10478196, 8544890},
2266 },
2267 {
2268 {32173121, -16129311, 24896207, 3921497, 22579056, -3410854,
2269 19270449, 12217473, 17789017, -3395995},
2270 {-30552961, -2228401, -15578829, -10147201, 13243889, 517024,
2271 15479401, -3853233, 30460520, 1052596},
2272 {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687,
2273 27491595, -4612359, 3179268, -9478891},
2274 },
2275 {
2276 {31947069, -14366651, -4640583, -15339921, -15125977, -6039709,
2277 -14756777, -16411740, 19072640, -9511060},
2278 {11685058, 11822410, 3158003, -13952594, 33402194, -4165066,
2279 5977896, -5215017, 473099, 5040608},
2280 {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760,
2281 28326862, 1721092, -19558642, -3131606},
2282 },
2283 },
2284 {
2285 {
2286 {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
2287 8076149, -27868496, 11538389},
2288 {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211,
2289 8754525, 7446702, -5676054, 5797016},
2290 {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199,
2291 2014099, -9050574, -2369172, -5877341},
2292 },
2293 {
2294 {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559,
2295 1192730, -3714199, 15123619, 10811505},
2296 {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
2297 15776356, -28886779, -11974553},
2298 {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569,
2299 -20654173, -16484855, 4714547, -9600655},
2300 },
2301 {
2302 {15200332, 8368572, 19679101, 15970074, -31872674, 1959451,
2303 24611599, -4543832, -11745876, 12340220},
2304 {12876937, -10480056, 33134381, 6590940, -6307776, 14872440,
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4189 {
4190 {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591,
4191 -1853465, 1367120, 25127874, 6671743},
4192 {29701166, -14373934, -10878120, 9279288, -17568, 13127210,
4193 21382910, 11042292, 25838796, 4642684},
4194 {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470,
4195 30468147, -13900640, 18423289, 4177476},
4196 },
4197 },
4198};
4199
4200static uint8_t negative(signed char b)
4201{
4202 uint32_t x = b;
4203
4204 x >>= 31; /* 1: yes; 0: no */
4205 return x;
4206}
4207
4208static void table_select(ge_precomp *t, int pos, signed char b)
4209{
4210 ge_precomp minust;
4211 uint8_t bnegative = negative(b);
4212 uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1);
4213
4214 ge_precomp_0(t);
4215 cmov(t, &k25519Precomp[pos][0], equal(babs, 1));
4216 cmov(t, &k25519Precomp[pos][1], equal(babs, 2));
4217 cmov(t, &k25519Precomp[pos][2], equal(babs, 3));
4218 cmov(t, &k25519Precomp[pos][3], equal(babs, 4));
4219 cmov(t, &k25519Precomp[pos][4], equal(babs, 5));
4220 cmov(t, &k25519Precomp[pos][5], equal(babs, 6));
4221 cmov(t, &k25519Precomp[pos][6], equal(babs, 7));
4222 cmov(t, &k25519Precomp[pos][7], equal(babs, 8));
4223 fe_copy(minust.yplusx, t->yminusx);
4224 fe_copy(minust.yminusx, t->yplusx);
4225 fe_neg(minust.xy2d, t->xy2d);
4226 cmov(t, &minust, bnegative);
4227}
4228
4229/*
4230 * h = a * B
4231 *
4232 * where a = a[0]+256*a[1]+...+256^31 a[31]
4233 * B is the Ed25519 base point (x,4/5) with x positive.
4234 *
4235 * Preconditions:
4236 * a[31] <= 127
4237 */
4238static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a)
4239{
4240 signed char e[64];
4241 signed char carry;
4242 ge_p1p1 r;
4243 ge_p2 s;
4244 ge_precomp t;
4245 int i;
4246
4247 for (i = 0; i < 32; ++i) {
4248 e[2 * i + 0] = (a[i] >> 0) & 15;
4249 e[2 * i + 1] = (a[i] >> 4) & 15;
4250 }
4251 /* each e[i] is between 0 and 15 */
4252 /* e[63] is between 0 and 7 */
4253
4254 carry = 0;
4255 for (i = 0; i < 63; ++i) {
4256 e[i] += carry;
4257 carry = e[i] + 8;
4258 carry >>= 4;
4259 e[i] -= carry << 4;
4260 }
4261 e[63] += carry;
4262 /* each e[i] is between -8 and 8 */
4263
4264 ge_p3_0(h);
4265 for (i = 1; i < 64; i += 2) {
4266 table_select(&t, i / 2, e[i]);
4267 ge_madd(&r, h, &t);
4268 ge_p1p1_to_p3(h, &r);
4269 }
4270
4271 ge_p3_dbl(&r, h);
4272 ge_p1p1_to_p2(&s, &r);
4273 ge_p2_dbl(&r, &s);
4274 ge_p1p1_to_p2(&s, &r);
4275 ge_p2_dbl(&r, &s);
4276 ge_p1p1_to_p2(&s, &r);
4277 ge_p2_dbl(&r, &s);
4278 ge_p1p1_to_p3(h, &r);
4279
4280 for (i = 0; i < 64; i += 2) {
4281 table_select(&t, i / 2, e[i]);
4282 ge_madd(&r, h, &t);
4283 ge_p1p1_to_p3(h, &r);
4284 }
4285
4286 OPENSSL_cleanse(e, sizeof(e));
4287}
4288
4289#if !defined(BASE_2_51_IMPLEMENTED)
4290/*
4291 * Replace (f,g) with (g,f) if b == 1;
4292 * replace (f,g) with (f,g) if b == 0.
4293 *
4294 * Preconditions: b in {0,1}.
4295 */
4296static void fe_cswap(fe f, fe g, unsigned int b)
4297{
4298 size_t i;
4299
4300 b = 0-b;
4301 for (i = 0; i < 10; i++) {
4302 int32_t x = f[i] ^ g[i];
4303 x &= b;
4304 f[i] ^= x;
4305 g[i] ^= x;
4306 }
4307}
4308
4309/*
4310 * h = f * 121666
4311 *
4312 * Can overlap h with f.
4313 *
4314 * Preconditions:
4315 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
4316 *
4317 * Postconditions:
4318 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
4319 */
4320static void fe_mul121666(fe h, fe f)
4321{
4322 int32_t f0 = f[0];
4323 int32_t f1 = f[1];
4324 int32_t f2 = f[2];
4325 int32_t f3 = f[3];
4326 int32_t f4 = f[4];
4327 int32_t f5 = f[5];
4328 int32_t f6 = f[6];
4329 int32_t f7 = f[7];
4330 int32_t f8 = f[8];
4331 int32_t f9 = f[9];
4332 int64_t h0 = f0 * (int64_t) 121666;
4333 int64_t h1 = f1 * (int64_t) 121666;
4334 int64_t h2 = f2 * (int64_t) 121666;
4335 int64_t h3 = f3 * (int64_t) 121666;
4336 int64_t h4 = f4 * (int64_t) 121666;
4337 int64_t h5 = f5 * (int64_t) 121666;
4338 int64_t h6 = f6 * (int64_t) 121666;
4339 int64_t h7 = f7 * (int64_t) 121666;
4340 int64_t h8 = f8 * (int64_t) 121666;
4341 int64_t h9 = f9 * (int64_t) 121666;
4342 int64_t carry0;
4343 int64_t carry1;
4344 int64_t carry2;
4345 int64_t carry3;
4346 int64_t carry4;
4347 int64_t carry5;
4348 int64_t carry6;
4349 int64_t carry7;
4350 int64_t carry8;
4351 int64_t carry9;
4352
4353 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits;
4354 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits;
4355 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits;
4356 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits;
4357 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits;
4358
4359 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits;
4360 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits;
4361 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits;
4362 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits;
4363 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits;
4364
4365 h[0] = (int32_t)h0;
4366 h[1] = (int32_t)h1;
4367 h[2] = (int32_t)h2;
4368 h[3] = (int32_t)h3;
4369 h[4] = (int32_t)h4;
4370 h[5] = (int32_t)h5;
4371 h[6] = (int32_t)h6;
4372 h[7] = (int32_t)h7;
4373 h[8] = (int32_t)h8;
4374 h[9] = (int32_t)h9;
4375}
4376
4377static void x25519_scalar_mult_generic(uint8_t out[32],
4378 const uint8_t scalar[32],
4379 const uint8_t point[32]) {
4380 fe x1, x2, z2, x3, z3, tmp0, tmp1;
4381 uint8_t e[32];
4382 unsigned swap = 0;
4383 int pos;
4384
4385 memcpy(e, scalar, 32);
4386 e[0] &= 248;
4387 e[31] &= 127;
4388 e[31] |= 64;
4389 fe_frombytes(x1, point);
4390 fe_1(x2);
4391 fe_0(z2);
4392 fe_copy(x3, x1);
4393 fe_1(z3);
4394
4395 for (pos = 254; pos >= 0; --pos) {
4396 unsigned b = 1 & (e[pos / 8] >> (pos & 7));
4397 swap ^= b;
4398 fe_cswap(x2, x3, swap);
4399 fe_cswap(z2, z3, swap);
4400 swap = b;
4401 fe_sub(tmp0, x3, z3);
4402 fe_sub(tmp1, x2, z2);
4403 fe_add(x2, x2, z2);
4404 fe_add(z2, x3, z3);
4405 fe_mul(z3, tmp0, x2);
4406 fe_mul(z2, z2, tmp1);
4407 fe_sq(tmp0, tmp1);
4408 fe_sq(tmp1, x2);
4409 fe_add(x3, z3, z2);
4410 fe_sub(z2, z3, z2);
4411 fe_mul(x2, tmp1, tmp0);
4412 fe_sub(tmp1, tmp1, tmp0);
4413 fe_sq(z2, z2);
4414 fe_mul121666(z3, tmp1);
4415 fe_sq(x3, x3);
4416 fe_add(tmp0, tmp0, z3);
4417 fe_mul(z3, x1, z2);
4418 fe_mul(z2, tmp1, tmp0);
4419 }
4420
4421 fe_invert(z2, z2);
4422 fe_mul(x2, x2, z2);
4423 fe_tobytes(out, x2);
4424
4425 OPENSSL_cleanse(e, sizeof(e));
4426}
4427
4428static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32],
4429 const uint8_t point[32]) {
4430 x25519_scalar_mult_generic(out, scalar, point);
4431}
4432#endif
4433
4434static void slide(signed char *r, const uint8_t *a)
4435{
4436 int i;
4437 int b;
4438 int k;
4439
4440 for (i = 0; i < 256; ++i) {
4441 r[i] = 1 & (a[i >> 3] >> (i & 7));
4442 }
4443
4444 for (i = 0; i < 256; ++i) {
4445 if (r[i]) {
4446 for (b = 1; b <= 6 && i + b < 256; ++b) {
4447 if (r[i + b]) {
4448 if (r[i] + (r[i + b] << b) <= 15) {
4449 r[i] += r[i + b] << b;
4450 r[i + b] = 0;
4451 } else if (r[i] - (r[i + b] << b) >= -15) {
4452 r[i] -= r[i + b] << b;
4453 for (k = i + b; k < 256; ++k) {
4454 if (!r[k]) {
4455 r[k] = 1;
4456 break;
4457 }
4458 r[k] = 0;
4459 }
4460 } else {
4461 break;
4462 }
4463 }
4464 }
4465 }
4466 }
4467}
4468
4469static const ge_precomp Bi[8] = {
4470 {
4471 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
4472 -11754271, -6079156, 2047605},
4473 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692,
4474 5043384, 19500929, -15469378},
4475 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
4476 11864899, -24514362, -4438546},
4477 },
4478 {
4479 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
4480 -14772189, 28944400, -1550024},
4481 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
4482 -11775962, 7689662, 11199574},
4483 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
4484 10017326, -17749093, -9920357},
4485 },
4486 {
4487 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
4488 14515107, -15438304, 10819380},
4489 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
4490 12483688, -12668491, 5581306},
4491 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
4492 13850243, -23678021, -15815942},
4493 },
4494 {
4495 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852,
4496 5230134, -23952439, -15175766},
4497 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
4498 16520125, 30598449, 7715701},
4499 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
4500 1370708, 29794553, -1409300},
4501 },
4502 {
4503 {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211,
4504 -1361450, -13062696, 13821877},
4505 {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028,
4506 -7212327, 18853322, -14220951},
4507 {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
4508 -10431137, 2207753, -3209784},
4509 },
4510 {
4511 {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
4512 -663000, -31111463, -16132436},
4513 {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
4514 15725684, 171356, 6466918},
4515 {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
4516 -14088058, -30714912, 16193877},
4517 },
4518 {
4519 {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
4520 4729455, -18074513, 9256800},
4521 {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
4522 9761698, -19827198, 630305},
4523 {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
4524 -15960994, -2449256, -14291300},
4525 },
4526 {
4527 {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
4528 15033784, 25105118, -7894876},
4529 {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925,
4530 1573892, -2625887, 2198790, -15804619},
4531 {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
4532 -16236442, -32461234, -12290683},
4533 },
4534};
4535
4536/*
4537 * r = a * A + b * B
4538 *
4539 * where a = a[0]+256*a[1]+...+256^31 a[31].
4540 * and b = b[0]+256*b[1]+...+256^31 b[31].
4541 * B is the Ed25519 base point (x,4/5) with x positive.
4542 */
4543static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a,
4544 const ge_p3 *A, const uint8_t *b)
4545{
4546 signed char aslide[256];
4547 signed char bslide[256];
4548 ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
4549 ge_p1p1 t;
4550 ge_p3 u;
4551 ge_p3 A2;
4552 int i;
4553
4554 slide(aslide, a);
4555 slide(bslide, b);
4556
4557 ge_p3_to_cached(&Ai[0], A);
4558 ge_p3_dbl(&t, A);
4559 ge_p1p1_to_p3(&A2, &t);
4560 ge_add(&t, &A2, &Ai[0]);
4561 ge_p1p1_to_p3(&u, &t);
4562 ge_p3_to_cached(&Ai[1], &u);
4563 ge_add(&t, &A2, &Ai[1]);
4564 ge_p1p1_to_p3(&u, &t);
4565 ge_p3_to_cached(&Ai[2], &u);
4566 ge_add(&t, &A2, &Ai[2]);
4567 ge_p1p1_to_p3(&u, &t);
4568 ge_p3_to_cached(&Ai[3], &u);
4569 ge_add(&t, &A2, &Ai[3]);
4570 ge_p1p1_to_p3(&u, &t);
4571 ge_p3_to_cached(&Ai[4], &u);
4572 ge_add(&t, &A2, &Ai[4]);
4573 ge_p1p1_to_p3(&u, &t);
4574 ge_p3_to_cached(&Ai[5], &u);
4575 ge_add(&t, &A2, &Ai[5]);
4576 ge_p1p1_to_p3(&u, &t);
4577 ge_p3_to_cached(&Ai[6], &u);
4578 ge_add(&t, &A2, &Ai[6]);
4579 ge_p1p1_to_p3(&u, &t);
4580 ge_p3_to_cached(&Ai[7], &u);
4581
4582 ge_p2_0(r);
4583
4584 for (i = 255; i >= 0; --i) {
4585 if (aslide[i] || bslide[i]) {
4586 break;
4587 }
4588 }
4589
4590 for (; i >= 0; --i) {
4591 ge_p2_dbl(&t, r);
4592
4593 if (aslide[i] > 0) {
4594 ge_p1p1_to_p3(&u, &t);
4595 ge_add(&t, &u, &Ai[aslide[i] / 2]);
4596 } else if (aslide[i] < 0) {
4597 ge_p1p1_to_p3(&u, &t);
4598 ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]);
4599 }
4600
4601 if (bslide[i] > 0) {
4602 ge_p1p1_to_p3(&u, &t);
4603 ge_madd(&t, &u, &Bi[bslide[i] / 2]);
4604 } else if (bslide[i] < 0) {
4605 ge_p1p1_to_p3(&u, &t);
4606 ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]);
4607 }
4608
4609 ge_p1p1_to_p2(r, &t);
4610 }
4611}
4612
4613/*
4614 * The set of scalars is \Z/l
4615 * where l = 2^252 + 27742317777372353535851937790883648493.
4616 *
4617 * Input:
4618 * s[0]+256*s[1]+...+256^63*s[63] = s
4619 *
4620 * Output:
4621 * s[0]+256*s[1]+...+256^31*s[31] = s mod l
4622 * where l = 2^252 + 27742317777372353535851937790883648493.
4623 * Overwrites s in place.
4624*/
4625static void x25519_sc_reduce(uint8_t *s)
4626{
4627 int64_t s0 = kBottom21Bits & load_3(s);
4628 int64_t s1 = kBottom21Bits & (load_4(s + 2) >> 5);
4629 int64_t s2 = kBottom21Bits & (load_3(s + 5) >> 2);
4630 int64_t s3 = kBottom21Bits & (load_4(s + 7) >> 7);
4631 int64_t s4 = kBottom21Bits & (load_4(s + 10) >> 4);
4632 int64_t s5 = kBottom21Bits & (load_3(s + 13) >> 1);
4633 int64_t s6 = kBottom21Bits & (load_4(s + 15) >> 6);
4634 int64_t s7 = kBottom21Bits & (load_3(s + 18) >> 3);
4635 int64_t s8 = kBottom21Bits & load_3(s + 21);
4636 int64_t s9 = kBottom21Bits & (load_4(s + 23) >> 5);
4637 int64_t s10 = kBottom21Bits & (load_3(s + 26) >> 2);
4638 int64_t s11 = kBottom21Bits & (load_4(s + 28) >> 7);
4639 int64_t s12 = kBottom21Bits & (load_4(s + 31) >> 4);
4640 int64_t s13 = kBottom21Bits & (load_3(s + 34) >> 1);
4641 int64_t s14 = kBottom21Bits & (load_4(s + 36) >> 6);
4642 int64_t s15 = kBottom21Bits & (load_3(s + 39) >> 3);
4643 int64_t s16 = kBottom21Bits & load_3(s + 42);
4644 int64_t s17 = kBottom21Bits & (load_4(s + 44) >> 5);
4645 int64_t s18 = kBottom21Bits & (load_3(s + 47) >> 2);
4646 int64_t s19 = kBottom21Bits & (load_4(s + 49) >> 7);
4647 int64_t s20 = kBottom21Bits & (load_4(s + 52) >> 4);
4648 int64_t s21 = kBottom21Bits & (load_3(s + 55) >> 1);
4649 int64_t s22 = kBottom21Bits & (load_4(s + 57) >> 6);
4650 int64_t s23 = (load_4(s + 60) >> 3);
4651 int64_t carry0;
4652 int64_t carry1;
4653 int64_t carry2;
4654 int64_t carry3;
4655 int64_t carry4;
4656 int64_t carry5;
4657 int64_t carry6;
4658 int64_t carry7;
4659 int64_t carry8;
4660 int64_t carry9;
4661 int64_t carry10;
4662 int64_t carry11;
4663 int64_t carry12;
4664 int64_t carry13;
4665 int64_t carry14;
4666 int64_t carry15;
4667 int64_t carry16;
4668
4669 s11 += s23 * 666643;
4670 s12 += s23 * 470296;
4671 s13 += s23 * 654183;
4672 s14 -= s23 * 997805;
4673 s15 += s23 * 136657;
4674 s16 -= s23 * 683901;
4675 s23 = 0;
4676
4677 s10 += s22 * 666643;
4678 s11 += s22 * 470296;
4679 s12 += s22 * 654183;
4680 s13 -= s22 * 997805;
4681 s14 += s22 * 136657;
4682 s15 -= s22 * 683901;
4683 s22 = 0;
4684
4685 s9 += s21 * 666643;
4686 s10 += s21 * 470296;
4687 s11 += s21 * 654183;
4688 s12 -= s21 * 997805;
4689 s13 += s21 * 136657;
4690 s14 -= s21 * 683901;
4691 s21 = 0;
4692
4693 s8 += s20 * 666643;
4694 s9 += s20 * 470296;
4695 s10 += s20 * 654183;
4696 s11 -= s20 * 997805;
4697 s12 += s20 * 136657;
4698 s13 -= s20 * 683901;
4699 s20 = 0;
4700
4701 s7 += s19 * 666643;
4702 s8 += s19 * 470296;
4703 s9 += s19 * 654183;
4704 s10 -= s19 * 997805;
4705 s11 += s19 * 136657;
4706 s12 -= s19 * 683901;
4707 s19 = 0;
4708
4709 s6 += s18 * 666643;
4710 s7 += s18 * 470296;
4711 s8 += s18 * 654183;
4712 s9 -= s18 * 997805;
4713 s10 += s18 * 136657;
4714 s11 -= s18 * 683901;
4715 s18 = 0;
4716
4717 carry6 = (s6 + (1 << 20)) >> 21;
4718 s7 += carry6;
4719 s6 -= carry6 * (1 << 21);
4720 carry8 = (s8 + (1 << 20)) >> 21;
4721 s9 += carry8;
4722 s8 -= carry8 * (1 << 21);
4723 carry10 = (s10 + (1 << 20)) >> 21;
4724 s11 += carry10;
4725 s10 -= carry10 * (1 << 21);
4726 carry12 = (s12 + (1 << 20)) >> 21;
4727 s13 += carry12;
4728 s12 -= carry12 * (1 << 21);
4729 carry14 = (s14 + (1 << 20)) >> 21;
4730 s15 += carry14;
4731 s14 -= carry14 * (1 << 21);
4732 carry16 = (s16 + (1 << 20)) >> 21;
4733 s17 += carry16;
4734 s16 -= carry16 * (1 << 21);
4735
4736 carry7 = (s7 + (1 << 20)) >> 21;
4737 s8 += carry7;
4738 s7 -= carry7 * (1 << 21);
4739 carry9 = (s9 + (1 << 20)) >> 21;
4740 s10 += carry9;
4741 s9 -= carry9 * (1 << 21);
4742 carry11 = (s11 + (1 << 20)) >> 21;
4743 s12 += carry11;
4744 s11 -= carry11 * (1 << 21);
4745 carry13 = (s13 + (1 << 20)) >> 21;
4746 s14 += carry13;
4747 s13 -= carry13 * (1 << 21);
4748 carry15 = (s15 + (1 << 20)) >> 21;
4749 s16 += carry15;
4750 s15 -= carry15 * (1 << 21);
4751
4752 s5 += s17 * 666643;
4753 s6 += s17 * 470296;
4754 s7 += s17 * 654183;
4755 s8 -= s17 * 997805;
4756 s9 += s17 * 136657;
4757 s10 -= s17 * 683901;
4758 s17 = 0;
4759
4760 s4 += s16 * 666643;
4761 s5 += s16 * 470296;
4762 s6 += s16 * 654183;
4763 s7 -= s16 * 997805;
4764 s8 += s16 * 136657;
4765 s9 -= s16 * 683901;
4766 s16 = 0;
4767
4768 s3 += s15 * 666643;
4769 s4 += s15 * 470296;
4770 s5 += s15 * 654183;
4771 s6 -= s15 * 997805;
4772 s7 += s15 * 136657;
4773 s8 -= s15 * 683901;
4774 s15 = 0;
4775
4776 s2 += s14 * 666643;
4777 s3 += s14 * 470296;
4778 s4 += s14 * 654183;
4779 s5 -= s14 * 997805;
4780 s6 += s14 * 136657;
4781 s7 -= s14 * 683901;
4782 s14 = 0;
4783
4784 s1 += s13 * 666643;
4785 s2 += s13 * 470296;
4786 s3 += s13 * 654183;
4787 s4 -= s13 * 997805;
4788 s5 += s13 * 136657;
4789 s6 -= s13 * 683901;
4790 s13 = 0;
4791
4792 s0 += s12 * 666643;
4793 s1 += s12 * 470296;
4794 s2 += s12 * 654183;
4795 s3 -= s12 * 997805;
4796 s4 += s12 * 136657;
4797 s5 -= s12 * 683901;
4798 s12 = 0;
4799
4800 carry0 = (s0 + (1 << 20)) >> 21;
4801 s1 += carry0;
4802 s0 -= carry0 * (1 << 21);
4803 carry2 = (s2 + (1 << 20)) >> 21;
4804 s3 += carry2;
4805 s2 -= carry2 * (1 << 21);
4806 carry4 = (s4 + (1 << 20)) >> 21;
4807 s5 += carry4;
4808 s4 -= carry4 * (1 << 21);
4809 carry6 = (s6 + (1 << 20)) >> 21;
4810 s7 += carry6;
4811 s6 -= carry6 * (1 << 21);
4812 carry8 = (s8 + (1 << 20)) >> 21;
4813 s9 += carry8;
4814 s8 -= carry8 * (1 << 21);
4815 carry10 = (s10 + (1 << 20)) >> 21;
4816 s11 += carry10;
4817 s10 -= carry10 * (1 << 21);
4818
4819 carry1 = (s1 + (1 << 20)) >> 21;
4820 s2 += carry1;
4821 s1 -= carry1 * (1 << 21);
4822 carry3 = (s3 + (1 << 20)) >> 21;
4823 s4 += carry3;
4824 s3 -= carry3 * (1 << 21);
4825 carry5 = (s5 + (1 << 20)) >> 21;
4826 s6 += carry5;
4827 s5 -= carry5 * (1 << 21);
4828 carry7 = (s7 + (1 << 20)) >> 21;
4829 s8 += carry7;
4830 s7 -= carry7 * (1 << 21);
4831 carry9 = (s9 + (1 << 20)) >> 21;
4832 s10 += carry9;
4833 s9 -= carry9 * (1 << 21);
4834 carry11 = (s11 + (1 << 20)) >> 21;
4835 s12 += carry11;
4836 s11 -= carry11 * (1 << 21);
4837
4838 s0 += s12 * 666643;
4839 s1 += s12 * 470296;
4840 s2 += s12 * 654183;
4841 s3 -= s12 * 997805;
4842 s4 += s12 * 136657;
4843 s5 -= s12 * 683901;
4844 s12 = 0;
4845
4846 carry0 = s0 >> 21;
4847 s1 += carry0;
4848 s0 -= carry0 * (1 << 21);
4849 carry1 = s1 >> 21;
4850 s2 += carry1;
4851 s1 -= carry1 * (1 << 21);
4852 carry2 = s2 >> 21;
4853 s3 += carry2;
4854 s2 -= carry2 * (1 << 21);
4855 carry3 = s3 >> 21;
4856 s4 += carry3;
4857 s3 -= carry3 * (1 << 21);
4858 carry4 = s4 >> 21;
4859 s5 += carry4;
4860 s4 -= carry4 * (1 << 21);
4861 carry5 = s5 >> 21;
4862 s6 += carry5;
4863 s5 -= carry5 * (1 << 21);
4864 carry6 = s6 >> 21;
4865 s7 += carry6;
4866 s6 -= carry6 * (1 << 21);
4867 carry7 = s7 >> 21;
4868 s8 += carry7;
4869 s7 -= carry7 * (1 << 21);
4870 carry8 = s8 >> 21;
4871 s9 += carry8;
4872 s8 -= carry8 * (1 << 21);
4873 carry9 = s9 >> 21;
4874 s10 += carry9;
4875 s9 -= carry9 * (1 << 21);
4876 carry10 = s10 >> 21;
4877 s11 += carry10;
4878 s10 -= carry10 * (1 << 21);
4879 carry11 = s11 >> 21;
4880 s12 += carry11;
4881 s11 -= carry11 * (1 << 21);
4882
4883 s0 += s12 * 666643;
4884 s1 += s12 * 470296;
4885 s2 += s12 * 654183;
4886 s3 -= s12 * 997805;
4887 s4 += s12 * 136657;
4888 s5 -= s12 * 683901;
4889 s12 = 0;
4890
4891 carry0 = s0 >> 21;
4892 s1 += carry0;
4893 s0 -= carry0 * (1 << 21);
4894 carry1 = s1 >> 21;
4895 s2 += carry1;
4896 s1 -= carry1 * (1 << 21);
4897 carry2 = s2 >> 21;
4898 s3 += carry2;
4899 s2 -= carry2 * (1 << 21);
4900 carry3 = s3 >> 21;
4901 s4 += carry3;
4902 s3 -= carry3 * (1 << 21);
4903 carry4 = s4 >> 21;
4904 s5 += carry4;
4905 s4 -= carry4 * (1 << 21);
4906 carry5 = s5 >> 21;
4907 s6 += carry5;
4908 s5 -= carry5 * (1 << 21);
4909 carry6 = s6 >> 21;
4910 s7 += carry6;
4911 s6 -= carry6 * (1 << 21);
4912 carry7 = s7 >> 21;
4913 s8 += carry7;
4914 s7 -= carry7 * (1 << 21);
4915 carry8 = s8 >> 21;
4916 s9 += carry8;
4917 s8 -= carry8 * (1 << 21);
4918 carry9 = s9 >> 21;
4919 s10 += carry9;
4920 s9 -= carry9 * (1 << 21);
4921 carry10 = s10 >> 21;
4922 s11 += carry10;
4923 s10 -= carry10 * (1 << 21);
4924
4925 s[ 0] = (uint8_t) (s0 >> 0);
4926 s[ 1] = (uint8_t) (s0 >> 8);
4927 s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5));
4928 s[ 3] = (uint8_t) (s1 >> 3);
4929 s[ 4] = (uint8_t) (s1 >> 11);
4930 s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2));
4931 s[ 6] = (uint8_t) (s2 >> 6);
4932 s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7));
4933 s[ 8] = (uint8_t) (s3 >> 1);
4934 s[ 9] = (uint8_t) (s3 >> 9);
4935 s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
4936 s[11] = (uint8_t) (s4 >> 4);
4937 s[12] = (uint8_t) (s4 >> 12);
4938 s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
4939 s[14] = (uint8_t) (s5 >> 7);
4940 s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
4941 s[16] = (uint8_t) (s6 >> 2);
4942 s[17] = (uint8_t) (s6 >> 10);
4943 s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
4944 s[19] = (uint8_t) (s7 >> 5);
4945 s[20] = (uint8_t) (s7 >> 13);
4946 s[21] = (uint8_t) (s8 >> 0);
4947 s[22] = (uint8_t) (s8 >> 8);
4948 s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
4949 s[24] = (uint8_t) (s9 >> 3);
4950 s[25] = (uint8_t) (s9 >> 11);
4951 s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
4952 s[27] = (uint8_t) (s10 >> 6);
4953 s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
4954 s[29] = (uint8_t) (s11 >> 1);
4955 s[30] = (uint8_t) (s11 >> 9);
4956 s[31] = (uint8_t) (s11 >> 17);
4957}
4958
4959/*
4960 * Input:
4961 * a[0]+256*a[1]+...+256^31*a[31] = a
4962 * b[0]+256*b[1]+...+256^31*b[31] = b
4963 * c[0]+256*c[1]+...+256^31*c[31] = c
4964 *
4965 * Output:
4966 * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
4967 * where l = 2^252 + 27742317777372353535851937790883648493.
4968 */
4969static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b,
4970 const uint8_t *c)
4971{
4972 int64_t a0 = kBottom21Bits & load_3(a);
4973 int64_t a1 = kBottom21Bits & (load_4(a + 2) >> 5);
4974 int64_t a2 = kBottom21Bits & (load_3(a + 5) >> 2);
4975 int64_t a3 = kBottom21Bits & (load_4(a + 7) >> 7);
4976 int64_t a4 = kBottom21Bits & (load_4(a + 10) >> 4);
4977 int64_t a5 = kBottom21Bits & (load_3(a + 13) >> 1);
4978 int64_t a6 = kBottom21Bits & (load_4(a + 15) >> 6);
4979 int64_t a7 = kBottom21Bits & (load_3(a + 18) >> 3);
4980 int64_t a8 = kBottom21Bits & load_3(a + 21);
4981 int64_t a9 = kBottom21Bits & (load_4(a + 23) >> 5);
4982 int64_t a10 = kBottom21Bits & (load_3(a + 26) >> 2);
4983 int64_t a11 = (load_4(a + 28) >> 7);
4984 int64_t b0 = kBottom21Bits & load_3(b);
4985 int64_t b1 = kBottom21Bits & (load_4(b + 2) >> 5);
4986 int64_t b2 = kBottom21Bits & (load_3(b + 5) >> 2);
4987 int64_t b3 = kBottom21Bits & (load_4(b + 7) >> 7);
4988 int64_t b4 = kBottom21Bits & (load_4(b + 10) >> 4);
4989 int64_t b5 = kBottom21Bits & (load_3(b + 13) >> 1);
4990 int64_t b6 = kBottom21Bits & (load_4(b + 15) >> 6);
4991 int64_t b7 = kBottom21Bits & (load_3(b + 18) >> 3);
4992 int64_t b8 = kBottom21Bits & load_3(b + 21);
4993 int64_t b9 = kBottom21Bits & (load_4(b + 23) >> 5);
4994 int64_t b10 = kBottom21Bits & (load_3(b + 26) >> 2);
4995 int64_t b11 = (load_4(b + 28) >> 7);
4996 int64_t c0 = kBottom21Bits & load_3(c);
4997 int64_t c1 = kBottom21Bits & (load_4(c + 2) >> 5);
4998 int64_t c2 = kBottom21Bits & (load_3(c + 5) >> 2);
4999 int64_t c3 = kBottom21Bits & (load_4(c + 7) >> 7);
5000 int64_t c4 = kBottom21Bits & (load_4(c + 10) >> 4);
5001 int64_t c5 = kBottom21Bits & (load_3(c + 13) >> 1);
5002 int64_t c6 = kBottom21Bits & (load_4(c + 15) >> 6);
5003 int64_t c7 = kBottom21Bits & (load_3(c + 18) >> 3);
5004 int64_t c8 = kBottom21Bits & load_3(c + 21);
5005 int64_t c9 = kBottom21Bits & (load_4(c + 23) >> 5);
5006 int64_t c10 = kBottom21Bits & (load_3(c + 26) >> 2);
5007 int64_t c11 = (load_4(c + 28) >> 7);
5008 int64_t s0;
5009 int64_t s1;
5010 int64_t s2;
5011 int64_t s3;
5012 int64_t s4;
5013 int64_t s5;
5014 int64_t s6;
5015 int64_t s7;
5016 int64_t s8;
5017 int64_t s9;
5018 int64_t s10;
5019 int64_t s11;
5020 int64_t s12;
5021 int64_t s13;
5022 int64_t s14;
5023 int64_t s15;
5024 int64_t s16;
5025 int64_t s17;
5026 int64_t s18;
5027 int64_t s19;
5028 int64_t s20;
5029 int64_t s21;
5030 int64_t s22;
5031 int64_t s23;
5032 int64_t carry0;
5033 int64_t carry1;
5034 int64_t carry2;
5035 int64_t carry3;
5036 int64_t carry4;
5037 int64_t carry5;
5038 int64_t carry6;
5039 int64_t carry7;
5040 int64_t carry8;
5041 int64_t carry9;
5042 int64_t carry10;
5043 int64_t carry11;
5044 int64_t carry12;
5045 int64_t carry13;
5046 int64_t carry14;
5047 int64_t carry15;
5048 int64_t carry16;
5049 int64_t carry17;
5050 int64_t carry18;
5051 int64_t carry19;
5052 int64_t carry20;
5053 int64_t carry21;
5054 int64_t carry22;
5055
5056 s0 = c0 + a0 * b0;
5057 s1 = c1 + a0 * b1 + a1 * b0;
5058 s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0;
5059 s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0;
5060 s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0;
5061 s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0;
5062 s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0;
5063 s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + a6 * b1 + a7 * b0;
5064 s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + a6 * b2 + a7 * b1 + a8 * b0;
5065 s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0;
5066 s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0;
5067 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;
5068 s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1;
5069 s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2;
5070 s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + a10 * b4 + a11 * b3;
5071 s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + a11 * b4;
5072 s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5;
5073 s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6;
5074 s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7;
5075 s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8;
5076 s20 = a9 * b11 + a10 * b10 + a11 * b9;
5077 s21 = a10 * b11 + a11 * b10;
5078 s22 = a11 * b11;
5079 s23 = 0;
5080
5081 carry0 = (s0 + (1 << 20)) >> 21;
5082 s1 += carry0;
5083 s0 -= carry0 * (1 << 21);
5084 carry2 = (s2 + (1 << 20)) >> 21;
5085 s3 += carry2;
5086 s2 -= carry2 * (1 << 21);
5087 carry4 = (s4 + (1 << 20)) >> 21;
5088 s5 += carry4;
5089 s4 -= carry4 * (1 << 21);
5090 carry6 = (s6 + (1 << 20)) >> 21;
5091 s7 += carry6;
5092 s6 -= carry6 * (1 << 21);
5093 carry8 = (s8 + (1 << 20)) >> 21;
5094 s9 += carry8;
5095 s8 -= carry8 * (1 << 21);
5096 carry10 = (s10 + (1 << 20)) >> 21;
5097 s11 += carry10;
5098 s10 -= carry10 * (1 << 21);
5099 carry12 = (s12 + (1 << 20)) >> 21;
5100 s13 += carry12;
5101 s12 -= carry12 * (1 << 21);
5102 carry14 = (s14 + (1 << 20)) >> 21;
5103 s15 += carry14;
5104 s14 -= carry14 * (1 << 21);
5105 carry16 = (s16 + (1 << 20)) >> 21;
5106 s17 += carry16;
5107 s16 -= carry16 * (1 << 21);
5108 carry18 = (s18 + (1 << 20)) >> 21;
5109 s19 += carry18;
5110 s18 -= carry18 * (1 << 21);
5111 carry20 = (s20 + (1 << 20)) >> 21;
5112 s21 += carry20;
5113 s20 -= carry20 * (1 << 21);
5114 carry22 = (s22 + (1 << 20)) >> 21;
5115 s23 += carry22;
5116 s22 -= carry22 * (1 << 21);
5117
5118 carry1 = (s1 + (1 << 20)) >> 21;
5119 s2 += carry1;
5120 s1 -= carry1 * (1 << 21);
5121 carry3 = (s3 + (1 << 20)) >> 21;
5122 s4 += carry3;
5123 s3 -= carry3 * (1 << 21);
5124 carry5 = (s5 + (1 << 20)) >> 21;
5125 s6 += carry5;
5126 s5 -= carry5 * (1 << 21);
5127 carry7 = (s7 + (1 << 20)) >> 21;
5128 s8 += carry7;
5129 s7 -= carry7 * (1 << 21);
5130 carry9 = (s9 + (1 << 20)) >> 21;
5131 s10 += carry9;
5132 s9 -= carry9 * (1 << 21);
5133 carry11 = (s11 + (1 << 20)) >> 21;
5134 s12 += carry11;
5135 s11 -= carry11 * (1 << 21);
5136 carry13 = (s13 + (1 << 20)) >> 21;
5137 s14 += carry13;
5138 s13 -= carry13 * (1 << 21);
5139 carry15 = (s15 + (1 << 20)) >> 21;
5140 s16 += carry15;
5141 s15 -= carry15 * (1 << 21);
5142 carry17 = (s17 + (1 << 20)) >> 21;
5143 s18 += carry17;
5144 s17 -= carry17 * (1 << 21);
5145 carry19 = (s19 + (1 << 20)) >> 21;
5146 s20 += carry19;
5147 s19 -= carry19 * (1 << 21);
5148 carry21 = (s21 + (1 << 20)) >> 21;
5149 s22 += carry21;
5150 s21 -= carry21 * (1 << 21);
5151
5152 s11 += s23 * 666643;
5153 s12 += s23 * 470296;
5154 s13 += s23 * 654183;
5155 s14 -= s23 * 997805;
5156 s15 += s23 * 136657;
5157 s16 -= s23 * 683901;
5158 s23 = 0;
5159
5160 s10 += s22 * 666643;
5161 s11 += s22 * 470296;
5162 s12 += s22 * 654183;
5163 s13 -= s22 * 997805;
5164 s14 += s22 * 136657;
5165 s15 -= s22 * 683901;
5166 s22 = 0;
5167
5168 s9 += s21 * 666643;
5169 s10 += s21 * 470296;
5170 s11 += s21 * 654183;
5171 s12 -= s21 * 997805;
5172 s13 += s21 * 136657;
5173 s14 -= s21 * 683901;
5174 s21 = 0;
5175
5176 s8 += s20 * 666643;
5177 s9 += s20 * 470296;
5178 s10 += s20 * 654183;
5179 s11 -= s20 * 997805;
5180 s12 += s20 * 136657;
5181 s13 -= s20 * 683901;
5182 s20 = 0;
5183
5184 s7 += s19 * 666643;
5185 s8 += s19 * 470296;
5186 s9 += s19 * 654183;
5187 s10 -= s19 * 997805;
5188 s11 += s19 * 136657;
5189 s12 -= s19 * 683901;
5190 s19 = 0;
5191
5192 s6 += s18 * 666643;
5193 s7 += s18 * 470296;
5194 s8 += s18 * 654183;
5195 s9 -= s18 * 997805;
5196 s10 += s18 * 136657;
5197 s11 -= s18 * 683901;
5198 s18 = 0;
5199
5200 carry6 = (s6 + (1 << 20)) >> 21;
5201 s7 += carry6;
5202 s6 -= carry6 * (1 << 21);
5203 carry8 = (s8 + (1 << 20)) >> 21;
5204 s9 += carry8;
5205 s8 -= carry8 * (1 << 21);
5206 carry10 = (s10 + (1 << 20)) >> 21;
5207 s11 += carry10;
5208 s10 -= carry10 * (1 << 21);
5209 carry12 = (s12 + (1 << 20)) >> 21;
5210 s13 += carry12;
5211 s12 -= carry12 * (1 << 21);
5212 carry14 = (s14 + (1 << 20)) >> 21;
5213 s15 += carry14;
5214 s14 -= carry14 * (1 << 21);
5215 carry16 = (s16 + (1 << 20)) >> 21;
5216 s17 += carry16;
5217 s16 -= carry16 * (1 << 21);
5218
5219 carry7 = (s7 + (1 << 20)) >> 21;
5220 s8 += carry7;
5221 s7 -= carry7 * (1 << 21);
5222 carry9 = (s9 + (1 << 20)) >> 21;
5223 s10 += carry9;
5224 s9 -= carry9 * (1 << 21);
5225 carry11 = (s11 + (1 << 20)) >> 21;
5226 s12 += carry11;
5227 s11 -= carry11 * (1 << 21);
5228 carry13 = (s13 + (1 << 20)) >> 21;
5229 s14 += carry13;
5230 s13 -= carry13 * (1 << 21);
5231 carry15 = (s15 + (1 << 20)) >> 21;
5232 s16 += carry15;
5233 s15 -= carry15 * (1 << 21);
5234
5235 s5 += s17 * 666643;
5236 s6 += s17 * 470296;
5237 s7 += s17 * 654183;
5238 s8 -= s17 * 997805;
5239 s9 += s17 * 136657;
5240 s10 -= s17 * 683901;
5241 s17 = 0;
5242
5243 s4 += s16 * 666643;
5244 s5 += s16 * 470296;
5245 s6 += s16 * 654183;
5246 s7 -= s16 * 997805;
5247 s8 += s16 * 136657;
5248 s9 -= s16 * 683901;
5249 s16 = 0;
5250
5251 s3 += s15 * 666643;
5252 s4 += s15 * 470296;
5253 s5 += s15 * 654183;
5254 s6 -= s15 * 997805;
5255 s7 += s15 * 136657;
5256 s8 -= s15 * 683901;
5257 s15 = 0;
5258
5259 s2 += s14 * 666643;
5260 s3 += s14 * 470296;
5261 s4 += s14 * 654183;
5262 s5 -= s14 * 997805;
5263 s6 += s14 * 136657;
5264 s7 -= s14 * 683901;
5265 s14 = 0;
5266
5267 s1 += s13 * 666643;
5268 s2 += s13 * 470296;
5269 s3 += s13 * 654183;
5270 s4 -= s13 * 997805;
5271 s5 += s13 * 136657;
5272 s6 -= s13 * 683901;
5273 s13 = 0;
5274
5275 s0 += s12 * 666643;
5276 s1 += s12 * 470296;
5277 s2 += s12 * 654183;
5278 s3 -= s12 * 997805;
5279 s4 += s12 * 136657;
5280 s5 -= s12 * 683901;
5281 s12 = 0;
5282
5283 carry0 = (s0 + (1 << 20)) >> 21;
5284 s1 += carry0;
5285 s0 -= carry0 * (1 << 21);
5286 carry2 = (s2 + (1 << 20)) >> 21;
5287 s3 += carry2;
5288 s2 -= carry2 * (1 << 21);
5289 carry4 = (s4 + (1 << 20)) >> 21;
5290 s5 += carry4;
5291 s4 -= carry4 * (1 << 21);
5292 carry6 = (s6 + (1 << 20)) >> 21;
5293 s7 += carry6;
5294 s6 -= carry6 * (1 << 21);
5295 carry8 = (s8 + (1 << 20)) >> 21;
5296 s9 += carry8;
5297 s8 -= carry8 * (1 << 21);
5298 carry10 = (s10 + (1 << 20)) >> 21;
5299 s11 += carry10;
5300 s10 -= carry10 * (1 << 21);
5301
5302 carry1 = (s1 + (1 << 20)) >> 21;
5303 s2 += carry1;
5304 s1 -= carry1 * (1 << 21);
5305 carry3 = (s3 + (1 << 20)) >> 21;
5306 s4 += carry3;
5307 s3 -= carry3 * (1 << 21);
5308 carry5 = (s5 + (1 << 20)) >> 21;
5309 s6 += carry5;
5310 s5 -= carry5 * (1 << 21);
5311 carry7 = (s7 + (1 << 20)) >> 21;
5312 s8 += carry7;
5313 s7 -= carry7 * (1 << 21);
5314 carry9 = (s9 + (1 << 20)) >> 21;
5315 s10 += carry9;
5316 s9 -= carry9 * (1 << 21);
5317 carry11 = (s11 + (1 << 20)) >> 21;
5318 s12 += carry11;
5319 s11 -= carry11 * (1 << 21);
5320
5321 s0 += s12 * 666643;
5322 s1 += s12 * 470296;
5323 s2 += s12 * 654183;
5324 s3 -= s12 * 997805;
5325 s4 += s12 * 136657;
5326 s5 -= s12 * 683901;
5327 s12 = 0;
5328
5329 carry0 = s0 >> 21;
5330 s1 += carry0;
5331 s0 -= carry0 * (1 << 21);
5332 carry1 = s1 >> 21;
5333 s2 += carry1;
5334 s1 -= carry1 * (1 << 21);
5335 carry2 = s2 >> 21;
5336 s3 += carry2;
5337 s2 -= carry2 * (1 << 21);
5338 carry3 = s3 >> 21;
5339 s4 += carry3;
5340 s3 -= carry3 * (1 << 21);
5341 carry4 = s4 >> 21;
5342 s5 += carry4;
5343 s4 -= carry4 * (1 << 21);
5344 carry5 = s5 >> 21;
5345 s6 += carry5;
5346 s5 -= carry5 * (1 << 21);
5347 carry6 = s6 >> 21;
5348 s7 += carry6;
5349 s6 -= carry6 * (1 << 21);
5350 carry7 = s7 >> 21;
5351 s8 += carry7;
5352 s7 -= carry7 * (1 << 21);
5353 carry8 = s8 >> 21;
5354 s9 += carry8;
5355 s8 -= carry8 * (1 << 21);
5356 carry9 = s9 >> 21;
5357 s10 += carry9;
5358 s9 -= carry9 * (1 << 21);
5359 carry10 = s10 >> 21;
5360 s11 += carry10;
5361 s10 -= carry10 * (1 << 21);
5362 carry11 = s11 >> 21;
5363 s12 += carry11;
5364 s11 -= carry11 * (1 << 21);
5365
5366 s0 += s12 * 666643;
5367 s1 += s12 * 470296;
5368 s2 += s12 * 654183;
5369 s3 -= s12 * 997805;
5370 s4 += s12 * 136657;
5371 s5 -= s12 * 683901;
5372 s12 = 0;
Value stored to 's12' is never read
5373
5374 carry0 = s0 >> 21;
5375 s1 += carry0;
5376 s0 -= carry0 * (1 << 21);
5377 carry1 = s1 >> 21;
5378 s2 += carry1;
5379 s1 -= carry1 * (1 << 21);
5380 carry2 = s2 >> 21;
5381 s3 += carry2;
5382 s2 -= carry2 * (1 << 21);
5383 carry3 = s3 >> 21;
5384 s4 += carry3;
5385 s3 -= carry3 * (1 << 21);
5386 carry4 = s4 >> 21;
5387 s5 += carry4;
5388 s4 -= carry4 * (1 << 21);
5389 carry5 = s5 >> 21;
5390 s6 += carry5;
5391 s5 -= carry5 * (1 << 21);
5392 carry6 = s6 >> 21;
5393 s7 += carry6;
5394 s6 -= carry6 * (1 << 21);
5395 carry7 = s7 >> 21;
5396 s8 += carry7;
5397 s7 -= carry7 * (1 << 21);
5398 carry8 = s8 >> 21;
5399 s9 += carry8;
5400 s8 -= carry8 * (1 << 21);
5401 carry9 = s9 >> 21;
5402 s10 += carry9;
5403 s9 -= carry9 * (1 << 21);
5404 carry10 = s10 >> 21;
5405 s11 += carry10;
5406 s10 -= carry10 * (1 << 21);
5407
5408 s[ 0] = (uint8_t) (s0 >> 0);
5409 s[ 1] = (uint8_t) (s0 >> 8);
5410 s[ 2] = (uint8_t)((s0 >> 16) | (s1 << 5));
5411 s[ 3] = (uint8_t) (s1 >> 3);
5412 s[ 4] = (uint8_t) (s1 >> 11);
5413 s[ 5] = (uint8_t)((s1 >> 19) | (s2 << 2));
5414 s[ 6] = (uint8_t) (s2 >> 6);
5415 s[ 7] = (uint8_t)((s2 >> 14) | (s3 << 7));
5416 s[ 8] = (uint8_t) (s3 >> 1);
5417 s[ 9] = (uint8_t) (s3 >> 9);
5418 s[10] = (uint8_t)((s3 >> 17) | (s4 << 4));
5419 s[11] = (uint8_t) (s4 >> 4);
5420 s[12] = (uint8_t) (s4 >> 12);
5421 s[13] = (uint8_t)((s4 >> 20) | (s5 << 1));
5422 s[14] = (uint8_t) (s5 >> 7);
5423 s[15] = (uint8_t)((s5 >> 15) | (s6 << 6));
5424 s[16] = (uint8_t) (s6 >> 2);
5425 s[17] = (uint8_t) (s6 >> 10);
5426 s[18] = (uint8_t)((s6 >> 18) | (s7 << 3));
5427 s[19] = (uint8_t) (s7 >> 5);
5428 s[20] = (uint8_t) (s7 >> 13);
5429 s[21] = (uint8_t) (s8 >> 0);
5430 s[22] = (uint8_t) (s8 >> 8);
5431 s[23] = (uint8_t)((s8 >> 16) | (s9 << 5));
5432 s[24] = (uint8_t) (s9 >> 3);
5433 s[25] = (uint8_t) (s9 >> 11);
5434 s[26] = (uint8_t)((s9 >> 19) | (s10 << 2));
5435 s[27] = (uint8_t) (s10 >> 6);
5436 s[28] = (uint8_t)((s10 >> 14) | (s11 << 7));
5437 s[29] = (uint8_t) (s11 >> 1);
5438 s[30] = (uint8_t) (s11 >> 9);
5439 s[31] = (uint8_t) (s11 >> 17);
5440}
5441
5442int
5443ossl_ed25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len,
5444 const uint8_t public_key[32], const uint8_t private_key[32],
5445 OSSL_LIB_CTX *libctx, const char *propq)
5446{
5447 uint8_t az[SHA512_DIGEST_LENGTH64];
5448 uint8_t nonce[SHA512_DIGEST_LENGTH64];
5449 ge_p3 R;
5450 uint8_t hram[SHA512_DIGEST_LENGTH64];
5451 EVP_MD *sha512 = EVP_MD_fetch(libctx, SN_sha512"SHA512", propq);
5452 EVP_MD_CTX *hash_ctx = EVP_MD_CTX_new();
5453 unsigned int sz;
5454 int res = 0;
5455
5456 if (sha512 == NULL((void*)0) || hash_ctx == NULL((void*)0))
5457 goto err;
5458
5459 if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL((void*)0))
5460 || !EVP_DigestUpdate(hash_ctx, private_key, 32)
5461 || !EVP_DigestFinal_ex(hash_ctx, az, &sz))
5462 goto err;
5463
5464 az[0] &= 248;
5465 az[31] &= 63;
5466 az[31] |= 64;
5467
5468 if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL((void*)0))
5469 || !EVP_DigestUpdate(hash_ctx, az + 32, 32)
5470 || !EVP_DigestUpdate(hash_ctx, message, message_len)
5471 || !EVP_DigestFinal_ex(hash_ctx, nonce, &sz))
5472 goto err;
5473
5474 x25519_sc_reduce(nonce);
5475 ge_scalarmult_base(&R, nonce);
5476 ge_p3_tobytes(out_sig, &R);
5477
5478 if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL((void*)0))
5479 || !EVP_DigestUpdate(hash_ctx, out_sig, 32)
5480 || !EVP_DigestUpdate(hash_ctx, public_key, 32)
5481 || !EVP_DigestUpdate(hash_ctx, message, message_len)
5482 || !EVP_DigestFinal_ex(hash_ctx, hram, &sz))
5483 goto err;
5484
5485 x25519_sc_reduce(hram);
5486 sc_muladd(out_sig + 32, hram, az, nonce);
5487
5488 res = 1;
5489err:
5490 OPENSSL_cleanse(nonce, sizeof(nonce));
5491 OPENSSL_cleanse(az, sizeof(az));
5492 EVP_MD_free(sha512);
5493 EVP_MD_CTX_free(hash_ctx);
5494 return res;
5495}
5496
5497static const char allzeroes[15];
5498
5499int
5500ossl_ed25519_verify(const uint8_t *message, size_t message_len,
5501 const uint8_t signature[64], const uint8_t public_key[32],
5502 OSSL_LIB_CTX *libctx, const char *propq)
5503{
5504 int i;
5505 ge_p3 A;
5506 const uint8_t *r, *s;
5507 EVP_MD *sha512;
5508 EVP_MD_CTX *hash_ctx = NULL((void*)0);
5509 unsigned int sz;
5510 int res = 0;
5511 ge_p2 R;
5512 uint8_t rcheck[32];
5513 uint8_t h[SHA512_DIGEST_LENGTH64];
5514 /* 27742317777372353535851937790883648493 in little endian format */
5515 const uint8_t l_low[16] = {
5516 0xED, 0xD3, 0xF5, 0x5C, 0x1A, 0x63, 0x12, 0x58, 0xD6, 0x9C, 0xF7, 0xA2,
5517 0xDE, 0xF9, 0xDE, 0x14
5518 };
5519
5520 r = signature;
5521 s = signature + 32;
5522
5523 /*
5524 * Check 0 <= s < L where L = 2^252 + 27742317777372353535851937790883648493
5525 *
5526 * If not the signature is publicly invalid. Since it's public we can do the
5527 * check in variable time.
5528 *
5529 * First check the most significant byte
5530 */
5531 if (s[31] > 0x10)
5532 return 0;
5533 if (s[31] == 0x10) {
5534 /*
5535 * Most significant byte indicates a value close to 2^252 so check the
5536 * rest
5537 */
5538 if (memcmp(s + 16, allzeroes, sizeof(allzeroes)) != 0)
5539 return 0;
5540 for (i = 15; i >= 0; i--) {
5541 if (s[i] < l_low[i])
5542 break;
5543 if (s[i] > l_low[i])
5544 return 0;
5545 }
5546 if (i < 0)
5547 return 0;
5548 }
5549
5550 if (ge_frombytes_vartime(&A, public_key) != 0) {
5551 return 0;
5552 }
5553
5554 fe_neg(A.X, A.X);
5555 fe_neg(A.T, A.T);
5556
5557 sha512 = EVP_MD_fetch(libctx, SN_sha512"SHA512", propq);
5558 if (sha512 == NULL((void*)0))
5559 return 0;
5560 hash_ctx = EVP_MD_CTX_new();
5561 if (hash_ctx == NULL((void*)0))
5562 goto err;
5563
5564 if (!EVP_DigestInit_ex(hash_ctx, sha512, NULL((void*)0))
5565 || !EVP_DigestUpdate(hash_ctx, r, 32)
5566 || !EVP_DigestUpdate(hash_ctx, public_key, 32)
5567 || !EVP_DigestUpdate(hash_ctx, message, message_len)
5568 || !EVP_DigestFinal_ex(hash_ctx, h, &sz))
5569 goto err;
5570
5571 x25519_sc_reduce(h);
5572
5573 ge_double_scalarmult_vartime(&R, h, &A, s);
5574
5575 ge_tobytes(rcheck, &R);
5576
5577 res = CRYPTO_memcmp(rcheck, r, sizeof(rcheck)) == 0;
5578err:
5579 EVP_MD_free(sha512);
5580 EVP_MD_CTX_free(hash_ctx);
5581 return res;
5582}
5583
5584int
5585ossl_ed25519_public_from_private(OSSL_LIB_CTX *ctx, uint8_t out_public_key[32],
5586 const uint8_t private_key[32],
5587 const char *propq)
5588{
5589 uint8_t az[SHA512_DIGEST_LENGTH64];
5590 ge_p3 A;
5591 int r;
5592 EVP_MD *sha512 = NULL((void*)0);
5593
5594 sha512 = EVP_MD_fetch(ctx, SN_sha512"SHA512", propq);
5595 if (sha512 == NULL((void*)0))
5596 return 0;
5597 r = EVP_Digest(private_key, 32, az, NULL((void*)0), sha512, NULL((void*)0));
5598 EVP_MD_free(sha512);
5599 if (!r) {
5600 OPENSSL_cleanse(az, sizeof(az));
5601 return 0;
5602 }
5603
5604 az[0] &= 248;
5605 az[31] &= 63;
5606 az[31] |= 64;
5607
5608 ge_scalarmult_base(&A, az);
5609 ge_p3_tobytes(out_public_key, &A);
5610
5611 OPENSSL_cleanse(az, sizeof(az));
5612 return 1;
5613}
5614
5615int
5616ossl_x25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
5617 const uint8_t peer_public_value[32])
5618{
5619 static const uint8_t kZeros[32] = {0};
5620 x25519_scalar_mult(out_shared_key, private_key, peer_public_value);
5621 /* The all-zero output results when the input is a point of small order. */
5622 return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;
5623}
5624
5625void
5626ossl_x25519_public_from_private(uint8_t out_public_value[32],
5627 const uint8_t private_key[32])
5628{
5629 uint8_t e[32];
5630 ge_p3 A;
5631 fe zplusy, zminusy, zminusy_inv;
5632
5633 memcpy(e, private_key, 32);
5634 e[0] &= 248;
5635 e[31] &= 127;
5636 e[31] |= 64;
5637
5638 ge_scalarmult_base(&A, e);
5639
5640 /*
5641 * We only need the u-coordinate of the curve25519 point.
5642 * The map is u=(y+1)/(1-y). Since y=Y/Z, this gives
5643 * u=(Z+Y)/(Z-Y).
5644 */
5645 fe_add(zplusy, A.Z, A.Y);
5646 fe_sub(zminusy, A.Z, A.Y);
5647 fe_invert(zminusy_inv, zminusy);
5648 fe_mul(zplusy, zplusy, zminusy_inv);
5649 fe_tobytes(out_public_value, zplusy);
5650
5651 OPENSSL_cleanse(e, sizeof(e));
5652}