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curve25519.c

Absolute File Name:

/home/opencoverage/opencoverage/guest-scripts/openssl/src/crypto/ec/curve25519.c

Source code

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1 /* -

3 * -

4 * Licensed under the OpenSSL license (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 #include <string.h> -

11 #include "ec_lcl.h" -

12 #include <openssl/sha.h> -

13 -

14 #if defined(X25519_ASM) && (defined(__x86_64) || defined(__x86_64__) || \ -

15 defined(_M_AMD64) || defined(_M_X64)) -

16 -

17 # define BASE_2_64_IMPLEMENTED -

18 -

19 typedef uint64_t fe64[4]; -

20 -

21 int x25519_fe64_eligible(void); -

22 -

23 /* -

24 * Following subroutines perform corresponding operations modulo -

25 * 2^256-38, i.e. double the curve modulus. However, inputs and -

26 * outputs are permitted to be partially reduced, i.e. to remain -

27 * in [0..2^256) range. It's all tied up in final fe64_tobytes -

28 * that performs full reduction modulo 2^255-19. -

29 * -

30 * There are no reference C implementations for these. -

31 */ -

32 void x25519_fe64_mul(fe64 h, const fe64 f, const fe64 g); -

33 void x25519_fe64_sqr(fe64 h, const fe64 f); -

34 void x25519_fe64_mul121666(fe64 h, fe64 f); -

35 void x25519_fe64_add(fe64 h, const fe64 f, const fe64 g); -

36 void x25519_fe64_sub(fe64 h, const fe64 f, const fe64 g); -

37 void x25519_fe64_tobytes(uint8_t *s, const fe64 f); -

38 # define fe64_mul x25519_fe64_mul -

39 # define fe64_sqr x25519_fe64_sqr -

40 # define fe64_mul121666 x25519_fe64_mul121666 -

41 # define fe64_add x25519_fe64_add -

42 # define fe64_sub x25519_fe64_sub -

43 # define fe64_tobytes x25519_fe64_tobytes -

44 -

45 static uint64_t load_8(const uint8_t *in) -

46 { -

47 uint64_t result; -

48 -

49 result = in[0]; -

50 result |= ((uint64_t)in[1]) << 8; -

51 result |= ((uint64_t)in[2]) << 16; -

52 result |= ((uint64_t)in[3]) << 24; -

53 result |= ((uint64_t)in[4]) << 32; -

54 result |= ((uint64_t)in[5]) << 40; -

55 result |= ((uint64_t)in[6]) << 48; -

56 result |= ((uint64_t)in[7]) << 56; -

57 -

return result;

never executed: return result;

59 } -

60 -

61 static void fe64_frombytes(fe64 h, const uint8_t *s) -

62 { -

63 h[0] = load_8(s); -

64 h[1] = load_8(s + 8); -

65 h[2] = load_8(s + 16); -

66 h[3] = load_8(s + 24) & 0x7fffffffffffffff; -

}

never executed: end of block

68 -

69 static void fe64_0(fe64 h) -

70 { -

71 h[0] = 0; -

72 h[1] = 0; -

73 h[2] = 0; -

74 h[3] = 0; -

}

never executed: end of block

76 -

77 static void fe64_1(fe64 h) -

78 { -

79 h[0] = 1; -

80 h[1] = 0; -

81 h[2] = 0; -

82 h[3] = 0; -

}

never executed: end of block

84 -

85 static void fe64_copy(fe64 h, const fe64 f) -

86 { -

87 h[0] = f[0]; -

88 h[1] = f[1]; -

89 h[2] = f[2]; -

90 h[3] = f[3]; -

}

never executed: end of block

92 -

93 static void fe64_cswap(fe64 f, fe64 g, unsigned int b) -

94 { -

95 int i; -

96 uint64_t mask = 0 - (uint64_t)b; -

97 -

for (i = 0; i < 4; i++) {

i < 4	Description
TRUE	never evaluated
FALSE	never evaluated

99 uint64_t x = f[i] ^ g[i]; -

100 x &= mask; -

101 f[i] ^= x; -

102 g[i] ^= x; -

103

}

never executed: end of block

104

}

never executed: end of block

105 -

106 static void fe64_invert(fe64 out, const fe64 z) -

107 { -

108 fe64 t0; -

109 fe64 t1; -

110 fe64 t2; -

111 fe64 t3; -

112 int i; -

113 -

114 /* -

115 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as -

116 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. -

117 */ -

118 -

119 /* t0 = z ** 2 */ -

120 fe64_sqr(t0, z); -

121 -

122 /* t1 = t0 ** (2 ** 2) = z ** 8 */ -

123 fe64_sqr(t1, t0); -

124 fe64_sqr(t1, t1); -

125 -

126 /* t1 = z * t1 = z ** 9 */ -

127 fe64_mul(t1, z, t1); -

128 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ -

129 fe64_mul(t0, t0, t1); -

130 -

131 /* t2 = t0 ** 2 = z ** 22 */ -

132 fe64_sqr(t2, t0); -

133 -

134 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ -

135 fe64_mul(t1, t1, t2); -

136 -

137 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ -

138 fe64_sqr(t2, t1); -

139

for (i = 1; i < 5; ++i)

i < 5	Description
TRUE	never evaluated
FALSE	never evaluated

140

fe64_sqr(t2, t2);

never executed: x25519_fe64_sqr(t2, t2);

141 -

142 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ -

143 fe64_mul(t1, t2, t1); -

144 -

145 /* Continuing similarly... */ -

146 -

147 /* t2 = z ** (2 ** 20 - 1) */ -

148 fe64_sqr(t2, t1); -

149

for (i = 1; i < 10; ++i)

i < 10	Description
TRUE	never evaluated
FALSE	never evaluated

150

fe64_sqr(t2, t2);

never executed: x25519_fe64_sqr(t2, t2);

151 -

152 fe64_mul(t2, t2, t1); -

153 -

154 /* t2 = z ** (2 ** 40 - 1) */ -

155 fe64_sqr(t3, t2); -

156

for (i = 1; i < 20; ++i)

i < 20	Description
TRUE	never evaluated
FALSE	never evaluated

157

fe64_sqr(t3, t3);

never executed: x25519_fe64_sqr(t3, t3);

158 -

159 fe64_mul(t2, t3, t2); -

160 -

161 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ -

162

for (i = 0; i < 10; ++i)

i < 10	Description
TRUE	never evaluated
FALSE	never evaluated

163

fe64_sqr(t2, t2);

never executed: x25519_fe64_sqr(t2, t2);

164 -

165 /* t1 = z ** (2 ** 50 - 1) */ -

166 fe64_mul(t1, t2, t1); -

167 -

168 /* t2 = z ** (2 ** 100 - 1) */ -

169 fe64_sqr(t2, t1); -

170

for (i = 1; i < 50; ++i)

i < 50	Description
TRUE	never evaluated
FALSE	never evaluated

171

fe64_sqr(t2, t2);

never executed: x25519_fe64_sqr(t2, t2);

172 -

173 fe64_mul(t2, t2, t1); -

174 -

175 /* t2 = z ** (2 ** 200 - 1) */ -

176 fe64_sqr(t3, t2); -

177

for (i = 1; i < 100; ++i)

i < 100	Description
TRUE	never evaluated
FALSE	never evaluated

178

fe64_sqr(t3, t3);

never executed: x25519_fe64_sqr(t3, t3);

179 -

180 fe64_mul(t2, t3, t2); -

181 -

182 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ -

183

for (i = 0; i < 50; ++i)

i < 50	Description
TRUE	never evaluated
FALSE	never evaluated

184

fe64_sqr(t2, t2);

never executed: x25519_fe64_sqr(t2, t2);

185 -

186 /* t1 = z ** (2 ** 250 - 1) */ -

187 fe64_mul(t1, t2, t1); -

188 -

189 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ -

190

for (i = 0; i < 5; ++i)

i < 5	Description
TRUE	never evaluated
FALSE	never evaluated

191

fe64_sqr(t1, t1);

never executed: x25519_fe64_sqr(t1, t1);

192 -

193 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ -

194 fe64_mul(out, t1, t0); -

195

}

never executed: end of block

196 -

197 /* -

198 * Duplicate of original x25519_scalar_mult_generic, but using -

199 * fe64_* subroutines. -

200 */ -

201 static void x25519_scalar_mulx(uint8_t out[32], const uint8_t scalar[32], -

202 const uint8_t point[32]) -

203 { -

204 fe64 x1, x2, z2, x3, z3, tmp0, tmp1; -

205 uint8_t e[32]; -

206 unsigned swap = 0; -

207 int pos; -

208 -

209 memcpy(e, scalar, 32); -

210 e[0] &= 0xf8; -

211 e[31] &= 0x7f; -

212 e[31] |= 0x40; -

213 fe64_frombytes(x1, point); -

214 fe64_1(x2); -

215 fe64_0(z2); -

216 fe64_copy(x3, x1); -

217 fe64_1(z3); -

218 -

219

for (pos = 254; pos >= 0; --pos) {

pos >= 0	Description
TRUE	never evaluated
FALSE	never evaluated

220 unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); -

221 -

222 swap ^= b; -

223 fe64_cswap(x2, x3, swap); -

224 fe64_cswap(z2, z3, swap); -

225 swap = b; -

226 fe64_sub(tmp0, x3, z3); -

227 fe64_sub(tmp1, x2, z2); -

228 fe64_add(x2, x2, z2); -

229 fe64_add(z2, x3, z3); -

230 fe64_mul(z3, x2, tmp0); -

231 fe64_mul(z2, z2, tmp1); -

232 fe64_sqr(tmp0, tmp1); -

233 fe64_sqr(tmp1, x2); -

234 fe64_add(x3, z3, z2); -

235 fe64_sub(z2, z3, z2); -

236 fe64_mul(x2, tmp1, tmp0); -

237 fe64_sub(tmp1, tmp1, tmp0); -

238 fe64_sqr(z2, z2); -

239 fe64_mul121666(z3, tmp1); -

240 fe64_sqr(x3, x3); -

241 fe64_add(tmp0, tmp0, z3); -

242 fe64_mul(z3, x1, z2); -

243 fe64_mul(z2, tmp1, tmp0); -

244

}

never executed: end of block

245 -

246 fe64_invert(z2, z2); -

247 fe64_mul(x2, x2, z2); -

248 fe64_tobytes(out, x2); -

249 -

250 OPENSSL_cleanse(e, sizeof(e)); -

251

}

never executed: end of block

252 #endif -

253 -

254 #if defined(X25519_ASM) \ -

255 || ( (defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ == 16) \ -

256 && !defined(__sparc__) \ -

257 && !(defined(__ANDROID__) && !defined(__clang__)) ) -

258 /* -

259 * Base 2^51 implementation. It's virtually no different from reference -

260 * base 2^25.5 implementation in respect to lax boundary conditions for -

261 * intermediate values and even individual limbs. So that whatever you -

262 * know about the reference, applies even here... -

263 */ -

264 # define BASE_2_51_IMPLEMENTED -

265 -

266 typedef uint64_t fe51[5]; -

267 -

268 static const uint64_t MASK51 = 0x7ffffffffffff; -

269 -

270 static uint64_t load_7(const uint8_t *in) -

271 { -

272 uint64_t result; -

273 -

274 result = in[0]; -

275 result |= ((uint64_t)in[1]) << 8; -

276 result |= ((uint64_t)in[2]) << 16; -

277 result |= ((uint64_t)in[3]) << 24; -

278 result |= ((uint64_t)in[4]) << 32; -

279 result |= ((uint64_t)in[5]) << 40; -

280 result |= ((uint64_t)in[6]) << 48; -

281 -

282

return result;

executed 5832 times by 1 test: return result;

Executed by:

libcrypto.so.1.1

5832

283 } -

284 -

285 static uint64_t load_6(const uint8_t *in) -

286 { -

287 uint64_t result; -

288 -

289 result = in[0]; -

290 result |= ((uint64_t)in[1]) << 8; -

291 result |= ((uint64_t)in[2]) << 16; -

292 result |= ((uint64_t)in[3]) << 24; -

293 result |= ((uint64_t)in[4]) << 32; -

294 result |= ((uint64_t)in[5]) << 40; -

295 -

296

return result;

executed 8748 times by 1 test: return result;

Executed by:

libcrypto.so.1.1

8748

297 } -

298 -

299 static void fe51_frombytes(fe51 h, const uint8_t *s) -

300 { -

301 uint64_t h0 = load_7(s); /* 56 bits */ -

302 uint64_t h1 = load_6(s + 7) << 5; /* 53 bits */ -

303 uint64_t h2 = load_7(s + 13) << 2; /* 58 bits */ -

304 uint64_t h3 = load_6(s + 20) << 7; /* 55 bits */ -

305 uint64_t h4 = (load_6(s + 26) & 0x7fffffffffff) << 4; /* 51 bits */ -

306 -

307 h1 |= h0 >> 51; h0 &= MASK51; -

308 h2 |= h1 >> 51; h1 &= MASK51; -

309 h3 |= h2 >> 51; h2 &= MASK51; -

310 h4 |= h3 >> 51; h3 &= MASK51; -

311 -

312 h[0] = h0; -

313 h[1] = h1; -

314 h[2] = h2; -

315 h[3] = h3; -

316 h[4] = h4; -

317

}

executed 2916 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2916

318 -

319 static void fe51_tobytes(uint8_t *s, const fe51 h) -

320 { -

321 uint64_t h0 = h[0]; -

322 uint64_t h1 = h[1]; -

323 uint64_t h2 = h[2]; -

324 uint64_t h3 = h[3]; -

325 uint64_t h4 = h[4]; -

326 uint64_t q; -

327 -

328 /* compare to modulus */ -

329 q = (h0 + 19) >> 51; -

330 q = (h1 + q) >> 51; -

331 q = (h2 + q) >> 51; -

332 q = (h3 + q) >> 51; -

333 q = (h4 + q) >> 51; -

334 -

335 /* full reduce */ -

336 h0 += 19 * q; -

337 h1 += h0 >> 51; h0 &= MASK51; -

338 h2 += h1 >> 51; h1 &= MASK51; -

339 h3 += h2 >> 51; h2 &= MASK51; -

340 h4 += h3 >> 51; h3 &= MASK51; -

341 h4 &= MASK51; -

342 -

343 /* smash */ -

344 s[0] = (uint8_t)(h0 >> 0); -

345 s[1] = (uint8_t)(h0 >> 8); -

346 s[2] = (uint8_t)(h0 >> 16); -

347 s[3] = (uint8_t)(h0 >> 24); -

348 s[4] = (uint8_t)(h0 >> 32); -

349 s[5] = (uint8_t)(h0 >> 40); -

350 s[6] = (uint8_t)((h0 >> 48) | ((uint32_t)h1 << 3)); -

351 s[7] = (uint8_t)(h1 >> 5); -

352 s[8] = (uint8_t)(h1 >> 13); -

353 s[9] = (uint8_t)(h1 >> 21); -

354 s[10] = (uint8_t)(h1 >> 29); -

355 s[11] = (uint8_t)(h1 >> 37); -

356 s[12] = (uint8_t)((h1 >> 45) | ((uint32_t)h2 << 6)); -

357 s[13] = (uint8_t)(h2 >> 2); -

358 s[14] = (uint8_t)(h2 >> 10); -

359 s[15] = (uint8_t)(h2 >> 18); -

360 s[16] = (uint8_t)(h2 >> 26); -

361 s[17] = (uint8_t)(h2 >> 34); -

362 s[18] = (uint8_t)(h2 >> 42); -

363 s[19] = (uint8_t)((h2 >> 50) | ((uint32_t)h3 << 1)); -

364 s[20] = (uint8_t)(h3 >> 7); -

365 s[21] = (uint8_t)(h3 >> 15); -

366 s[22] = (uint8_t)(h3 >> 23); -

367 s[23] = (uint8_t)(h3 >> 31); -

368 s[24] = (uint8_t)(h3 >> 39); -

369 s[25] = (uint8_t)((h3 >> 47) | ((uint32_t)h4 << 4)); -

370 s[26] = (uint8_t)(h4 >> 4); -

371 s[27] = (uint8_t)(h4 >> 12); -

372 s[28] = (uint8_t)(h4 >> 20); -

373 s[29] = (uint8_t)(h4 >> 28); -

374 s[30] = (uint8_t)(h4 >> 36); -

375 s[31] = (uint8_t)(h4 >> 44); -

376

}

executed 2916 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2916

377 -

378 # if defined(X25519_ASM) -

379 void x25519_fe51_mul(fe51 h, const fe51 f, const fe51 g); -

380 void x25519_fe51_sqr(fe51 h, const fe51 f); -

381 void x25519_fe51_mul121666(fe51 h, fe51 f); -

382 # define fe51_mul x25519_fe51_mul -

383 # define fe51_sq x25519_fe51_sqr -

384 # define fe51_mul121666 x25519_fe51_mul121666 -

385 # else -

386 -

387 typedef __uint128_t u128; -

388 -

389 static void fe51_mul(fe51 h, const fe51 f, const fe51 g) -

390 { -

391 u128 h0, h1, h2, h3, h4; -

392 uint64_t f_i, g0, g1, g2, g3, g4; -

393 -

394 f_i = f[0]; -

395 h0 = (u128)f_i * (g0 = g[0]); -

396 h1 = (u128)f_i * (g1 = g[1]); -

397 h2 = (u128)f_i * (g2 = g[2]); -

398 h3 = (u128)f_i * (g3 = g[3]); -

399 h4 = (u128)f_i * (g4 = g[4]); -

400 -

401 f_i = f[1]; -

402 h0 += (u128)f_i * (g4 *= 19); -

403 h1 += (u128)f_i * g0; -

404 h2 += (u128)f_i * g1; -

405 h3 += (u128)f_i * g2; -

406 h4 += (u128)f_i * g3; -

407 -

408 f_i = f[2]; -

409 h0 += (u128)f_i * (g3 *= 19); -

410 h1 += (u128)f_i * g4; -

411 h2 += (u128)f_i * g0; -

412 h3 += (u128)f_i * g1; -

413 h4 += (u128)f_i * g2; -

414 -

415 f_i = f[3]; -

416 h0 += (u128)f_i * (g2 *= 19); -

417 h1 += (u128)f_i * g3; -

418 h2 += (u128)f_i * g4; -

419 h3 += (u128)f_i * g0; -

420 h4 += (u128)f_i * g1; -

421 -

422 f_i = f[4]; -

423 h0 += (u128)f_i * (g1 *= 19); -

424 h1 += (u128)f_i * g2; -

425 h2 += (u128)f_i * g3; -

426 h3 += (u128)f_i * g4; -

427 h4 += (u128)f_i * g0; -

428 -

429 /* partial [lazy] reduction */ -

430 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; -

431 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; -

432 -

433 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; -

434 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; -

435 -

436 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; -

437 g3 += g2 >> 51; g2 &= MASK51; -

438 g1 += g0 >> 51; g0 &= MASK51; -

439 -

440 h[0] = g0; -

441 h[1] = g1; -

442 h[2] = g2; -

443 h[3] = g3; -

444 h[4] = g4; -

445 } -

446 -

447 static void fe51_sq(fe51 h, const fe51 f) -

448 { -

449 # if defined(OPENSSL_SMALL_FOOTPRINT) -

450 fe51_mul(h, f, f); -

451 # else -

452 /* dedicated squaring gives 16-25% overall improvement */ -

453 uint64_t g0 = f[0]; -

454 uint64_t g1 = f[1]; -

455 uint64_t g2 = f[2]; -

456 uint64_t g3 = f[3]; -

457 uint64_t g4 = f[4]; -

458 u128 h0, h1, h2, h3, h4; -

459 -

460 h0 = (u128)g0 * g0; g0 *= 2; -

461 h1 = (u128)g0 * g1; -

462 h2 = (u128)g0 * g2; -

463 h3 = (u128)g0 * g3; -

464 h4 = (u128)g0 * g4; -

465 -

466 g0 = g4; /* borrow g0 */ -

467 h3 += (u128)g0 * (g4 *= 19); -

468 -

469 h2 += (u128)g1 * g1; g1 *= 2; -

470 h3 += (u128)g1 * g2; -

471 h4 += (u128)g1 * g3; -

472 h0 += (u128)g1 * g4; -

473 -

474 g0 = g3; /* borrow g0 */ -

475 h1 += (u128)g0 * (g3 *= 19); -

476 h2 += (u128)(g0 * 2) * g4; -

477 -

478 h4 += (u128)g2 * g2; g2 *= 2; -

479 h0 += (u128)g2 * g3; -

480 h1 += (u128)g2 * g4; -

481 -

482 /* partial [lazy] reduction */ -

483 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; -

484 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; -

485 -

486 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; -

487 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; -

488 -

489 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; -

490 g3 += g2 >> 51; g2 &= MASK51; -

491 g1 += g0 >> 51; g0 &= MASK51; -

492 -

493 h[0] = g0; -

494 h[1] = g1; -

495 h[2] = g2; -

496 h[3] = g3; -

497 h[4] = g4; -

498 # endif -

499 } -

500 -

501 static void fe51_mul121666(fe51 h, fe51 f) -

502 { -

503 u128 h0 = f[0] * (u128)121666; -

504 u128 h1 = f[1] * (u128)121666; -

505 u128 h2 = f[2] * (u128)121666; -

506 u128 h3 = f[3] * (u128)121666; -

507 u128 h4 = f[4] * (u128)121666; -

508 uint64_t g0, g1, g2, g3, g4; -

509 -

510 h3 += (uint64_t)(h2 >> 51); g2 = (uint64_t)h2 & MASK51; -

511 h1 += (uint64_t)(h0 >> 51); g0 = (uint64_t)h0 & MASK51; -

512 -

513 h4 += (uint64_t)(h3 >> 51); g3 = (uint64_t)h3 & MASK51; -

514 g2 += (uint64_t)(h1 >> 51); g1 = (uint64_t)h1 & MASK51; -

515 -

516 g0 += (uint64_t)(h4 >> 51) * 19; g4 = (uint64_t)h4 & MASK51; -

517 g3 += g2 >> 51; g2 &= MASK51; -

518 g1 += g0 >> 51; g0 &= MASK51; -

519 -

520 h[0] = g0; -

521 h[1] = g1; -

522 h[2] = g2; -

523 h[3] = g3; -

524 h[4] = g4; -

525 } -

526 # endif -

527 -

528 static void fe51_add(fe51 h, const fe51 f, const fe51 g) -

529 { -

530 h[0] = f[0] + g[0]; -

531 h[1] = f[1] + g[1]; -

532 h[2] = f[2] + g[2]; -

533 h[3] = f[3] + g[3]; -

534 h[4] = f[4] + g[4]; -

535

}

executed 2974320 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2974320

536 -

537 static void fe51_sub(fe51 h, const fe51 f, const fe51 g) -

538 { -

539 /* -

540 * Add 2*modulus to ensure that result remains positive -

541 * even if subtrahend is partially reduced. -

542 */ -

543 h[0] = (f[0] + 0xfffffffffffda) - g[0]; -

544 h[1] = (f[1] + 0xffffffffffffe) - g[1]; -

545 h[2] = (f[2] + 0xffffffffffffe) - g[2]; -

546 h[3] = (f[3] + 0xffffffffffffe) - g[3]; -

547 h[4] = (f[4] + 0xffffffffffffe) - g[4]; -

548

}

executed 2974320 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2974320

549 -

550 static void fe51_0(fe51 h) -

551 { -

552 h[0] = 0; -

553 h[1] = 0; -

554 h[2] = 0; -

555 h[3] = 0; -

556 h[4] = 0; -

557

}

executed 2916 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2916

558 -

559 static void fe51_1(fe51 h) -

560 { -

561 h[0] = 1; -

562 h[1] = 0; -

563 h[2] = 0; -

564 h[3] = 0; -

565 h[4] = 0; -

566

}

executed 5832 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

5832

567 -

568 static void fe51_copy(fe51 h, const fe51 f) -

569 { -

570 h[0] = f[0]; -

571 h[1] = f[1]; -

572 h[2] = f[2]; -

573 h[3] = f[3]; -

574 h[4] = f[4]; -

575

}

executed 2916 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2916

576 -

577 static void fe51_cswap(fe51 f, fe51 g, unsigned int b) -

578 { -

579 int i; -

580 uint64_t mask = 0 - (uint64_t)b; -

581 -

582

for (i = 0; i < 5; i++) {

i < 5	Description
TRUE	evaluated 7435800 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 1487160 times by 1 test Evaluated by: libcrypto.so.1.1

1487160-7435800

583 int64_t x = f[i] ^ g[i]; -

584 x &= mask; -

585 f[i] ^= x; -

586 g[i] ^= x; -

587

}

executed 7435800 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

7435800

588

}

executed 1487160 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1487160

589 -

590 static void fe51_invert(fe51 out, const fe51 z) -

591 { -

592 fe51 t0; -

593 fe51 t1; -

594 fe51 t2; -

595 fe51 t3; -

596 int i; -

597 -

598 /* -

599 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as -

600 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. -

601 */ -

602 -

603 /* t0 = z ** 2 */ -

604 fe51_sq(t0, z); -

605 -

606 /* t1 = t0 ** (2 ** 2) = z ** 8 */ -

607 fe51_sq(t1, t0); -

608 fe51_sq(t1, t1); -

609 -

610 /* t1 = z * t1 = z ** 9 */ -

611 fe51_mul(t1, z, t1); -

612 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ -

613 fe51_mul(t0, t0, t1); -

614 -

615 /* t2 = t0 ** 2 = z ** 22 */ -

616 fe51_sq(t2, t0); -

617 -

618 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ -

619 fe51_mul(t1, t1, t2); -

620 -

621 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ -

622 fe51_sq(t2, t1); -

623

for (i = 1; i < 5; ++i)

i < 5	Description
TRUE	evaluated 11664 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-11664

624

fe51_sq(t2, t2);

executed 11664 times by 1 test: x25519_fe51_sqr(t2, t2);

Executed by:

libcrypto.so.1.1

11664

625 -

626 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ -

627 fe51_mul(t1, t2, t1); -

628 -

629 /* Continuing similarly... */ -

630 -

631 /* t2 = z ** (2 ** 20 - 1) */ -

632 fe51_sq(t2, t1); -

633

for (i = 1; i < 10; ++i)

i < 10	Description
TRUE	evaluated 26244 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-26244

634

fe51_sq(t2, t2);

executed 26244 times by 1 test: x25519_fe51_sqr(t2, t2);

Executed by:

libcrypto.so.1.1

26244

635 -

636 fe51_mul(t2, t2, t1); -

637 -

638 /* t2 = z ** (2 ** 40 - 1) */ -

639 fe51_sq(t3, t2); -

640

for (i = 1; i < 20; ++i)

i < 20	Description
TRUE	evaluated 55404 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-55404

641

fe51_sq(t3, t3);

executed 55404 times by 1 test: x25519_fe51_sqr(t3, t3);

Executed by:

libcrypto.so.1.1

55404

642 -

643 fe51_mul(t2, t3, t2); -

644 -

645 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ -

646

for (i = 0; i < 10; ++i)

i < 10	Description
TRUE	evaluated 29160 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-29160

647

fe51_sq(t2, t2);

executed 29160 times by 1 test: x25519_fe51_sqr(t2, t2);

Executed by:

libcrypto.so.1.1

29160

648 -

649 /* t1 = z ** (2 ** 50 - 1) */ -

650 fe51_mul(t1, t2, t1); -

651 -

652 /* t2 = z ** (2 ** 100 - 1) */ -

653 fe51_sq(t2, t1); -

654

for (i = 1; i < 50; ++i)

i < 50	Description
TRUE	evaluated 142884 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-142884

655

fe51_sq(t2, t2);

executed 142884 times by 1 test: x25519_fe51_sqr(t2, t2);

Executed by:

libcrypto.so.1.1

142884

656 -

657 fe51_mul(t2, t2, t1); -

658 -

659 /* t2 = z ** (2 ** 200 - 1) */ -

660 fe51_sq(t3, t2); -

661

for (i = 1; i < 100; ++i)

i < 100	Description
TRUE	evaluated 288684 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-288684

662

fe51_sq(t3, t3);

executed 288684 times by 1 test: x25519_fe51_sqr(t3, t3);

Executed by:

libcrypto.so.1.1

288684

663 -

664 fe51_mul(t2, t3, t2); -

665 -

666 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ -

667

for (i = 0; i < 50; ++i)

i < 50	Description
TRUE	evaluated 145800 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-145800

668

fe51_sq(t2, t2);

executed 145800 times by 1 test: x25519_fe51_sqr(t2, t2);

Executed by:

libcrypto.so.1.1

145800

669 -

670 /* t1 = z ** (2 ** 250 - 1) */ -

671 fe51_mul(t1, t2, t1); -

672 -

673 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ -

674

for (i = 0; i < 5; ++i)

i < 5	Description
TRUE	evaluated 14580 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-14580

675

fe51_sq(t1, t1);

executed 14580 times by 1 test: x25519_fe51_sqr(t1, t1);

Executed by:

libcrypto.so.1.1

14580

676 -

677 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ -

678 fe51_mul(out, t1, t0); -

679

}

executed 2916 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2916

680 -

681 /* -

682 * Duplicate of original x25519_scalar_mult_generic, but using -

683 * fe51_* subroutines. -

684 */ -

685 static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], -

686 const uint8_t point[32]) -

687 { -

688 fe51 x1, x2, z2, x3, z3, tmp0, tmp1; -

689 uint8_t e[32]; -

690 unsigned swap = 0; -

691 int pos; -

692 -

693 # ifdef BASE_2_64_IMPLEMENTED -

694

if (x25519_fe64_eligible()) {

x25519_fe64_eligible()	Description
TRUE	never evaluated
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

0-2916

695 x25519_scalar_mulx(out, scalar, point); -

696

return;

never executed: return;

697 } -

698 # endif -

699 -

700 memcpy(e, scalar, 32); -

701 e[0] &= 0xf8; -

702 e[31] &= 0x7f; -

703 e[31] |= 0x40; -

704 fe51_frombytes(x1, point); -

705 fe51_1(x2); -

706 fe51_0(z2); -

707 fe51_copy(x3, x1); -

708 fe51_1(z3); -

709 -

710

for (pos = 254; pos >= 0; --pos) {

pos >= 0	Description
TRUE	evaluated 743580 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2916 times by 1 test Evaluated by: libcrypto.so.1.1

2916-743580

711 unsigned int b = 1 & (e[pos / 8] >> (pos & 7)); -

712 -

713 swap ^= b; -

714 fe51_cswap(x2, x3, swap); -

715 fe51_cswap(z2, z3, swap); -

716 swap = b; -

717 fe51_sub(tmp0, x3, z3); -

718 fe51_sub(tmp1, x2, z2); -

719 fe51_add(x2, x2, z2); -

720 fe51_add(z2, x3, z3); -

721 fe51_mul(z3, tmp0, x2); -

722 fe51_mul(z2, z2, tmp1); -

723 fe51_sq(tmp0, tmp1); -

724 fe51_sq(tmp1, x2); -

725 fe51_add(x3, z3, z2); -

726 fe51_sub(z2, z3, z2); -

727 fe51_mul(x2, tmp1, tmp0); -

728 fe51_sub(tmp1, tmp1, tmp0); -

729 fe51_sq(z2, z2); -

730 fe51_mul121666(z3, tmp1); -

731 fe51_sq(x3, x3); -

732 fe51_add(tmp0, tmp0, z3); -

733 fe51_mul(z3, x1, z2); -

734 fe51_mul(z2, tmp1, tmp0); -

735

}

executed 743580 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

743580

736 -

737 fe51_invert(z2, z2); -

738 fe51_mul(x2, x2, z2); -

739 fe51_tobytes(out, x2); -

740 -

741 OPENSSL_cleanse(e, sizeof(e)); -

742

}

executed 2916 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2916

743 #endif -

744 -

745 /* -

746 * Reference base 2^25.5 implementation. -

747 */ -

748 /* -

749 * This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP -

750 * 20141124 (http://bench.cr.yp.to/supercop.html). -

751 * -

752 * The field functions are shared by Ed25519 and X25519 where possible. -

753 */ -

754 -

755 /* fe means field element. Here the field is \Z/(2^255-19). An element t, -

756 * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 -

757 * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on -

758 * context. */ -

759 typedef int32_t fe[10]; -

760 -

761 static const int64_t kBottom25Bits = 0x1ffffffLL; -

762 static const int64_t kBottom26Bits = 0x3ffffffLL; -

763 static const int64_t kTop39Bits = 0xfffffffffe000000LL; -

764 static const int64_t kTop38Bits = 0xfffffffffc000000LL; -

765 -

766 static uint64_t load_3(const uint8_t *in) { -

767 uint64_t result; -

768 result = (uint64_t)in[0]; -

769 result |= ((uint64_t)in[1]) << 8; -

770 result |= ((uint64_t)in[2]) << 16; -

771

return result;

executed 630 times by 1 test: return result;

Executed by:

libcrypto.so.1.1

630

772 } -

773 -

774 static uint64_t load_4(const uint8_t *in) { -

775 uint64_t result; -

776 result = (uint64_t)in[0]; -

777 result |= ((uint64_t)in[1]) << 8; -

778 result |= ((uint64_t)in[2]) << 16; -

779 result |= ((uint64_t)in[3]) << 24; -

780

return result;

executed 634 times by 1 test: return result;

Executed by:

libcrypto.so.1.1

634

781 } -

782 -

783 static void fe_frombytes(fe h, const uint8_t *s) { -

784 /* Ignores top bit of h. */ -

785 int64_t h0 = load_4(s); -

786 int64_t h1 = load_3(s + 4) << 6; -

787 int64_t h2 = load_3(s + 7) << 5; -

788 int64_t h3 = load_3(s + 10) << 3; -

789 int64_t h4 = load_3(s + 13) << 2; -

790 int64_t h5 = load_4(s + 16); -

791 int64_t h6 = load_3(s + 20) << 7; -

792 int64_t h7 = load_3(s + 23) << 5; -

793 int64_t h8 = load_3(s + 26) << 4; -

794 int64_t h9 = (load_3(s + 29) & 8388607) << 2; -

795 int64_t carry0; -

796 int64_t carry1; -

797 int64_t carry2; -

798 int64_t carry3; -

799 int64_t carry4; -

800 int64_t carry5; -

801 int64_t carry6; -

802 int64_t carry7; -

803 int64_t carry8; -

804 int64_t carry9; -

805 -

806 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; -

807 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; -

808 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; -

809 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; -

810 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; -

811 -

812 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

813 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; -

814 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

815 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; -

816 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; -

817 -

818 h[0] = (int32_t)h0; -

819 h[1] = (int32_t)h1; -

820 h[2] = (int32_t)h2; -

821 h[3] = (int32_t)h3; -

822 h[4] = (int32_t)h4; -

823 h[5] = (int32_t)h5; -

824 h[6] = (int32_t)h6; -

825 h[7] = (int32_t)h7; -

826 h[8] = (int32_t)h8; -

827 h[9] = (int32_t)h9; -

828

}

executed 10 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

829 -

830 /* Preconditions: -

831 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -

832 * -

833 * Write p=2^255-19; q=floor(h/p). -

834 * Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). -

835 * -

836 * Proof: -

837 * Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. -

838 * Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. -

839 * -

840 * Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). -

841 * Then 0<y<1. -

842 * -

843 * Write r=h-pq. -

844 * Have 0<=r<=p-1=2^255-20. -

845 * Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. -

846 * -

847 * Write x=r+19(2^-255)r+y. -

848 * Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. -

849 * -

850 * Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) -

851 * so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. */ -

852 static void fe_tobytes(uint8_t *s, const fe h) { -

853 int32_t h0 = h[0]; -

854 int32_t h1 = h[1]; -

855 int32_t h2 = h[2]; -

856 int32_t h3 = h[3]; -

857 int32_t h4 = h[4]; -

858 int32_t h5 = h[5]; -

859 int32_t h6 = h[6]; -

860 int32_t h7 = h[7]; -

861 int32_t h8 = h[8]; -

862 int32_t h9 = h[9]; -

863 int32_t q; -

864 -

865 q = (19 * h9 + (((int32_t) 1) << 24)) >> 25; -

866 q = (h0 + q) >> 26; -

867 q = (h1 + q) >> 25; -

868 q = (h2 + q) >> 26; -

869 q = (h3 + q) >> 25; -

870 q = (h4 + q) >> 26; -

871 q = (h5 + q) >> 25; -

872 q = (h6 + q) >> 26; -

873 q = (h7 + q) >> 25; -

874 q = (h8 + q) >> 26; -

875 q = (h9 + q) >> 25; -

876 -

877 /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ -

878 h0 += 19 * q; -

879 /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ -

880 -

881 h1 += h0 >> 26; h0 &= kBottom26Bits; -

882 h2 += h1 >> 25; h1 &= kBottom25Bits; -

883 h3 += h2 >> 26; h2 &= kBottom26Bits; -

884 h4 += h3 >> 25; h3 &= kBottom25Bits; -

885 h5 += h4 >> 26; h4 &= kBottom26Bits; -

886 h6 += h5 >> 25; h5 &= kBottom25Bits; -

887 h7 += h6 >> 26; h6 &= kBottom26Bits; -

888 h8 += h7 >> 25; h7 &= kBottom25Bits; -

889 h9 += h8 >> 26; h8 &= kBottom26Bits; -

890 h9 &= kBottom25Bits; -

891 /* h10 = carry9 */ -

892 -

893 /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. -

894 * Have h0+...+2^230 h9 between 0 and 2^255-1; -

895 * evidently 2^255 h10-2^255 q = 0. -

896 * Goal: Output h0+...+2^230 h9. */ -

897 -

898 s[0] = (uint8_t)(h0 >> 0); -

899 s[1] = (uint8_t)(h0 >> 8); -

900 s[2] = (uint8_t)(h0 >> 16); -

901 s[3] = (uint8_t)((h0 >> 24) | ((uint32_t)(h1) << 2)); -

902 s[4] = (uint8_t)(h1 >> 6); -

903 s[5] = (uint8_t)(h1 >> 14); -

904 s[6] = (uint8_t)((h1 >> 22) | ((uint32_t)(h2) << 3)); -

905 s[7] = (uint8_t)(h2 >> 5); -

906 s[8] = (uint8_t)(h2 >> 13); -

907 s[9] = (uint8_t)((h2 >> 21) | ((uint32_t)(h3) << 5)); -

908 s[10] = (uint8_t)(h3 >> 3); -

909 s[11] = (uint8_t)(h3 >> 11); -

910 s[12] = (uint8_t)((h3 >> 19) | ((uint32_t)(h4) << 6)); -

911 s[13] = (uint8_t)(h4 >> 2); -

912 s[14] = (uint8_t)(h4 >> 10); -

913 s[15] = (uint8_t)(h4 >> 18); -

914 s[16] = (uint8_t)(h5 >> 0); -

915 s[17] = (uint8_t)(h5 >> 8); -

916 s[18] = (uint8_t)(h5 >> 16); -

917 s[19] = (uint8_t)((h5 >> 24) | ((uint32_t)(h6) << 1)); -

918 s[20] = (uint8_t)(h6 >> 7); -

919 s[21] = (uint8_t)(h6 >> 15); -

920 s[22] = (uint8_t)((h6 >> 23) | ((uint32_t)(h7) << 3)); -

921 s[23] = (uint8_t)(h7 >> 5); -

922 s[24] = (uint8_t)(h7 >> 13); -

923 s[25] = (uint8_t)((h7 >> 21) | ((uint32_t)(h8) << 4)); -

924 s[26] = (uint8_t)(h8 >> 4); -

925 s[27] = (uint8_t)(h8 >> 12); -

926 s[28] = (uint8_t)((h8 >> 20) | ((uint32_t)(h9) << 6)); -

927 s[29] = (uint8_t)(h9 >> 2); -

928 s[30] = (uint8_t)(h9 >> 10); -

929 s[31] = (uint8_t)(h9 >> 18); -

930

}

executed 6366 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

6366

931 -

932 /* h = f */ -

933 static void fe_copy(fe h, const fe f) { -

934 memmove(h, f, sizeof(int32_t) * 10); -

935

}

executed 822135 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

822135

936 -

937 /* h = 0 */ -

938

static

executed 414160 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); }

executed 414160 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

414160

939 -

940 /* h = 1 */ -

941 static void fe_1(fe h) { -

942 memset(h, 0, sizeof(int32_t) * 10); -

943 h[0] = 1; -

944

}

executed 815780 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

815780

945 -

946 /* h = f + g -

947 * Can overlap h with f or g. -

948 * -

949 * Preconditions: -

950 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -

951 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -

952 * -

953 * Postconditions: -

954 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ -

955 static void fe_add(fe h, const fe f, const fe g) { -

956 unsigned i; -

957

for (i = 0; i < 10; i++) {

i < 10	Description
TRUE	evaluated 16716520 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 1671652 times by 1 test Evaluated by: libcrypto.so.1.1

1671652-16716520

958 h[i] = f[i] + g[i]; -

959

}

executed 16716520 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

16716520

960

}

executed 1671652 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1671652

961 -

962 /* h = f - g -

963 * Can overlap h with f or g. -

964 * -

965 * Preconditions: -

966 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -

967 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -

968 * -

969 * Postconditions: -

970 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ -

971 static void fe_sub(fe h, const fe f, const fe g) { -

972 unsigned i; -

973

for (i = 0; i < 10; i++) {

i < 10	Description
TRUE	evaluated 12967580 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 1296758 times by 1 test Evaluated by: libcrypto.so.1.1

1296758-12967580

974 h[i] = f[i] - g[i]; -

975

}

executed 12967580 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

12967580

976

}

executed 1296758 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1296758

977 -

978 /* h = f * g -

979 * Can overlap h with f or g. -

980 * -

981 * Preconditions: -

982 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. -

983 * |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. -

984 * -

985 * Postconditions: -

986 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. -

987 * -

988 * Notes on implementation strategy: -

989 * -

990 * Using schoolbook multiplication. -

991 * Karatsuba would save a little in some cost models. -

992 * -

993 * Most multiplications by 2 and 19 are 32-bit precomputations; -

994 * cheaper than 64-bit postcomputations. -

995 * -

996 * There is one remaining multiplication by 19 in the carry chain; -

997 * one *19 precomputation can be merged into this, -

998 * but the resulting data flow is considerably less clean. -

999 * -

1000 * There are 12 carries below. -

1001 * 10 of them are 2-way parallelizable and vectorizable. -

1002 * Can get away with 11 carries, but then data flow is much deeper. -

1003 * -

1004 * With tighter constraints on inputs can squeeze carries into int32. */ -

1005 static void fe_mul(fe h, const fe f, const fe g) { -

1006 int32_t f0 = f[0]; -

1007 int32_t f1 = f[1]; -

1008 int32_t f2 = f[2]; -

1009 int32_t f3 = f[3]; -

1010 int32_t f4 = f[4]; -

1011 int32_t f5 = f[5]; -

1012 int32_t f6 = f[6]; -

1013 int32_t f7 = f[7]; -

1014 int32_t f8 = f[8]; -

1015 int32_t f9 = f[9]; -

1016 int32_t g0 = g[0]; -

1017 int32_t g1 = g[1]; -

1018 int32_t g2 = g[2]; -

1019 int32_t g3 = g[3]; -

1020 int32_t g4 = g[4]; -

1021 int32_t g5 = g[5]; -

1022 int32_t g6 = g[6]; -

1023 int32_t g7 = g[7]; -

1024 int32_t g8 = g[8]; -

1025 int32_t g9 = g[9]; -

1026 int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ -

1027 int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ -

1028 int32_t g3_19 = 19 * g3; -

1029 int32_t g4_19 = 19 * g4; -

1030 int32_t g5_19 = 19 * g5; -

1031 int32_t g6_19 = 19 * g6; -

1032 int32_t g7_19 = 19 * g7; -

1033 int32_t g8_19 = 19 * g8; -

1034 int32_t g9_19 = 19 * g9; -

1035 int32_t f1_2 = 2 * f1; -

1036 int32_t f3_2 = 2 * f3; -

1037 int32_t f5_2 = 2 * f5; -

1038 int32_t f7_2 = 2 * f7; -

1039 int32_t f9_2 = 2 * f9; -

1040 int64_t f0g0 = f0 * (int64_t) g0; -

1041 int64_t f0g1 = f0 * (int64_t) g1; -

1042 int64_t f0g2 = f0 * (int64_t) g2; -

1043 int64_t f0g3 = f0 * (int64_t) g3; -

1044 int64_t f0g4 = f0 * (int64_t) g4; -

1045 int64_t f0g5 = f0 * (int64_t) g5; -

1046 int64_t f0g6 = f0 * (int64_t) g6; -

1047 int64_t f0g7 = f0 * (int64_t) g7; -

1048 int64_t f0g8 = f0 * (int64_t) g8; -

1049 int64_t f0g9 = f0 * (int64_t) g9; -

1050 int64_t f1g0 = f1 * (int64_t) g0; -

1051 int64_t f1g1_2 = f1_2 * (int64_t) g1; -

1052 int64_t f1g2 = f1 * (int64_t) g2; -

1053 int64_t f1g3_2 = f1_2 * (int64_t) g3; -

1054 int64_t f1g4 = f1 * (int64_t) g4; -

1055 int64_t f1g5_2 = f1_2 * (int64_t) g5; -

1056 int64_t f1g6 = f1 * (int64_t) g6; -

1057 int64_t f1g7_2 = f1_2 * (int64_t) g7; -

1058 int64_t f1g8 = f1 * (int64_t) g8; -

1059 int64_t f1g9_38 = f1_2 * (int64_t) g9_19; -

1060 int64_t f2g0 = f2 * (int64_t) g0; -

1061 int64_t f2g1 = f2 * (int64_t) g1; -

1062 int64_t f2g2 = f2 * (int64_t) g2; -

1063 int64_t f2g3 = f2 * (int64_t) g3; -

1064 int64_t f2g4 = f2 * (int64_t) g4; -

1065 int64_t f2g5 = f2 * (int64_t) g5; -

1066 int64_t f2g6 = f2 * (int64_t) g6; -

1067 int64_t f2g7 = f2 * (int64_t) g7; -

1068 int64_t f2g8_19 = f2 * (int64_t) g8_19; -

1069 int64_t f2g9_19 = f2 * (int64_t) g9_19; -

1070 int64_t f3g0 = f3 * (int64_t) g0; -

1071 int64_t f3g1_2 = f3_2 * (int64_t) g1; -

1072 int64_t f3g2 = f3 * (int64_t) g2; -

1073 int64_t f3g3_2 = f3_2 * (int64_t) g3; -

1074 int64_t f3g4 = f3 * (int64_t) g4; -

1075 int64_t f3g5_2 = f3_2 * (int64_t) g5; -

1076 int64_t f3g6 = f3 * (int64_t) g6; -

1077 int64_t f3g7_38 = f3_2 * (int64_t) g7_19; -

1078 int64_t f3g8_19 = f3 * (int64_t) g8_19; -

1079 int64_t f3g9_38 = f3_2 * (int64_t) g9_19; -

1080 int64_t f4g0 = f4 * (int64_t) g0; -

1081 int64_t f4g1 = f4 * (int64_t) g1; -

1082 int64_t f4g2 = f4 * (int64_t) g2; -

1083 int64_t f4g3 = f4 * (int64_t) g3; -

1084 int64_t f4g4 = f4 * (int64_t) g4; -

1085 int64_t f4g5 = f4 * (int64_t) g5; -

1086 int64_t f4g6_19 = f4 * (int64_t) g6_19; -

1087 int64_t f4g7_19 = f4 * (int64_t) g7_19; -

1088 int64_t f4g8_19 = f4 * (int64_t) g8_19; -

1089 int64_t f4g9_19 = f4 * (int64_t) g9_19; -

1090 int64_t f5g0 = f5 * (int64_t) g0; -

1091 int64_t f5g1_2 = f5_2 * (int64_t) g1; -

1092 int64_t f5g2 = f5 * (int64_t) g2; -

1093 int64_t f5g3_2 = f5_2 * (int64_t) g3; -

1094 int64_t f5g4 = f5 * (int64_t) g4; -

1095 int64_t f5g5_38 = f5_2 * (int64_t) g5_19; -

1096 int64_t f5g6_19 = f5 * (int64_t) g6_19; -

1097 int64_t f5g7_38 = f5_2 * (int64_t) g7_19; -

1098 int64_t f5g8_19 = f5 * (int64_t) g8_19; -

1099 int64_t f5g9_38 = f5_2 * (int64_t) g9_19; -

1100 int64_t f6g0 = f6 * (int64_t) g0; -

1101 int64_t f6g1 = f6 * (int64_t) g1; -

1102 int64_t f6g2 = f6 * (int64_t) g2; -

1103 int64_t f6g3 = f6 * (int64_t) g3; -

1104 int64_t f6g4_19 = f6 * (int64_t) g4_19; -

1105 int64_t f6g5_19 = f6 * (int64_t) g5_19; -

1106 int64_t f6g6_19 = f6 * (int64_t) g6_19; -

1107 int64_t f6g7_19 = f6 * (int64_t) g7_19; -

1108 int64_t f6g8_19 = f6 * (int64_t) g8_19; -

1109 int64_t f6g9_19 = f6 * (int64_t) g9_19; -

1110 int64_t f7g0 = f7 * (int64_t) g0; -

1111 int64_t f7g1_2 = f7_2 * (int64_t) g1; -

1112 int64_t f7g2 = f7 * (int64_t) g2; -

1113 int64_t f7g3_38 = f7_2 * (int64_t) g3_19; -

1114 int64_t f7g4_19 = f7 * (int64_t) g4_19; -

1115 int64_t f7g5_38 = f7_2 * (int64_t) g5_19; -

1116 int64_t f7g6_19 = f7 * (int64_t) g6_19; -

1117 int64_t f7g7_38 = f7_2 * (int64_t) g7_19; -

1118 int64_t f7g8_19 = f7 * (int64_t) g8_19; -

1119 int64_t f7g9_38 = f7_2 * (int64_t) g9_19; -

1120 int64_t f8g0 = f8 * (int64_t) g0; -

1121 int64_t f8g1 = f8 * (int64_t) g1; -

1122 int64_t f8g2_19 = f8 * (int64_t) g2_19; -

1123 int64_t f8g3_19 = f8 * (int64_t) g3_19; -

1124 int64_t f8g4_19 = f8 * (int64_t) g4_19; -

1125 int64_t f8g5_19 = f8 * (int64_t) g5_19; -

1126 int64_t f8g6_19 = f8 * (int64_t) g6_19; -

1127 int64_t f8g7_19 = f8 * (int64_t) g7_19; -

1128 int64_t f8g8_19 = f8 * (int64_t) g8_19; -

1129 int64_t f8g9_19 = f8 * (int64_t) g9_19; -

1130 int64_t f9g0 = f9 * (int64_t) g0; -

1131 int64_t f9g1_38 = f9_2 * (int64_t) g1_19; -

1132 int64_t f9g2_19 = f9 * (int64_t) g2_19; -

1133 int64_t f9g3_38 = f9_2 * (int64_t) g3_19; -

1134 int64_t f9g4_19 = f9 * (int64_t) g4_19; -

1135 int64_t f9g5_38 = f9_2 * (int64_t) g5_19; -

1136 int64_t f9g6_19 = f9 * (int64_t) g6_19; -

1137 int64_t f9g7_38 = f9_2 * (int64_t) g7_19; -

1138 int64_t f9g8_19 = f9 * (int64_t) g8_19; -

1139 int64_t f9g9_38 = f9_2 * (int64_t) g9_19; -

1140 int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; -

1141 int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; -

1142 int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; -

1143 int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; -

1144 int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; -

1145 int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; -

1146 int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; -

1147 int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; -

1148 int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; -

1149 int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; -

1150 int64_t carry0; -

1151 int64_t carry1; -

1152 int64_t carry2; -

1153 int64_t carry3; -

1154 int64_t carry4; -

1155 int64_t carry5; -

1156 int64_t carry6; -

1157 int64_t carry7; -

1158 int64_t carry8; -

1159 int64_t carry9; -

1160 -

1161 /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) -

1162 * i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 -

1163 * |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) -

1164 * i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ -

1165 -

1166 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

1167 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

1168 /* |h0| <= 2^25 */ -

1169 /* |h4| <= 2^25 */ -

1170 /* |h1| <= 1.71*2^59 */ -

1171 /* |h5| <= 1.71*2^59 */ -

1172 -

1173 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; -

1174 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; -

1175 /* |h1| <= 2^24; from now on fits into int32 */ -

1176 /* |h5| <= 2^24; from now on fits into int32 */ -

1177 /* |h2| <= 1.41*2^60 */ -

1178 /* |h6| <= 1.41*2^60 */ -

1179 -

1180 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; -

1181 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; -

1182 /* |h2| <= 2^25; from now on fits into int32 unchanged */ -

1183 /* |h6| <= 2^25; from now on fits into int32 unchanged */ -

1184 /* |h3| <= 1.71*2^59 */ -

1185 /* |h7| <= 1.71*2^59 */ -

1186 -

1187 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; -

1188 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; -

1189 /* |h3| <= 2^24; from now on fits into int32 unchanged */ -

1190 /* |h7| <= 2^24; from now on fits into int32 unchanged */ -

1191 /* |h4| <= 1.72*2^34 */ -

1192 /* |h8| <= 1.41*2^60 */ -

1193 -

1194 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

1195 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; -

1196 /* |h4| <= 2^25; from now on fits into int32 unchanged */ -

1197 /* |h8| <= 2^25; from now on fits into int32 unchanged */ -

1198 /* |h5| <= 1.01*2^24 */ -

1199 /* |h9| <= 1.71*2^59 */ -

1200 -

1201 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; -

1202 /* |h9| <= 2^24; from now on fits into int32 unchanged */ -

1203 /* |h0| <= 1.1*2^39 */ -

1204 -

1205 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

1206 /* |h0| <= 2^25; from now on fits into int32 unchanged */ -

1207 /* |h1| <= 1.01*2^24 */ -

1208 -

1209 h[0] = (int32_t)h0; -

1210 h[1] = (int32_t)h1; -

1211 h[2] = (int32_t)h2; -

1212 h[3] = (int32_t)h3; -

1213 h[4] = (int32_t)h4; -

1214 h[5] = (int32_t)h5; -

1215 h[6] = (int32_t)h6; -

1216 h[7] = (int32_t)h7; -

1217 h[8] = (int32_t)h8; -

1218 h[9] = (int32_t)h9; -

1219

}

executed 2983050 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2983050

1220 -

1221 /* h = f * f -

1222 * Can overlap h with f. -

1223 * -

1224 * Preconditions: -

1225 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. -

1226 * -

1227 * Postconditions: -

1228 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. -

1229 * -

1230 * See fe_mul.c for discussion of implementation strategy. */ -

1231 static void fe_sq(fe h, const fe f) { -

1232 int32_t f0 = f[0]; -

1233 int32_t f1 = f[1]; -

1234 int32_t f2 = f[2]; -

1235 int32_t f3 = f[3]; -

1236 int32_t f4 = f[4]; -

1237 int32_t f5 = f[5]; -

1238 int32_t f6 = f[6]; -

1239 int32_t f7 = f[7]; -

1240 int32_t f8 = f[8]; -

1241 int32_t f9 = f[9]; -

1242 int32_t f0_2 = 2 * f0; -

1243 int32_t f1_2 = 2 * f1; -

1244 int32_t f2_2 = 2 * f2; -

1245 int32_t f3_2 = 2 * f3; -

1246 int32_t f4_2 = 2 * f4; -

1247 int32_t f5_2 = 2 * f5; -

1248 int32_t f6_2 = 2 * f6; -

1249 int32_t f7_2 = 2 * f7; -

1250 int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ -

1251 int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ -

1252 int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ -

1253 int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ -

1254 int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ -

1255 int64_t f0f0 = f0 * (int64_t) f0; -

1256 int64_t f0f1_2 = f0_2 * (int64_t) f1; -

1257 int64_t f0f2_2 = f0_2 * (int64_t) f2; -

1258 int64_t f0f3_2 = f0_2 * (int64_t) f3; -

1259 int64_t f0f4_2 = f0_2 * (int64_t) f4; -

1260 int64_t f0f5_2 = f0_2 * (int64_t) f5; -

1261 int64_t f0f6_2 = f0_2 * (int64_t) f6; -

1262 int64_t f0f7_2 = f0_2 * (int64_t) f7; -

1263 int64_t f0f8_2 = f0_2 * (int64_t) f8; -

1264 int64_t f0f9_2 = f0_2 * (int64_t) f9; -

1265 int64_t f1f1_2 = f1_2 * (int64_t) f1; -

1266 int64_t f1f2_2 = f1_2 * (int64_t) f2; -

1267 int64_t f1f3_4 = f1_2 * (int64_t) f3_2; -

1268 int64_t f1f4_2 = f1_2 * (int64_t) f4; -

1269 int64_t f1f5_4 = f1_2 * (int64_t) f5_2; -

1270 int64_t f1f6_2 = f1_2 * (int64_t) f6; -

1271 int64_t f1f7_4 = f1_2 * (int64_t) f7_2; -

1272 int64_t f1f8_2 = f1_2 * (int64_t) f8; -

1273 int64_t f1f9_76 = f1_2 * (int64_t) f9_38; -

1274 int64_t f2f2 = f2 * (int64_t) f2; -

1275 int64_t f2f3_2 = f2_2 * (int64_t) f3; -

1276 int64_t f2f4_2 = f2_2 * (int64_t) f4; -

1277 int64_t f2f5_2 = f2_2 * (int64_t) f5; -

1278 int64_t f2f6_2 = f2_2 * (int64_t) f6; -

1279 int64_t f2f7_2 = f2_2 * (int64_t) f7; -

1280 int64_t f2f8_38 = f2_2 * (int64_t) f8_19; -

1281 int64_t f2f9_38 = f2 * (int64_t) f9_38; -

1282 int64_t f3f3_2 = f3_2 * (int64_t) f3; -

1283 int64_t f3f4_2 = f3_2 * (int64_t) f4; -

1284 int64_t f3f5_4 = f3_2 * (int64_t) f5_2; -

1285 int64_t f3f6_2 = f3_2 * (int64_t) f6; -

1286 int64_t f3f7_76 = f3_2 * (int64_t) f7_38; -

1287 int64_t f3f8_38 = f3_2 * (int64_t) f8_19; -

1288 int64_t f3f9_76 = f3_2 * (int64_t) f9_38; -

1289 int64_t f4f4 = f4 * (int64_t) f4; -

1290 int64_t f4f5_2 = f4_2 * (int64_t) f5; -

1291 int64_t f4f6_38 = f4_2 * (int64_t) f6_19; -

1292 int64_t f4f7_38 = f4 * (int64_t) f7_38; -

1293 int64_t f4f8_38 = f4_2 * (int64_t) f8_19; -

1294 int64_t f4f9_38 = f4 * (int64_t) f9_38; -

1295 int64_t f5f5_38 = f5 * (int64_t) f5_38; -

1296 int64_t f5f6_38 = f5_2 * (int64_t) f6_19; -

1297 int64_t f5f7_76 = f5_2 * (int64_t) f7_38; -

1298 int64_t f5f8_38 = f5_2 * (int64_t) f8_19; -

1299 int64_t f5f9_76 = f5_2 * (int64_t) f9_38; -

1300 int64_t f6f6_19 = f6 * (int64_t) f6_19; -

1301 int64_t f6f7_38 = f6 * (int64_t) f7_38; -

1302 int64_t f6f8_38 = f6_2 * (int64_t) f8_19; -

1303 int64_t f6f9_38 = f6 * (int64_t) f9_38; -

1304 int64_t f7f7_38 = f7 * (int64_t) f7_38; -

1305 int64_t f7f8_38 = f7_2 * (int64_t) f8_19; -

1306 int64_t f7f9_76 = f7_2 * (int64_t) f9_38; -

1307 int64_t f8f8_19 = f8 * (int64_t) f8_19; -

1308 int64_t f8f9_38 = f8 * (int64_t) f9_38; -

1309 int64_t f9f9_38 = f9 * (int64_t) f9_38; -

1310 int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; -

1311 int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; -

1312 int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; -

1313 int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; -

1314 int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; -

1315 int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; -

1316 int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; -

1317 int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; -

1318 int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; -

1319 int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; -

1320 int64_t carry0; -

1321 int64_t carry1; -

1322 int64_t carry2; -

1323 int64_t carry3; -

1324 int64_t carry4; -

1325 int64_t carry5; -

1326 int64_t carry6; -

1327 int64_t carry7; -

1328 int64_t carry8; -

1329 int64_t carry9; -

1330 -

1331 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

1332 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

1333 -

1334 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; -

1335 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; -

1336 -

1337 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; -

1338 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; -

1339 -

1340 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; -

1341 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; -

1342 -

1343 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

1344 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; -

1345 -

1346 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; -

1347 -

1348 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

1349 -

1350 h[0] = (int32_t)h0; -

1351 h[1] = (int32_t)h1; -

1352 h[2] = (int32_t)h2; -

1353 h[3] = (int32_t)h3; -

1354 h[4] = (int32_t)h4; -

1355 h[5] = (int32_t)h5; -

1356 h[6] = (int32_t)h6; -

1357 h[7] = (int32_t)h7; -

1358 h[8] = (int32_t)h8; -

1359 h[9] = (int32_t)h9; -

1360

}

executed 1681806 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1681806

1361 -

1362 static void fe_invert(fe out, const fe z) { -

1363 fe t0; -

1364 fe t1; -

1365 fe t2; -

1366 fe t3; -

1367 int i; -

1368 -

1369 /* -

1370 * Compute z ** -1 = z ** (2 ** 255 - 19 - 2) with the exponent as -

1371 * 2 ** 255 - 21 = (2 ** 5) * (2 ** 250 - 1) + 11. -

1372 */ -

1373 -

1374 /* t0 = z ** 2 */ -

1375 fe_sq(t0, z); -

1376 -

1377 /* t1 = t0 ** (2 ** 2) = z ** 8 */ -

1378 fe_sq(t1, t0); -

1379 fe_sq(t1, t1); -

1380 -

1381 /* t1 = z * t1 = z ** 9 */ -

1382 fe_mul(t1, z, t1); -

1383 /* t0 = t0 * t1 = z ** 11 -- stash t0 away for the end. */ -

1384 fe_mul(t0, t0, t1); -

1385 -

1386 /* t2 = t0 ** 2 = z ** 22 */ -

1387 fe_sq(t2, t0); -

1388 -

1389 /* t1 = t1 * t2 = z ** (2 ** 5 - 1) */ -

1390 fe_mul(t1, t1, t2); -

1391 -

1392 /* t2 = t1 ** (2 ** 5) = z ** ((2 ** 5) * (2 ** 5 - 1)) */ -

1393 fe_sq(t2, t1); -

1394

for (i = 1; i < 5; ++i) {

i < 5	Description
TRUE	evaluated 25140 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6285 times by 1 test Evaluated by: libcrypto.so.1.1

6285-25140

1395 fe_sq(t2, t2); -

1396

}

executed 25140 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

25140

1397 -

1398 /* t1 = t1 * t2 = z ** ((2 ** 5 + 1) * (2 ** 5 - 1)) = z ** (2 ** 10 - 1) */ -

1399 fe_mul(t1, t2, t1); -

1400 -

1401 /* Continuing similarly... */ -

1402 -

1403 /* t2 = z ** (2 ** 20 - 1) */ -

1404 fe_sq(t2, t1); -

1405

for (i = 1; i < 10; ++i) {

i < 10	Description
TRUE	evaluated 56565 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6285 times by 1 test Evaluated by: libcrypto.so.1.1

6285-56565

1406 fe_sq(t2, t2); -

1407

}

executed 56565 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

56565

1408 fe_mul(t2, t2, t1); -

1409 -

1410 /* t2 = z ** (2 ** 40 - 1) */ -

1411 fe_sq(t3, t2); -

1412

for (i = 1; i < 20; ++i) {

i < 20	Description
TRUE	evaluated 119415 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6285 times by 1 test Evaluated by: libcrypto.so.1.1

6285-119415

1413 fe_sq(t3, t3); -

1414

}

executed 119415 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

119415

1415 fe_mul(t2, t3, t2); -

1416 -

1417 /* t2 = z ** (2 ** 10) * (2 ** 40 - 1) */ -

1418

for (i = 0; i < 10; ++i) {

i < 10	Description
TRUE	evaluated 62850 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6285 times by 1 test Evaluated by: libcrypto.so.1.1

6285-62850

1419 fe_sq(t2, t2); -

1420

}

executed 62850 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

62850

1421 /* t1 = z ** (2 ** 50 - 1) */ -

1422 fe_mul(t1, t2, t1); -

1423 -

1424 /* t2 = z ** (2 ** 100 - 1) */ -

1425 fe_sq(t2, t1); -

1426

for (i = 1; i < 50; ++i) {

i < 50	Description
TRUE	evaluated 307965 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6285 times by 1 test Evaluated by: libcrypto.so.1.1

6285-307965

1427 fe_sq(t2, t2); -

1428

}

executed 307965 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

307965

1429 fe_mul(t2, t2, t1); -

1430 -

1431 /* t2 = z ** (2 ** 200 - 1) */ -

1432 fe_sq(t3, t2); -

1433

for (i = 1; i < 100; ++i) {

i < 100	Description
TRUE	evaluated 622215 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6285 times by 1 test Evaluated by: libcrypto.so.1.1

6285-622215

1434 fe_sq(t3, t3); -

1435

}

executed 622215 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

622215

1436 fe_mul(t2, t3, t2); -

1437 -

1438 /* t2 = z ** ((2 ** 50) * (2 ** 200 - 1) */ -

1439 fe_sq(t2, t2); -

1440

for (i = 1; i < 50; ++i) {

i < 50	Description
TRUE	evaluated 307965 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6285 times by 1 test Evaluated by: libcrypto.so.1.1

6285-307965

1441 fe_sq(t2, t2); -

1442

}

executed 307965 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

307965

1443 -

1444 /* t1 = z ** (2 ** 250 - 1) */ -

1445 fe_mul(t1, t2, t1); -

1446 -

1447 /* t1 = z ** ((2 ** 5) * (2 ** 250 - 1)) */ -

1448 fe_sq(t1, t1); -

1449

for (i = 1; i < 5; ++i) {

i < 5	Description
TRUE	evaluated 25140 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6285 times by 1 test Evaluated by: libcrypto.so.1.1

6285-25140

1450 fe_sq(t1, t1); -

1451

}

executed 25140 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

25140

1452 -

1453 /* Recall t0 = z ** 11; out = z ** (2 ** 255 - 21) */ -

1454 fe_mul(out, t1, t0); -

1455

}

executed 6285 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

6285

1456 -

1457 /* h = -f -

1458 * -

1459 * Preconditions: -

1460 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -

1461 * -

1462 * Postconditions: -

1463 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ -

1464 static void fe_neg(fe h, const fe f) { -

1465 unsigned i; -

1466

for (i = 0; i < 10; i++) {

i < 10	Description
TRUE	evaluated 4016270 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 401627 times by 1 test Evaluated by: libcrypto.so.1.1

401627-4016270

1467 h[i] = -f[i]; -

1468

}

executed 4016270 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

4016270

1469

}

executed 401627 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

401627

1470 -

1471 /* Replace (f,g) with (g,g) if b == 1; -

1472 * replace (f,g) with (f,g) if b == 0. -

1473 * -

1474 * Preconditions: b in {0,1}. */ -

1475 static void fe_cmov(fe f, const fe g, unsigned b) { -

1476 size_t i; -

1477 b = 0-b; -

1478

for (i = 0; i < 10; i++) {

i < 10	Description
TRUE	evaluated 108432000 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10843200 times by 1 test Evaluated by: libcrypto.so.1.1

10843200-108432000

1479 int32_t x = f[i] ^ g[i]; -

1480 x &= b; -

1481 f[i] ^= x; -

1482

}

executed 108432000 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

108432000

1483

}

executed 10843200 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

10843200

1484 -

1485 /* return 0 if f == 0 -

1486 * return 1 if f != 0 -

1487 * -

1488 * Preconditions: -

1489 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ -

1490 static int fe_isnonzero(const fe f) { -

1491 uint8_t s[32]; -

1492 static const uint8_t zero[32] = {0}; -

1493 fe_tobytes(s, f); -

1494 -

1495

return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;

executed 15 times by 1 test: return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0;

Executed by:

libcrypto.so.1.1

1496 } -

1497 -

1498 /* return 1 if f is in {1,3,5,...,q-2} -

1499 * return 0 if f is in {0,2,4,...,q-1} -

1500 * -

1501 * Preconditions: -

1502 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ -

1503 static int fe_isnegative(const fe f) { -

1504 uint8_t s[32]; -

1505 fe_tobytes(s, f); -

1506

return s[0] & 1;

executed 66 times by 1 test: return s[0] & 1;

Executed by:

libcrypto.so.1.1

1507 } -

1508 -

1509 /* h = 2 * f * f -

1510 * Can overlap h with f. -

1511 * -

1512 * Preconditions: -

1513 * |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. -

1514 * -

1515 * Postconditions: -

1516 * |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. -

1517 * -

1518 * See fe_mul.c for discussion of implementation strategy. */ -

1519 static void fe_sq2(fe h, const fe f) { -

1520 int32_t f0 = f[0]; -

1521 int32_t f1 = f[1]; -

1522 int32_t f2 = f[2]; -

1523 int32_t f3 = f[3]; -

1524 int32_t f4 = f[4]; -

1525 int32_t f5 = f[5]; -

1526 int32_t f6 = f[6]; -

1527 int32_t f7 = f[7]; -

1528 int32_t f8 = f[8]; -

1529 int32_t f9 = f[9]; -

1530 int32_t f0_2 = 2 * f0; -

1531 int32_t f1_2 = 2 * f1; -

1532 int32_t f2_2 = 2 * f2; -

1533 int32_t f3_2 = 2 * f3; -

1534 int32_t f4_2 = 2 * f4; -

1535 int32_t f5_2 = 2 * f5; -

1536 int32_t f6_2 = 2 * f6; -

1537 int32_t f7_2 = 2 * f7; -

1538 int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ -

1539 int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ -

1540 int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ -

1541 int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ -

1542 int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ -

1543 int64_t f0f0 = f0 * (int64_t) f0; -

1544 int64_t f0f1_2 = f0_2 * (int64_t) f1; -

1545 int64_t f0f2_2 = f0_2 * (int64_t) f2; -

1546 int64_t f0f3_2 = f0_2 * (int64_t) f3; -

1547 int64_t f0f4_2 = f0_2 * (int64_t) f4; -

1548 int64_t f0f5_2 = f0_2 * (int64_t) f5; -

1549 int64_t f0f6_2 = f0_2 * (int64_t) f6; -

1550 int64_t f0f7_2 = f0_2 * (int64_t) f7; -

1551 int64_t f0f8_2 = f0_2 * (int64_t) f8; -

1552 int64_t f0f9_2 = f0_2 * (int64_t) f9; -

1553 int64_t f1f1_2 = f1_2 * (int64_t) f1; -

1554 int64_t f1f2_2 = f1_2 * (int64_t) f2; -

1555 int64_t f1f3_4 = f1_2 * (int64_t) f3_2; -

1556 int64_t f1f4_2 = f1_2 * (int64_t) f4; -

1557 int64_t f1f5_4 = f1_2 * (int64_t) f5_2; -

1558 int64_t f1f6_2 = f1_2 * (int64_t) f6; -

1559 int64_t f1f7_4 = f1_2 * (int64_t) f7_2; -

1560 int64_t f1f8_2 = f1_2 * (int64_t) f8; -

1561 int64_t f1f9_76 = f1_2 * (int64_t) f9_38; -

1562 int64_t f2f2 = f2 * (int64_t) f2; -

1563 int64_t f2f3_2 = f2_2 * (int64_t) f3; -

1564 int64_t f2f4_2 = f2_2 * (int64_t) f4; -

1565 int64_t f2f5_2 = f2_2 * (int64_t) f5; -

1566 int64_t f2f6_2 = f2_2 * (int64_t) f6; -

1567 int64_t f2f7_2 = f2_2 * (int64_t) f7; -

1568 int64_t f2f8_38 = f2_2 * (int64_t) f8_19; -

1569 int64_t f2f9_38 = f2 * (int64_t) f9_38; -

1570 int64_t f3f3_2 = f3_2 * (int64_t) f3; -

1571 int64_t f3f4_2 = f3_2 * (int64_t) f4; -

1572 int64_t f3f5_4 = f3_2 * (int64_t) f5_2; -

1573 int64_t f3f6_2 = f3_2 * (int64_t) f6; -

1574 int64_t f3f7_76 = f3_2 * (int64_t) f7_38; -

1575 int64_t f3f8_38 = f3_2 * (int64_t) f8_19; -

1576 int64_t f3f9_76 = f3_2 * (int64_t) f9_38; -

1577 int64_t f4f4 = f4 * (int64_t) f4; -

1578 int64_t f4f5_2 = f4_2 * (int64_t) f5; -

1579 int64_t f4f6_38 = f4_2 * (int64_t) f6_19; -

1580 int64_t f4f7_38 = f4 * (int64_t) f7_38; -

1581 int64_t f4f8_38 = f4_2 * (int64_t) f8_19; -

1582 int64_t f4f9_38 = f4 * (int64_t) f9_38; -

1583 int64_t f5f5_38 = f5 * (int64_t) f5_38; -

1584 int64_t f5f6_38 = f5_2 * (int64_t) f6_19; -

1585 int64_t f5f7_76 = f5_2 * (int64_t) f7_38; -

1586 int64_t f5f8_38 = f5_2 * (int64_t) f8_19; -

1587 int64_t f5f9_76 = f5_2 * (int64_t) f9_38; -

1588 int64_t f6f6_19 = f6 * (int64_t) f6_19; -

1589 int64_t f6f7_38 = f6 * (int64_t) f7_38; -

1590 int64_t f6f8_38 = f6_2 * (int64_t) f8_19; -

1591 int64_t f6f9_38 = f6 * (int64_t) f9_38; -

1592 int64_t f7f7_38 = f7 * (int64_t) f7_38; -

1593 int64_t f7f8_38 = f7_2 * (int64_t) f8_19; -

1594 int64_t f7f9_76 = f7_2 * (int64_t) f9_38; -

1595 int64_t f8f8_19 = f8 * (int64_t) f8_19; -

1596 int64_t f8f9_38 = f8 * (int64_t) f9_38; -

1597 int64_t f9f9_38 = f9 * (int64_t) f9_38; -

1598 int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; -

1599 int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; -

1600 int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; -

1601 int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; -

1602 int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; -

1603 int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; -

1604 int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; -

1605 int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; -

1606 int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; -

1607 int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; -

1608 int64_t carry0; -

1609 int64_t carry1; -

1610 int64_t carry2; -

1611 int64_t carry3; -

1612 int64_t carry4; -

1613 int64_t carry5; -

1614 int64_t carry6; -

1615 int64_t carry7; -

1616 int64_t carry8; -

1617 int64_t carry9; -

1618 -

1619 h0 += h0; -

1620 h1 += h1; -

1621 h2 += h2; -

1622 h3 += h3; -

1623 h4 += h4; -

1624 h5 += h5; -

1625 h6 += h6; -

1626 h7 += h7; -

1627 h8 += h8; -

1628 h9 += h9; -

1629 -

1630 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

1631 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

1632 -

1633 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; -

1634 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; -

1635 -

1636 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; -

1637 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; -

1638 -

1639 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; -

1640 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; -

1641 -

1642 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

1643 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; -

1644 -

1645 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; -

1646 -

1647 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

1648 -

1649 h[0] = (int32_t)h0; -

1650 h[1] = (int32_t)h1; -

1651 h[2] = (int32_t)h2; -

1652 h[3] = (int32_t)h3; -

1653 h[4] = (int32_t)h4; -

1654 h[5] = (int32_t)h5; -

1655 h[6] = (int32_t)h6; -

1656 h[7] = (int32_t)h7; -

1657 h[8] = (int32_t)h8; -

1658 h[9] = (int32_t)h9; -

1659

}

executed 27622 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

27622

1660 -

1661 static void fe_pow22523(fe out, const fe z) { -

1662 fe t0; -

1663 fe t1; -

1664 fe t2; -

1665 int i; -

1666 -

1667 fe_sq(t0, z); -

1668 fe_sq(t1, t0); -

1669

for (i = 1; i < 2; ++i) {

i < 2	Description
TRUE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

1670 fe_sq(t1, t1); -

1671

}

executed 10 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1672 fe_mul(t1, z, t1); -

1673 fe_mul(t0, t0, t1); -

1674 fe_sq(t0, t0); -

1675 fe_mul(t0, t1, t0); -

1676 fe_sq(t1, t0); -

1677

for (i = 1; i < 5; ++i) {

i < 5	Description
TRUE	evaluated 40 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

10-40

1678 fe_sq(t1, t1); -

1679

}

executed 40 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1680 fe_mul(t0, t1, t0); -

1681 fe_sq(t1, t0); -

1682

for (i = 1; i < 10; ++i) {

i < 10	Description
TRUE	evaluated 90 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

10-90

1683 fe_sq(t1, t1); -

1684

}

executed 90 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1685 fe_mul(t1, t1, t0); -

1686 fe_sq(t2, t1); -

1687

for (i = 1; i < 20; ++i) {

i < 20	Description
TRUE	evaluated 190 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

10-190

1688 fe_sq(t2, t2); -

1689

}

executed 190 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

190

1690 fe_mul(t1, t2, t1); -

1691 fe_sq(t1, t1); -

1692

for (i = 1; i < 10; ++i) {

i < 10	Description
TRUE	evaluated 90 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

10-90

1693 fe_sq(t1, t1); -

1694

}

executed 90 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1695 fe_mul(t0, t1, t0); -

1696 fe_sq(t1, t0); -

1697

for (i = 1; i < 50; ++i) {

i < 50	Description
TRUE	evaluated 490 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

10-490

1698 fe_sq(t1, t1); -

1699

}

executed 490 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

490

1700 fe_mul(t1, t1, t0); -

1701 fe_sq(t2, t1); -

1702

for (i = 1; i < 100; ++i) {

i < 100	Description
TRUE	evaluated 990 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

10-990

1703 fe_sq(t2, t2); -

1704

}

executed 990 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

990

1705 fe_mul(t1, t2, t1); -

1706 fe_sq(t1, t1); -

1707

for (i = 1; i < 50; ++i) {

i < 50	Description
TRUE	evaluated 490 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

10-490

1708 fe_sq(t1, t1); -

1709

}

executed 490 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

490

1710 fe_mul(t0, t1, t0); -

1711 fe_sq(t0, t0); -

1712

for (i = 1; i < 2; ++i) {

i < 2	Description
TRUE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

1713 fe_sq(t0, t0); -

1714

}

executed 10 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1715 fe_mul(out, t0, z); -

1716

}

executed 10 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1717 -

1718 /* ge means group element. -

1719 -

1720 * Here the group is the set of pairs (x,y) of field elements (see fe.h) -

1721 * satisfying -x^2 + y^2 = 1 + d x^2y^2 -

1722 * where d = -121665/121666. -

1723 * -

1724 * Representations: -

1725 * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z -

1726 * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT -

1727 * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T -

1728 * ge_precomp (Duif): (y+x,y-x,2dxy) */ -

1729 -

1730 typedef struct { -

1731 fe X; -

1732 fe Y; -

1733 fe Z; -

1734 } ge_p2; -

1735 -

1736 typedef struct { -

1737 fe X; -

1738 fe Y; -

1739 fe Z; -

1740 fe T; -

1741 } ge_p3; -

1742 -

1743 typedef struct { -

1744 fe X; -

1745 fe Y; -

1746 fe Z; -

1747 fe T; -

1748 } ge_p1p1; -

1749 -

1750 typedef struct { -

1751 fe yplusx; -

1752 fe yminusx; -

1753 fe xy2d; -

1754 } ge_precomp; -

1755 -

1756 typedef struct { -

1757 fe YplusX; -

1758 fe YminusX; -

1759 fe Z; -

1760 fe T2d; -

1761 } ge_cached; -

1762 -

1763 static void ge_tobytes(uint8_t *s, const ge_p2 *h) { -

1764 fe recip; -

1765 fe x; -

1766 fe y; -

1767 -

1768 fe_invert(recip, h->Z); -

1769 fe_mul(x, h->X, recip); -

1770 fe_mul(y, h->Y, recip); -

1771 fe_tobytes(s, y); -

1772 s[31] ^= fe_isnegative(x) << 7; -

1773

}

executed 10 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1774 -

1775 static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) { -

1776 fe recip; -

1777 fe x; -

1778 fe y; -

1779 -

1780 fe_invert(recip, h->Z); -

1781 fe_mul(x, h->X, recip); -

1782 fe_mul(y, h->Y, recip); -

1783 fe_tobytes(s, y); -

1784 s[31] ^= fe_isnegative(x) << 7; -

1785

}

executed 46 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1786 -

1787 static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, -

1788 -8787816, -6275908, -3247719, -18696448, -12055116}; -

1789 -

1790 static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, -

1791 -272473, -25146209, -2005654, 326686, 11406482}; -

1792 -

1793 static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { -

1794 fe u; -

1795 fe v; -

1796 fe v3; -

1797 fe vxx; -

1798 fe check; -

1799 -

1800 fe_frombytes(h->Y, s); -

1801 fe_1(h->Z); -

1802 fe_sq(u, h->Y); -

1803 fe_mul(v, u, d); -

1804 fe_sub(u, u, h->Z); /* u = y^2-1 */ -

1805 fe_add(v, v, h->Z); /* v = dy^2+1 */ -

1806 -

1807 fe_sq(v3, v); -

1808 fe_mul(v3, v3, v); /* v3 = v^3 */ -

1809 fe_sq(h->X, v3); -

1810 fe_mul(h->X, h->X, v); -

1811 fe_mul(h->X, h->X, u); /* x = uv^7 */ -

1812 -

1813 fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ -

1814 fe_mul(h->X, h->X, v3); -

1815 fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ -

1816 -

1817 fe_sq(vxx, h->X); -

1818 fe_mul(vxx, vxx, v); -

1819 fe_sub(check, vxx, u); /* vx^2-u */ -

1820

if (fe_isnonzero(check)) {

fe_isnonzero(check)	Description
TRUE	evaluated 5 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 5 times by 1 test Evaluated by: libcrypto.so.1.1

1821 fe_add(check, vxx, u); /* vx^2+u */ -

1822

if (fe_isnonzero(check)) {

fe_isnonzero(check)	Description
TRUE	never evaluated
FALSE	evaluated 5 times by 1 test Evaluated by: libcrypto.so.1.1

0-5

1823

return -1;

never executed: return -1;

1824 } -

1825 fe_mul(h->X, h->X, sqrtm1); -

1826

}

executed 5 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1827 -

1828

if (fe_isnegative(h->X) != (s[31] >> 7)) {

fe_isnegative(...= (s[31] >> 7)	Description
TRUE	evaluated 7 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 3 times by 1 test Evaluated by: libcrypto.so.1.1

3-7

1829 fe_neg(h->X, h->X); -

1830

}

executed 7 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1831 -

1832 fe_mul(h->T, h->X, h->Y); -

1833

return 0;

executed 10 times by 1 test: return 0;

Executed by:

libcrypto.so.1.1

1834 } -

1835 -

1836 static void ge_p2_0(ge_p2 *h) { -

1837 fe_0(h->X); -

1838 fe_1(h->Y); -

1839 fe_1(h->Z); -

1840

}

executed 10 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1841 -

1842 static void ge_p3_0(ge_p3 *h) { -

1843 fe_0(h->X); -

1844 fe_1(h->Y); -

1845 fe_1(h->Z); -

1846 fe_0(h->T); -

1847

}

executed 6275 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

6275

1848 -

1849 static void ge_precomp_0(ge_precomp *h) { -

1850 fe_1(h->yplusx); -

1851 fe_1(h->yminusx); -

1852 fe_0(h->xy2d); -

1853

}

executed 401600 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

401600

1854 -

1855 /* r = p */ -

1856 static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { -

1857 fe_copy(r->X, p->X); -

1858 fe_copy(r->Y, p->Y); -

1859 fe_copy(r->Z, p->Z); -

1860

}

executed 6285 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

6285

1861 -

1862 static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, -

1863 15978800, -12551817, -6495438, 29715968, 9444199}; -

1864 -

1865 /* r = p */ -

1866 static void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { -

1867 fe_add(r->YplusX, p->Y, p->X); -

1868 fe_sub(r->YminusX, p->Y, p->X); -

1869 fe_copy(r->Z, p->Z); -

1870 fe_mul(r->T2d, p->T, d2); -

1871

}

executed 80 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

1872 -

1873 /* r = p */ -

1874 static void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { -

1875 fe_mul(r->X, p->X, p->T); -

1876 fe_mul(r->Y, p->Y, p->Z); -

1877 fe_mul(r->Z, p->Z, p->T); -

1878

}

executed 21337 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

21337

1879 -

1880 /* r = p */ -

1881 static void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { -

1882 fe_mul(r->X, p->X, p->T); -

1883 fe_mul(r->Y, p->Y, p->Z); -

1884 fe_mul(r->Z, p->Z, p->T); -

1885 fe_mul(r->T, p->X, p->Y); -

1886

}

executed 408806 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

408806

1887 -

1888 /* r = 2 * p */ -

1889 static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { -

1890 fe t0; -

1891 -

1892 fe_sq(r->X, p->X); -

1893 fe_sq(r->Z, p->Y); -

1894 fe_sq2(r->T, p->Z); -

1895 fe_add(r->Y, p->X, p->Y); -

1896 fe_sq(t0, r->Y); -

1897 fe_add(r->Y, r->Z, r->X); -

1898 fe_sub(r->Z, r->Z, r->X); -

1899 fe_sub(r->X, t0, r->Y); -

1900 fe_sub(r->T, r->T, r->Z); -

1901

}

executed 27622 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

27622

1902 -

1903 /* r = 2 * p */ -

1904 static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { -

1905 ge_p2 q; -

1906 ge_p3_to_p2(&q, p); -

1907 ge_p2_dbl(r, &q); -

1908

}

executed 6285 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

6285

1909 -

1910 /* r = p + q */ -

1911 static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { -

1912 fe t0; -

1913 -

1914 fe_add(r->X, p->Y, p->X); -

1915 fe_sub(r->Y, p->Y, p->X); -

1916 fe_mul(r->Z, r->X, q->yplusx); -

1917 fe_mul(r->Y, r->Y, q->yminusx); -

1918 fe_mul(r->T, q->xy2d, p->T); -

1919 fe_add(t0, p->Z, p->Z); -

1920 fe_sub(r->X, r->Z, r->Y); -

1921 fe_add(r->Y, r->Z, r->Y); -

1922 fe_add(r->Z, t0, r->T); -

1923 fe_sub(r->T, t0, r->T); -

1924

}

executed 401834 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

401834

1925 -

1926 /* r = p - q */ -

1927 static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { -

1928 fe t0; -

1929 -

1930 fe_add(r->X, p->Y, p->X); -

1931 fe_sub(r->Y, p->Y, p->X); -

1932 fe_mul(r->Z, r->X, q->yminusx); -

1933 fe_mul(r->Y, r->Y, q->yplusx); -

1934 fe_mul(r->T, q->xy2d, p->T); -

1935 fe_add(t0, p->Z, p->Z); -

1936 fe_sub(r->X, r->Z, r->Y); -

1937 fe_add(r->Y, r->Z, r->Y); -

1938 fe_sub(r->Z, t0, r->T); -

1939 fe_add(r->T, t0, r->T); -

1940

}

executed 186 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

186

1941 -

1942 /* r = p + q */ -

1943 static void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { -

1944 fe t0; -

1945 -

1946 fe_add(r->X, p->Y, p->X); -

1947 fe_sub(r->Y, p->Y, p->X); -

1948 fe_mul(r->Z, r->X, q->YplusX); -

1949 fe_mul(r->Y, r->Y, q->YminusX); -

1950 fe_mul(r->T, q->T2d, p->T); -

1951 fe_mul(r->X, p->Z, q->Z); -

1952 fe_add(t0, r->X, r->X); -

1953 fe_sub(r->X, r->Z, r->Y); -

1954 fe_add(r->Y, r->Z, r->Y); -

1955 fe_add(r->Z, t0, r->T); -

1956 fe_sub(r->T, t0, r->T); -

1957

}

executed 305 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

305

1958 -

1959 /* r = p - q */ -

1960 static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { -

1961 fe t0; -

1962 -

1963 fe_add(r->X, p->Y, p->X); -

1964 fe_sub(r->Y, p->Y, p->X); -

1965 fe_mul(r->Z, r->X, q->YminusX); -

1966 fe_mul(r->Y, r->Y, q->YplusX); -

1967 fe_mul(r->T, q->T2d, p->T); -

1968 fe_mul(r->X, p->Z, q->Z); -

1969 fe_add(t0, r->X, r->X); -

1970 fe_sub(r->X, r->Z, r->Y); -

1971 fe_add(r->Y, r->Z, r->Y); -

1972 fe_sub(r->Z, t0, r->T); -

1973 fe_add(r->T, t0, r->T); -

1974

}

executed 196 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

196

1975 -

1976 static uint8_t equal(signed char b, signed char c) { -

1977 uint8_t ub = b; -

1978 uint8_t uc = c; -

1979 uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ -

1980 uint32_t y = x; /* 0: yes; 1..255: no */ -

1981 y -= 1; /* 4294967295: yes; 0..254: no */ -

1982 y >>= 31; /* 1: yes; 0: no */ -

1983

return y;

executed 3212800 times by 1 test: return y;

Executed by:

libcrypto.so.1.1

3212800

1984 } -

1985 -

1986 static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { -

1987 fe_cmov(t->yplusx, u->yplusx, b); -

1988 fe_cmov(t->yminusx, u->yminusx, b); -

1989 fe_cmov(t->xy2d, u->xy2d, b); -

1990

}

executed 3614400 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

3614400

1991 -

1992 /* k25519Precomp[i][j] = (j+1)*256^i*B */ -

1993 static const ge_precomp k25519Precomp[32][8] = { -

1994 { -

1995 { -

1996 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, -

1997 27544626, -11754271, -6079156, 2047605}, -

1998 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, -

1999 5043384, 19500929, -15469378}, -

2000 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, -

2001 29287919, 11864899, -24514362, -4438546}, -

2002 }, -

2003 { -

2004 {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -

2005 -11717903, -3814571, -358445, -10211303}, -

2006 {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -

2007 -15616551, 11189268, -26829678, -5319081}, -

2008 {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -

2009 -3128826, -9541118, -15472047, -4166697}, -

2010 }, -

2011 { -

2012 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, -

2013 27787600, -14772189, 28944400, -1550024}, -

2014 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, -

2015 16354577, -11775962, 7689662, 11199574}, -

2016 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, -

2017 7512774, 10017326, -17749093, -9920357}, -

2018 }, -

2019 { -

2020 {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -

2021 -28926210, 15006023, 3284568, -6276540}, -

2022 {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, -

2023 7464579, 9656445, 13059162, 10374397}, -

2024 {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -

2025 -3839045, -641708, -101325}, -

2026 }, -

2027 { -

2028 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, -

2029 32867885, 14515107, -15438304, 10819380}, -

2030 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, -

2031 12483688, -12668491, 5581306}, -

2032 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, -

2033 28542350, 13850243, -23678021, -15815942}, -

2034 }, -

2035 { -

2036 {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -

2037 -19188627, -15224819, -9818940, -12085777}, -

2038 {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -

2039 -15689887, 1762328, 14866737}, -

2040 {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -

2041 -28236412, 3959421, 27914454, 4383652}, -

2042 }, -

2043 { -

2044 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, -

2045 5230134, -23952439, -15175766}, -

2046 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, -

2047 20654025, 16520125, 30598449, 7715701}, -

2048 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -

2049 -31400660, 1370708, 29794553, -1409300}, -

2050 }, -

2051 { -

2052 {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, -

2053 30290735, 10876454, -33154098, 2381726}, -

2054 {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -

2055 -6236617, 3696005, -32300832, 15351955}, -

2056 {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -

2057 -32961401, -2970515, 29551813, 10109425}, -

2058 }, -

2059 }, -

2060 { -

2061 { -

2062 {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -

2063 -2378284, -1627556, 10092783, -4764171}, -

2064 {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -

2065 -32508754, 12005538, -17810127, 12803510}, -

2066 {17228999, -15661624, -1233527, 300140, -1224870, -11714777, -

2067 30364213, -9038194, 18016357, 4397660}, -

2068 }, -

2069 { -

2070 {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -

2071 -26619106, 14544525, -17477504, 982639}, -

2072 {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -

2073 -4120128, -21047696, 9934963}, -

2074 {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -

2075 -14747930, 4559895, -30123922, -10897950}, -

2076 }, -

2077 { -

2078 {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, -

2079 24191034, 4541697, -13338309, 5500568}, -

2080 {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -

2081 -17430592, 12264343, 10874051, 13524335}, -

2082 {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, -

2083 5080568, -22528059, 5376628}, -

2084 }, -

2085 { -

2086 {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -

2087 -22321305, -9447443, 4535768, 1569007}, -

2088 {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -

2089 -30494562, 3044290, 31848280, 12543772}, -

2090 {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -

2091 -27377195, -2062731, 7718482, 14474653}, -

2092 }, -

2093 { -

2094 {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -

2095 -7236665, 24316168, -5253567}, -

2096 {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, -

2097 33040651, -13424532, -20729456, 8321686}, -

2098 {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, -

2099 23845965, -11874838, -9984458, 608372}, -

2100 }, -

2101 { -

2102 {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, -

2103 1123968, -6780577, 27229399, 23887}, -

2104 {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, -

2105 12797024, -6440308, -1633405, 16678954}, -

2106 {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -

2107 -1508144, -4795045, -17169265, 4904953}, -

2108 }, -

2109 { -

2110 {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, -

2111 5169211, 16191880, 2128236, -4326833}, -

2112 {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -

2113 -29806336, 916033, -6882542, -2986532}, -

2114 {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, -

2115 285431, 2763829, 15736322, 4143876}, -

2116 }, -

2117 { -

2118 {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -

2119 -14594663, 23527084, -16458268}, -

2120 {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -

2121 -32625340, 4087881, -15188911, -14416214}, -

2122 {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, -

2123 4357868, -4774191, -16323038}, -

2124 }, -

2125 }, -

2126 { -

2127 { -

2128 {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, -

2129 23365147, -3949732, 7390890, 2759800}, -

2130 {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -

2131 -4264057, 1244380, -12919645}, -

2132 {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, -

2133 9208236, 15886429, 16489664}, -

2134 }, -

2135 { -

2136 {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -

2137 -13693198, 398369, -30606455, -712933}, -

2138 {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, -

2139 13348553, 12076947, -30836462, 5113182}, -

2140 {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -

2141 -30341101, -7336386, 13847711, 5387222}, -

2142 }, -

2143 { -

2144 {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, -

2145 8763061, 3617786, -19600662, 10370991}, -

2146 {20246567, -14369378, 22358229, -543712, 18507283, -10413996, -

2147 14554437, -8746092, 32232924, 16763880}, -

2148 {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, -

2149 11094161, 15689506, 3140038, -16510092}, -

2150 }, -

2151 { -

2152 {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -

2153 -27224800, 9448613, -28774454, 366295}, -

2154 {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, -

2155 28344573, 8041113, 719605, 11671788}, -

2156 {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -

2157 -15266516, 27000813, -10195553}, -

2158 }, -

2159 { -

2160 {-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, -

2161 5336097, 6750977, -14521026}, -

2162 {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, -

2163 1695823, -8819122, 8169720, 16220347}, -

2164 {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -

2165 -11144307, -2627664, -5990708, -14166033}, -

2166 }, -

2167 { -

2168 {-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, -

2169 27884329, 2847284, 2655861, 1738395}, -

2170 {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, -

2171 21651608, -3239336, -19087449, -11005278}, -

2172 {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, -

2173 5821408, 10478196, 8544890}, -

2174 }, -

2175 { -

2176 {32173121, -16129311, 24896207, 3921497, 22579056, -3410854, -

2177 19270449, 12217473, 17789017, -3395995}, -

2178 {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, -

2179 15479401, -3853233, 30460520, 1052596}, -

2180 {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, -

2181 27491595, -4612359, 3179268, -9478891}, -

2182 }, -

2183 { -

2184 {31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -

2185 -14756777, -16411740, 19072640, -9511060}, -

2186 {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, -

2187 5977896, -5215017, 473099, 5040608}, -

2188 {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, -

2189 28326862, 1721092, -19558642, -3131606}, -

2190 }, -

2191 }, -

2192 { -

2193 { -

2194 {7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, -

2195 8076149, -27868496, 11538389}, -

2196 {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, -

2197 8754525, 7446702, -5676054, 5797016}, -

2198 {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, -

2199 2014099, -9050574, -2369172, -5877341}, -

2200 }, -

2201 { -

2202 {-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, -

2203 1192730, -3714199, 15123619, 10811505}, -

2204 {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, -

2205 15776356, -28886779, -11974553}, -

2206 {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -

2207 -20654173, -16484855, 4714547, -9600655}, -

2208 }, -

2209 { -

2210 {15200332, 8368572, 19679101, 15970074, -31872674, 1959451, -

2211 24611599, -4543832, -11745876, 12340220}, -

2212 {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, -

2213 9613953, 8241152, 15370987, 9608631}, -

2214 {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, -

2215 15866074, -28210621, -8814099}, -

2216 }, -

2217 { -

2218 {26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, -

2219 858697, 20571223, 8420556}, -

2220 {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, -

2221 33531827, 12516406, -21574435, -12476749}, -

2222 {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, -

2223 7256740, 8791136, 15069930}, -

2224 }, -

2225 { -

2226 {1276410, -9371918, 22949635, -16322807, -23493039, -5702186, -

2227 14711875, 4874229, -30663140, -2331391}, -

2228 {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -

2229 -7912378, -33069337, 9234253}, -

2230 {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, -

2231 31559055, -11609587, 18979186, 13396066}, -

2232 }, -

2233 { -

2234 {24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -

2235 -18816887, 13594782, 33514650, 7021958}, -

2236 {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -

2237 -25948728, -3916677, -21480480, 12868082}, -

2238 {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -

2239 -21446107, 2244500, -12455797, -8089383}, -

2240 }, -

2241 { -

2242 {-30595528, 13793479, -5852820, 319136, -25723172, -6263899, -

2243 33086546, 8957937, -15233648, 5540521}, -

2244 {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -

2245 -23710744, -1568984, -16128528, -14962807}, -

2246 {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, -

2247 892185, -11513277, -15205948}, -

2248 }, -

2249 { -

2250 {9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, -

2251 4763127, -19179614, 5867134}, -

2252 {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, -

2253 27846559, 5931263, -29749703, -16108455}, -

2254 {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, -

2255 7283490, -15148073, -19526700, 7734629}, -

2256 }, -

2257 }, -

2258 { -

2259 { -

2260 {-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, -

2261 7585295, -3176626, 18549497, 15302069}, -

2262 {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, -

2263 10458790, -6418461, -8872242, 8424746}, -

2264 {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, -

2265 19206234, 7134917, -11284482, -828919}, -

2266 }, -

2267 { -

2268 {11334899, -9218022, 8025293, 12707519, 17523892, -10476071, -

2269 10243738, -14685461, -5066034, 16498837}, -

2270 {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -

2271 -14124238, 6536641, 10543906}, -

2272 {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -

2273 -2669190, -16625574, -27235709, 8876771}, -

2274 }, -

2275 { -

2276 {-25742899, -12566864, -15649966, -846607, -33026686, -796288, -

2277 -33481822, 15824474, -604426, -9039817}, -

2278 {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -

2279 -4890037, 1657394, 3084098}, -

2280 {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, -

2281 31280319, 14396151, -30233575, 15272409}, -

2282 }, -

2283 { -

2284 {-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -

2285 -25173957, -12636138, -25014757, 1950504}, -

2286 {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -

2287 -8384306, -8767532, 15341279, 8373727}, -

2288 {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, -

2289 298136, -10232602, -2878207, 15190420}, -

2290 }, -

2291 { -

2292 {-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, -

2293 8669718, 2742393, -26033313, -6875003}, -

2294 {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, -

2295 9291594, -16247779, -12154742, 6048605}, -

2296 {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, -

2297 13934231, 5128323, 11213262, 9168384}, -

2298 }, -

2299 { -

2300 {-26280513, 11007847, 19408960, -940758, -18592965, -4328580, -

2301 -5088060, -11105150, 20470157, -16398701}, -

2302 {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -

2303 -22783952, 14461608, 14042978, 5230683}, -

2304 {29969567, -2741594, -16711867, -8552442, 9175486, -2468974, -

2305 21556951, 3506042, -5933891, -12449708}, -

2306 }, -

2307 { -

2308 {-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -

2309 -21284170, 8971513, -28539189, 15326563}, -

2310 {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -

2311 -15523050, 15300988, -20514118, 9168260}, -

2312 {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -

2313 -28948358, 9601605, 33087103, -9011387}, -

2314 }, -

2315 { -

2316 {-19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -

2317 -27444329, -15000531, -5996870, 15664672}, -

2318 {23294591, -16632613, -22650781, -8470978, 27844204, 11461195, -

2319 13099750, -2460356, 18151676, 13417686}, -

2320 {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, -

2321 1661597, -12551441, 15271676, -15452665}, -

2322 }, -

2323 }, -

2324 { -

2325 { -

2326 {11433042, -13228665, 8239631, -5279517, -1985436, -725718, -

2327 -18698764, 2167544, -6921301, -13440182}, -

2328 {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -

2329 -9917708, -8638997, 12215110, 12028277}, -

2330 {14098400, 6555944, 23007258, 5757252, -15427832, -12950502, -

2331 30123440, 4617780, -16900089, -655628}, -

2332 }, -

2333 { -

2334 {-4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -

2335 -15819999, 10154009, 23973261, -12684474}, -

2336 {-26531820, -3695990, -1908898, 2534301, -31870557, -16550355, -

2337 18341390, -11419951, 32013174, -10103539}, -

2338 {-25479301, 10876443, -11771086, -14625140, -12369567, 1838104, -

2339 21911214, 6354752, 4425632, -837822}, -

2340 }, -

2341 { -

2342 {-10433389, -14612966, 22229858, -3091047, -13191166, 776729, -

2343 -17415375, -12020462, 4725005, 14044970}, -

2344 {19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -

2345 -1411784, -19522291, -16109756}, -

2346 {-24864089, 12986008, -10898878, -5558584, -11312371, -148526, -

2347 19541418, 8180106, 9282262, 10282508}, -

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3788 {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -

3789 -1674433, -3758243, -2304625}, -

3790 {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -

3791 -1612713, -1535569, -16664475, 8194478}, -

3792 }, -

3793 { -

3794 {27338066, -7507420, -7414224, 10140405, -19026427, -6589889, -

3795 27277191, 8855376, 28572286, 3005164}, -

3796 {26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -

3797 -18008582, 1182479, -26094821, -13079595}, -

3798 {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -

3799 -21876275, -13982627, 32208683, -1198248}, -

3800 }, -

3801 { -

3802 {-16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -

3803 -27315504, -10497842, -27672585, -11539858}, -

3804 {15941029, -9405932, -21367050, 8062055, 31876073, -238629, -

3805 -15278393, -1444429, 15397331, -4130193}, -

3806 {8934485, -13485467, -23286397, -13423241, -32446090, 14047986, -

3807 31170398, -1441021, -27505566, 15087184}, -

3808 }, -

3809 { -

3810 {-18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -

3811 -15502406, 11461896, 16788528, -5868942}, -

3812 {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -

3813 -3770287, -10323320, 31322514, -11615635}, -

3814 {21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -

3815 -18275391, -14621414, 13040862, -12112948}, -

3816 }, -

3817 { -

3818 {11293895, 12478086, -27136401, 15083750, -29307421, 14748872, -

3819 14555558, -13417103, 1613711, 4896935}, -

3820 {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, -

3821 2825960, -4897045, -23971776, -11267415}, -

3822 {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, -

3823 20615400, 12405433, -23753030, -8436416}, -

3824 }, -

3825 { -

3826 {-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, -

3827 4378436, 2432030, 23097949, -566018}, -

3828 {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, -

3829 10103221, -18512313, 2424778}, -

3830 {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, -

3831 1344109, -3642553, 12412659}, -

3832 }, -

3833 { -

3834 {-24001791, 7690286, 14929416, -168257, -32210835, -13412986, -

3835 24162697, -15326504, -3141501, 11179385}, -

3836 {18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -

3837 -6001441, -1486897, -18684645, -11443503}, -

3838 {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, -

3839 13403813, 11052904, 5219329}, -

3840 }, -

3841 }, -

3842 { -

3843 { -

3844 {20678546, -8375738, -32671898, 8849123, -5009758, 14574752, -

3845 31186971, -3973730, 9014762, -8579056}, -

3846 {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -

3847 -33102500, 9160280, 8473550, -3256838}, -

3848 {24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -

3849 -7689309, -16335821, -24568481, 11788948}, -

3850 }, -

3851 { -

3852 {-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -

3853 -20037437, 10410733, -24568470, -1458691}, -

3854 {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, -

3855 11871841, -12505194, -18513325, 8464118}, -

3856 {-23400612, 8348507, -14585951, -861714, -3950205, -6373419, -

3857 14325289, 8628612, 33313881, -8370517}, -

3858 }, -

3859 { -

3860 {-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -

3861 -24805667, -10236854, -8940735, -5818269}, -

3862 {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, -

3863 15989197, -12838188, 28358192, -4253904}, -

3864 {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -

3865 -16637684, 4072016, -5351664, 5596589}, -

3866 }, -

3867 { -

3868 {-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, -

3869 29266239, 2557221, 1768301, 15373193}, -

3870 {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -

3871 -4504991, -24660491, 3442910}, -

3872 {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, -

3873 22597931, 7176455, -18585478, 13365930}, -

3874 }, -

3875 { -

3876 {-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -

3877 -8570186, -9689599, -3031667}, -

3878 {25008904, -10771599, -4305031, -9638010, 16265036, 15721635, -

3879 683793, -11823784, 15723479, -15163481}, -

3880 {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, -

3881 11879682, 5400171, 519526, -1235876}, -

3882 }, -

3883 { -

3884 {22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -

3885 -20353881, 7315967, 16648397, 7605640}, -

3886 {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, -

3887 23994942, -5281555, -9468848, 4763278}, -

3888 {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, -

3889 31088447, -7764523, -11356529, 728112}, -

3890 }, -

3891 { -

3892 {26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -

3893 -4273545, -12555558, -29365436, -5498272}, -

3894 {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, -

3895 12327945, 10750447, 10014012}, -

3896 {-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -

3897 -27481051, -666732, 3424691, 7540221}, -

3898 }, -

3899 { -

3900 {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -

3901 -16317219, -9244265, 15258046}, -

3902 {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, -

3903 2711395, 1062915, -5136345}, -

3904 {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -

3905 -6066489, 12194497, 32960380, 1459310}, -

3906 }, -

3907 }, -

3908 { -

3909 { -

3910 {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -

3911 -6101885, 18638003, -11174937}, -

3912 {31395534, 15098109, 26581030, 8030562, -16527914, -5007134, -

3913 9012486, -7584354, -6643087, -5442636}, -

3914 {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, -

3915 9677543, -32294889, -6456008}, -

3916 }, -

3917 { -

3918 {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -

3919 -7839692, -7852844, -8138429}, -

3920 {-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -

3921 -27333451, 10754588, -9431476, 5203576}, -

3922 {31834314, 14135496, -770007, 5159118, 20917671, -16768096, -

3923 -7467973, -7337524, 31809243, 7347066}, -

3924 }, -

3925 { -

3926 {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, -

3927 19797970, -12211255, 15192876, -2087490}, -

3928 {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, -

3929 10609330, 12694420, 33473243, -13382104}, -

3930 {33184999, 11180355, 15832085, -11385430, -1633671, 225884, -

3931 15089336, -11023903, -6135662, 14480053}, -

3932 }, -

3933 { -

3934 {31308717, -5619998, 31030840, -1897099, 15674547, -6582883, -

3935 5496208, 13685227, 27595050, 8737275}, -

3936 {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -

3937 -31008351, -12610604, 26498114, 66511}, -

3938 {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, -

3939 30540766, -4286747, -13327787, -7515095}, -

3940 }, -

3941 { -

3942 {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, -

3943 8205540, 13585437, -17127465, 15115439}, -

3944 {23711543, -672915, 31206561, -8362711, 6164647, -9709987, -

3945 -33535882, -1426096, 8236921, 16492939}, -

3946 {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, -

3947 19574902, 10071562, 6708380, -6222424}, -

3948 }, -

3949 { -

3950 {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, -

3951 9328700, 29955601, -11678310}, -

3952 {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -

3953 -25892142, -12635595, -9917575, 6216608}, -

3954 {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, -

3955 24822830, -6146567, -26767480, 7525079}, -

3956 }, -

3957 { -

3958 {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -

3959 -910336, -2782495, -19386633, 11994101}, -

3960 {21691500, -13624626, -641331, -14367021, 3285881, -3483596, -

3961 -25064666, 9718258, -7477437, 13381418}, -

3962 {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, -

3963 23111648, -6375247, 28535282, 15779576}, -

3964 }, -

3965 { -

3966 {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -

3967 -14068454, 12021730, 9955285, -16303356}, -

3968 {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -

3969 -18426029, 9924399, 20194861, 13380996}, -

3970 {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -

3971 -1984914, 15707771, 26342023, 10146099}, -

3972 }, -

3973 }, -

3974 { -

3975 { -

3976 {-26016874, -219943, 21339191, -41388, 19745256, -2878700, -

3977 -29637280, 2227040, 21612326, -545728}, -

3978 {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, -

3979 25764461, 12243797, -20856566, 11649658}, -

3980 {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, -

3981 6114064, 33514190, 2333242}, -

3982 }, -

3983 { -

3984 {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -

3985 -6679750, -12670638, 24350578, -13450001}, -

3986 {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -

3987 -31536088, -10406836, 8317860, 12352766}, -

3988 {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -

3989 -23552096, -2287550, 20712163, 6719373}, -

3990 }, -

3991 { -

3992 {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -

3993 -3763210, 26224235, -3297458}, -

3994 {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, -

3995 21728352, 9493610, 18620611, -16428628}, -

3996 {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -

3997 -5269471, -9725556, -30701573, -16479657}, -

3998 }, -

3999 { -

4000 {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, -

4001 12248509, -5240639, 13735342, 1934062}, -

4002 {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -

4003 -15136294, -3765346, -21277997, 5473616}, -

4004 {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -

4005 -7125085, 12469656, 29111212, -5451014}, -

4006 }, -

4007 { -

4008 {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, -

4009 24367466, 6388839, -10295587, 452383}, -

4010 {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -

4011 -24236251, -5915248, 15766062, 8407814}, -

4012 {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -

4013 -8917023, -4388953, -8067909, 2276718}, -

4014 }, -

4015 { -

4016 {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -

4017 -23827587, 5096219, 22740376, -7303417}, -

4018 {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, -

4019 24051124, 13742383, -15637599, 13295222}, -

4020 {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -

4021 -17720195, -4612972, -4451357, -14669444}, -

4022 }, -

4023 { -

4024 {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -

4025 -2469266, -4141880, 7770569, 9620597}, -

4026 {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -

4027 -1694323, -33502340, -14767970}, -

4028 {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, -

4029 1220118, 30494170, -11440799}, -

4030 }, -

4031 { -

4032 {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -

4033 -26739026, 926050, -1684339, -13333647}, -

4034 {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, -

4035 9021034, 9078865, 3353509, 4033511}, -

4036 {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, -

4037 23161163, 8839127, 27485041, 7356032}, -

4038 }, -

4039 }, -

4040 { -

4041 { -

4042 {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, -

4043 2625015, 28431036, -16771834}, -

4044 {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -

4045 -22545972, 14150565, 15970762, 4099461}, -

4046 {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, -

4047 13617293, -9937143, 11465739, 8317062}, -

4048 }, -

4049 { -

4050 {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, -

4051 14898637, 3848455, 20969334, -5157516}, -

4052 {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -

4053 -21610826, -3649888, 11177095, 14989547}, -

4054 {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, -

4055 13515641, 2581286, -28487508, 9930240}, -

4056 }, -

4057 { -

4058 {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, -

4059 18345767, -13403753, 16291481, -5314038}, -

4060 {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, -

4061 6957617, 4368891, 9788741}, -

4062 {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -

4063 -21722536, -8613148, 16250552, -11111103}, -

4064 }, -

4065 { -

4066 {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, -

4067 10604807, -30190403, 4782747}, -

4068 {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -

4069 -9981571, 4383045, 22546403, 437323}, -

4070 {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, -

4071 27343084, 2786261, -30633590, -14097016}, -

4072 }, -

4073 { -

4074 {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -

4075 -19690631, 2355319, -19284671, -6114373}, -

4076 {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, -

4077 18952177, 15496498, -29380133, 11754228}, -

4078 {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, -

4079 7141596, 11724556, 22761615, -10134141}, -

4080 }, -

4081 { -

4082 {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -

4083 -28741185, -12227393, 32851222, 11717399}, -

4084 {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, -

4085 31474879, 3483633, -1193175, -4030831}, -

4086 {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, -

4087 33142652, 6546660, -19985279, -3948376}, -

4088 }, -

4089 { -

4090 {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -

4091 -8537131, -12833048, -30772034, -15486313}, -

4092 {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -

4093 -31135347, -16049879, 10928917, 3011958}, -

4094 {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -

4095 -30831056, -12805180, 18008031, 10258577}, -

4096 }, -

4097 { -

4098 {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -

4099 -1853465, 1367120, 25127874, 6671743}, -

4100 {29701166, -14373934, -10878120, 9279288, -17568, 13127210, -

4101 21382910, 11042292, 25838796, 4642684}, -

4102 {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, -

4103 30468147, -13900640, 18423289, 4177476}, -

4104 }, -

4105 }, -

4106 }; -

4107 -

4108 static uint8_t negative(signed char b) { -

4109 uint32_t x = b; -

4110 x >>= 31; /* 1: yes; 0: no */ -

4111

return x;

executed 401600 times by 1 test: return x;

Executed by:

libcrypto.so.1.1

401600

4112 } -

4113 -

4114 static void table_select(ge_precomp *t, int pos, signed char b) { -

4115 ge_precomp minust; -

4116 uint8_t bnegative = negative(b); -

4117 uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); -

4118 -

4119 ge_precomp_0(t); -

4120 cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); -

4121 cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); -

4122 cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); -

4123 cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); -

4124 cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); -

4125 cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); -

4126 cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); -

4127 cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); -

4128 fe_copy(minust.yplusx, t->yminusx); -

4129 fe_copy(minust.yminusx, t->yplusx); -

4130 fe_neg(minust.xy2d, t->xy2d); -

4131 cmov(t, &minust, bnegative); -

4132

}

executed 401600 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

401600

4133 -

4134 /* h = a * B -

4135 * where a = a[0]+256*a[1]+...+256^31 a[31] -

4136 * B is the Ed25519 base point (x,4/5) with x positive. -

4137 * -

4138 * Preconditions: -

4139 * a[31] <= 127 */ -

4140 static void ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { -

4141 signed char e[64]; -

4142 signed char carry; -

4143 ge_p1p1 r; -

4144 ge_p2 s; -

4145 ge_precomp t; -

4146 int i; -

4147 -

4148

for (i = 0; i < 32; ++i) {

i < 32	Description
TRUE	evaluated 200800 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6275 times by 1 test Evaluated by: libcrypto.so.1.1

6275-200800

4149 e[2 * i + 0] = (a[i] >> 0) & 15; -

4150 e[2 * i + 1] = (a[i] >> 4) & 15; -

4151

}

executed 200800 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

200800

4152 /* each e[i] is between 0 and 15 */ -

4153 /* e[63] is between 0 and 7 */ -

4154 -

4155 carry = 0; -

4156

for (i = 0; i < 63; ++i) {

i < 63	Description
TRUE	evaluated 395325 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6275 times by 1 test Evaluated by: libcrypto.so.1.1

6275-395325

4157 e[i] += carry; -

4158 carry = e[i] + 8; -

4159 carry >>= 4; -

4160 e[i] -= carry << 4; -

4161

}

executed 395325 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

395325

4162 e[63] += carry; -

4163 /* each e[i] is between -8 and 8 */ -

4164 -

4165 ge_p3_0(h); -

4166

for (i = 1; i < 64; i += 2) {

i < 64	Description
TRUE	evaluated 200800 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6275 times by 1 test Evaluated by: libcrypto.so.1.1

6275-200800

4167 table_select(&t, i / 2, e[i]); -

4168 ge_madd(&r, h, &t); -

4169 ge_p1p1_to_p3(h, &r); -

4170

}

executed 200800 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

200800

4171 -

4172 ge_p3_dbl(&r, h); -

4173 ge_p1p1_to_p2(&s, &r); -

4174 ge_p2_dbl(&r, &s); -

4175 ge_p1p1_to_p2(&s, &r); -

4176 ge_p2_dbl(&r, &s); -

4177 ge_p1p1_to_p2(&s, &r); -

4178 ge_p2_dbl(&r, &s); -

4179 ge_p1p1_to_p3(h, &r); -

4180 -

4181

for (i = 0; i < 64; i += 2) {

i < 64	Description
TRUE	evaluated 200800 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 6275 times by 1 test Evaluated by: libcrypto.so.1.1

6275-200800

4182 table_select(&t, i / 2, e[i]); -

4183 ge_madd(&r, h, &t); -

4184 ge_p1p1_to_p3(h, &r); -

4185

}

executed 200800 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

200800

4186 -

4187 OPENSSL_cleanse(e, sizeof(e)); -

4188

}

executed 6275 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

6275

4189 -

4190 #if !defined(BASE_2_51_IMPLEMENTED) -

4191 /* Replace (f,g) with (g,f) if b == 1; -

4192 * replace (f,g) with (f,g) if b == 0. -

4193 * -

4194 * Preconditions: b in {0,1}. */ -

4195 static void fe_cswap(fe f, fe g, unsigned int b) { -

4196 size_t i; -

4197 b = 0-b; -

4198 for (i = 0; i < 10; i++) { -

4199 int32_t x = f[i] ^ g[i]; -

4200 x &= b; -

4201 f[i] ^= x; -

4202 g[i] ^= x; -

4203 } -

4204 } -

4205 -

4206 /* h = f * 121666 -

4207 * Can overlap h with f. -

4208 * -

4209 * Preconditions: -

4210 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -

4211 * -

4212 * Postconditions: -

4213 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ -

4214 static void fe_mul121666(fe h, fe f) { -

4215 int32_t f0 = f[0]; -

4216 int32_t f1 = f[1]; -

4217 int32_t f2 = f[2]; -

4218 int32_t f3 = f[3]; -

4219 int32_t f4 = f[4]; -

4220 int32_t f5 = f[5]; -

4221 int32_t f6 = f[6]; -

4222 int32_t f7 = f[7]; -

4223 int32_t f8 = f[8]; -

4224 int32_t f9 = f[9]; -

4225 int64_t h0 = f0 * (int64_t) 121666; -

4226 int64_t h1 = f1 * (int64_t) 121666; -

4227 int64_t h2 = f2 * (int64_t) 121666; -

4228 int64_t h3 = f3 * (int64_t) 121666; -

4229 int64_t h4 = f4 * (int64_t) 121666; -

4230 int64_t h5 = f5 * (int64_t) 121666; -

4231 int64_t h6 = f6 * (int64_t) 121666; -

4232 int64_t h7 = f7 * (int64_t) 121666; -

4233 int64_t h8 = f8 * (int64_t) 121666; -

4234 int64_t h9 = f9 * (int64_t) 121666; -

4235 int64_t carry0; -

4236 int64_t carry1; -

4237 int64_t carry2; -

4238 int64_t carry3; -

4239 int64_t carry4; -

4240 int64_t carry5; -

4241 int64_t carry6; -

4242 int64_t carry7; -

4243 int64_t carry8; -

4244 int64_t carry9; -

4245 -

4246 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; -

4247 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; -

4248 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; -

4249 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; -

4250 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; -

4251 -

4252 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

4253 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; -

4254 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

4255 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; -

4256 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; -

4257 -

4258 h[0] = (int32_t)h0; -

4259 h[1] = (int32_t)h1; -

4260 h[2] = (int32_t)h2; -

4261 h[3] = (int32_t)h3; -

4262 h[4] = (int32_t)h4; -

4263 h[5] = (int32_t)h5; -

4264 h[6] = (int32_t)h6; -

4265 h[7] = (int32_t)h7; -

4266 h[8] = (int32_t)h8; -

4267 h[9] = (int32_t)h9; -

4268 } -

4269 -

4270 static void x25519_scalar_mult_generic(uint8_t out[32], -

4271 const uint8_t scalar[32], -

4272 const uint8_t point[32]) { -

4273 fe x1, x2, z2, x3, z3, tmp0, tmp1; -

4274 uint8_t e[32]; -

4275 unsigned swap = 0; -

4276 int pos; -

4277 -

4278 memcpy(e, scalar, 32); -

4279 e[0] &= 248; -

4280 e[31] &= 127; -

4281 e[31] |= 64; -

4282 fe_frombytes(x1, point); -

4283 fe_1(x2); -

4284 fe_0(z2); -

4285 fe_copy(x3, x1); -

4286 fe_1(z3); -

4287 -

4288 for (pos = 254; pos >= 0; --pos) { -

4289 unsigned b = 1 & (e[pos / 8] >> (pos & 7)); -

4290 swap ^= b; -

4291 fe_cswap(x2, x3, swap); -

4292 fe_cswap(z2, z3, swap); -

4293 swap = b; -

4294 fe_sub(tmp0, x3, z3); -

4295 fe_sub(tmp1, x2, z2); -

4296 fe_add(x2, x2, z2); -

4297 fe_add(z2, x3, z3); -

4298 fe_mul(z3, tmp0, x2); -

4299 fe_mul(z2, z2, tmp1); -

4300 fe_sq(tmp0, tmp1); -

4301 fe_sq(tmp1, x2); -

4302 fe_add(x3, z3, z2); -

4303 fe_sub(z2, z3, z2); -

4304 fe_mul(x2, tmp1, tmp0); -

4305 fe_sub(tmp1, tmp1, tmp0); -

4306 fe_sq(z2, z2); -

4307 fe_mul121666(z3, tmp1); -

4308 fe_sq(x3, x3); -

4309 fe_add(tmp0, tmp0, z3); -

4310 fe_mul(z3, x1, z2); -

4311 fe_mul(z2, tmp1, tmp0); -

4312 } -

4313 -

4314 fe_invert(z2, z2); -

4315 fe_mul(x2, x2, z2); -

4316 fe_tobytes(out, x2); -

4317 -

4318 OPENSSL_cleanse(e, sizeof(e)); -

4319 } -

4320 -

4321 static void x25519_scalar_mult(uint8_t out[32], const uint8_t scalar[32], -

4322 const uint8_t point[32]) { -

4323 x25519_scalar_mult_generic(out, scalar, point); -

4324 } -

4325 #endif -

4326 -

4327 static void slide(signed char *r, const uint8_t *a) { -

4328 int i; -

4329 int b; -

4330 int k; -

4331 -

4332

for (i = 0; i < 256; ++i) {

i < 256	Description
TRUE	evaluated 5120 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 20 times by 1 test Evaluated by: libcrypto.so.1.1

20-5120

4333 r[i] = 1 & (a[i >> 3] >> (i & 7)); -

4334

}

executed 5120 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

5120

4335 -

4336

for (i = 0; i < 256; ++i) {

i < 256	Description
TRUE	evaluated 5120 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 20 times by 1 test Evaluated by: libcrypto.so.1.1

20-5120

4337

if (r[i]) {

r[i]	Description
TRUE	evaluated 851 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 4269 times by 1 test Evaluated by: libcrypto.so.1.1

851-4269

4338

for (b = 1; b <= 6 && i + b < 256; ++b) {

b <= 6	Description
TRUE	evaluated 4689 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 195 times by 1 test Evaluated by: libcrypto.so.1.1

i + b < 256	Description
TRUE	evaluated 4680 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 9 times by 1 test Evaluated by: libcrypto.so.1.1

9-4689

4339

if (r[i + b]) {

r[i + b]	Description
TRUE	evaluated 2249 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2431 times by 1 test Evaluated by: libcrypto.so.1.1

2249-2431

4340

if (r[i] + (r[i + b] << b) <= 15) {

r[i] + (r[i + b] << b) <= 15	Description
TRUE	evaluated 1220 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 1029 times by 1 test Evaluated by: libcrypto.so.1.1

1029-1220

4341 r[i] += r[i + b] << b; -

4342 r[i + b] = 0; -

4343

} else if (r[i] - (r[i + b] << b) >= -15) {

executed 1220 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

r[i] - (r[i + b] << b) >= -15	Description
TRUE	evaluated 382 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 647 times by 1 test Evaluated by: libcrypto.so.1.1

382-1220

4344 r[i] -= r[i + b] << b; -

4345

for (k = i + b; k < 256; ++k) {

k < 256	Description
TRUE	evaluated 1111 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	never evaluated

0-1111

4346

if (!r[k]) {

!r[k]	Description
TRUE	evaluated 382 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 729 times by 1 test Evaluated by: libcrypto.so.1.1

382-729

4347 r[k] = 1; -

4348

break;

executed 382 times by 1 test: break;

Executed by:

libcrypto.so.1.1

382

4349 } -

4350 r[k] = 0; -

4351

}

executed 729 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

729

4352

} else {

executed 382 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

382

4353

break;

executed 647 times by 1 test: break;

Executed by:

libcrypto.so.1.1

647

4354 } -

4355 } -

4356

}

executed 4033 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

4033

4357

}

executed 851 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

851

4358

}

executed 5120 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

5120

4359

}

executed 20 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

4360 -

4361 static const ge_precomp Bi[8] = { -

4362 { -

4363 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -

4364 -11754271, -6079156, 2047605}, -

4365 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, -

4366 5043384, 19500929, -15469378}, -

4367 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, -

4368 11864899, -24514362, -4438546}, -

4369 }, -

4370 { -

4371 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -

4372 -14772189, 28944400, -1550024}, -

4373 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -

4374 -11775962, 7689662, 11199574}, -

4375 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, -

4376 10017326, -17749093, -9920357}, -

4377 }, -

4378 { -

4379 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, -

4380 14515107, -15438304, 10819380}, -

4381 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, -

4382 12483688, -12668491, 5581306}, -

4383 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, -

4384 13850243, -23678021, -15815942}, -

4385 }, -

4386 { -

4387 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, -

4388 5230134, -23952439, -15175766}, -

4389 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, -

4390 16520125, 30598449, 7715701}, -

4391 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, -

4392 1370708, 29794553, -1409300}, -

4393 }, -

4394 { -

4395 {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -

4396 -1361450, -13062696, 13821877}, -

4397 {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -

4398 -7212327, 18853322, -14220951}, -

4399 {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -

4400 -10431137, 2207753, -3209784}, -

4401 }, -

4402 { -

4403 {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -

4404 -663000, -31111463, -16132436}, -

4405 {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, -

4406 15725684, 171356, 6466918}, -

4407 {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -

4408 -14088058, -30714912, 16193877}, -

4409 }, -

4410 { -

4411 {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, -

4412 4729455, -18074513, 9256800}, -

4413 {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, -

4414 9761698, -19827198, 630305}, -

4415 {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -

4416 -15960994, -2449256, -14291300}, -

4417 }, -

4418 { -

4419 {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, -

4420 15033784, 25105118, -7894876}, -

4421 {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, -

4422 1573892, -2625887, 2198790, -15804619}, -

4423 {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -

4424 -16236442, -32461234, -12290683}, -

4425 }, -

4426 }; -

4427 -

4428 /* r = a * A + b * B -

4429 * where a = a[0]+256*a[1]+...+256^31 a[31]. -

4430 * and b = b[0]+256*b[1]+...+256^31 b[31]. -

4431 * B is the Ed25519 base point (x,4/5) with x positive. */ -

4432 static void ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, -

4433 const ge_p3 *A, const uint8_t *b) { -

4434 signed char aslide[256]; -

4435 signed char bslide[256]; -

4436 ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ -

4437 ge_p1p1 t; -

4438 ge_p3 u; -

4439 ge_p3 A2; -

4440 int i; -

4441 -

4442 slide(aslide, a); -

4443 slide(bslide, b); -

4444 -

4445 ge_p3_to_cached(&Ai[0], A); -

4446 ge_p3_dbl(&t, A); -

4447 ge_p1p1_to_p3(&A2, &t); -

4448 ge_add(&t, &A2, &Ai[0]); -

4449 ge_p1p1_to_p3(&u, &t); -

4450 ge_p3_to_cached(&Ai[1], &u); -

4451 ge_add(&t, &A2, &Ai[1]); -

4452 ge_p1p1_to_p3(&u, &t); -

4453 ge_p3_to_cached(&Ai[2], &u); -

4454 ge_add(&t, &A2, &Ai[2]); -

4455 ge_p1p1_to_p3(&u, &t); -

4456 ge_p3_to_cached(&Ai[3], &u); -

4457 ge_add(&t, &A2, &Ai[3]); -

4458 ge_p1p1_to_p3(&u, &t); -

4459 ge_p3_to_cached(&Ai[4], &u); -

4460 ge_add(&t, &A2, &Ai[4]); -

4461 ge_p1p1_to_p3(&u, &t); -

4462 ge_p3_to_cached(&Ai[5], &u); -

4463 ge_add(&t, &A2, &Ai[5]); -

4464 ge_p1p1_to_p3(&u, &t); -

4465 ge_p3_to_cached(&Ai[6], &u); -

4466 ge_add(&t, &A2, &Ai[6]); -

4467 ge_p1p1_to_p3(&u, &t); -

4468 ge_p3_to_cached(&Ai[7], &u); -

4469 -

4470 ge_p2_0(r); -

4471 -

4472

for (i = 255; i >= 0; --i) {

i >= 0	Description
TRUE	evaluated 58 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	never evaluated

0-58

4473

if (aslide[i] || bslide[i]) {

aslide[i]	Description
TRUE	evaluated 4 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 54 times by 1 test Evaluated by: libcrypto.so.1.1

bslide[i]	Description
TRUE	evaluated 6 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 48 times by 1 test Evaluated by: libcrypto.so.1.1

4-54

4474

break;

executed 10 times by 1 test: break;

Executed by:

libcrypto.so.1.1

4475 } -

4476

}

executed 48 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

4477 -

4478

for (; i >= 0; --i) {

i >= 0	Description
TRUE	evaluated 2512 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

10-2512

4479 ge_p2_dbl(&t, r); -

4480 -

4481

if (aslide[i] > 0) {

aslide[i] > 0	Description
TRUE	evaluated 235 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2277 times by 1 test Evaluated by: libcrypto.so.1.1

235-2277

4482 ge_p1p1_to_p3(&u, &t); -

4483 ge_add(&t, &u, &Ai[aslide[i] / 2]); -

4484

} else if (aslide[i] < 0) {

executed 235 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

aslide[i] < 0	Description
TRUE	evaluated 196 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2081 times by 1 test Evaluated by: libcrypto.so.1.1

196-2081

4485 ge_p1p1_to_p3(&u, &t); -

4486 ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); -

4487

}

executed 196 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

196

4488 -

4489

if (bslide[i] > 0) {

bslide[i] > 0	Description
TRUE	evaluated 234 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2278 times by 1 test Evaluated by: libcrypto.so.1.1

234-2278

4490 ge_p1p1_to_p3(&u, &t); -

4491 ge_madd(&t, &u, &Bi[bslide[i] / 2]); -

4492

} else if (bslide[i] < 0) {

executed 234 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

bslide[i] < 0	Description
TRUE	evaluated 186 times by 1 test Evaluated by: libcrypto.so.1.1
FALSE	evaluated 2092 times by 1 test Evaluated by: libcrypto.so.1.1

186-2092

4493 ge_p1p1_to_p3(&u, &t); -

4494 ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); -

4495

}

executed 186 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

186

4496 -

4497 ge_p1p1_to_p2(r, &t); -

4498

}

executed 2512 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

2512

4499

}

executed 10 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

4500 -

4501 /* The set of scalars is \Z/l -

4502 * where l = 2^252 + 27742317777372353535851937790883648493. */ -

4503 -

4504 /* Input: -

4505 * s[0]+256*s[1]+...+256^63*s[63] = s -

4506 * -

4507 * Output: -

4508 * s[0]+256*s[1]+...+256^31*s[31] = s mod l -

4509 * where l = 2^252 + 27742317777372353535851937790883648493. -

4510 * Overwrites s in place. */ -

4511 static void x25519_sc_reduce(uint8_t *s) { -

4512 int64_t s0 = 2097151 & load_3(s); -

4513 int64_t s1 = 2097151 & (load_4(s + 2) >> 5); -

4514 int64_t s2 = 2097151 & (load_3(s + 5) >> 2); -

4515 int64_t s3 = 2097151 & (load_4(s + 7) >> 7); -

4516 int64_t s4 = 2097151 & (load_4(s + 10) >> 4); -

4517 int64_t s5 = 2097151 & (load_3(s + 13) >> 1); -

4518 int64_t s6 = 2097151 & (load_4(s + 15) >> 6); -

4519 int64_t s7 = 2097151 & (load_3(s + 18) >> 3); -

4520 int64_t s8 = 2097151 & load_3(s + 21); -

4521 int64_t s9 = 2097151 & (load_4(s + 23) >> 5); -

4522 int64_t s10 = 2097151 & (load_3(s + 26) >> 2); -

4523 int64_t s11 = 2097151 & (load_4(s + 28) >> 7); -

4524 int64_t s12 = 2097151 & (load_4(s + 31) >> 4); -

4525 int64_t s13 = 2097151 & (load_3(s + 34) >> 1); -

4526 int64_t s14 = 2097151 & (load_4(s + 36) >> 6); -

4527 int64_t s15 = 2097151 & (load_3(s + 39) >> 3); -

4528 int64_t s16 = 2097151 & load_3(s + 42); -

4529 int64_t s17 = 2097151 & (load_4(s + 44) >> 5); -

4530 int64_t s18 = 2097151 & (load_3(s + 47) >> 2); -

4531 int64_t s19 = 2097151 & (load_4(s + 49) >> 7); -

4532 int64_t s20 = 2097151 & (load_4(s + 52) >> 4); -

4533 int64_t s21 = 2097151 & (load_3(s + 55) >> 1); -

4534 int64_t s22 = 2097151 & (load_4(s + 57) >> 6); -

4535 int64_t s23 = (load_4(s + 60) >> 3); -

4536 int64_t carry0; -

4537 int64_t carry1; -

4538 int64_t carry2; -

4539 int64_t carry3; -

4540 int64_t carry4; -

4541 int64_t carry5; -

4542 int64_t carry6; -

4543 int64_t carry7; -

4544 int64_t carry8; -

4545 int64_t carry9; -

4546 int64_t carry10; -

4547 int64_t carry11; -

4548 int64_t carry12; -

4549 int64_t carry13; -

4550 int64_t carry14; -

4551 int64_t carry15; -

4552 int64_t carry16; -

4553 -

4554 s11 += s23 * 666643; -

4555 s12 += s23 * 470296; -

4556 s13 += s23 * 654183; -

4557 s14 -= s23 * 997805; -

4558 s15 += s23 * 136657; -

4559 s16 -= s23 * 683901; -

4560 s23 = 0; -

4561 -

4562 s10 += s22 * 666643; -

4563 s11 += s22 * 470296; -

4564 s12 += s22 * 654183; -

4565 s13 -= s22 * 997805; -

4566 s14 += s22 * 136657; -

4567 s15 -= s22 * 683901; -

4568 s22 = 0; -

4569 -

4570 s9 += s21 * 666643; -

4571 s10 += s21 * 470296; -

4572 s11 += s21 * 654183; -

4573 s12 -= s21 * 997805; -

4574 s13 += s21 * 136657; -

4575 s14 -= s21 * 683901; -

4576 s21 = 0; -

4577 -

4578 s8 += s20 * 666643; -

4579 s9 += s20 * 470296; -

4580 s10 += s20 * 654183; -

4581 s11 -= s20 * 997805; -

4582 s12 += s20 * 136657; -

4583 s13 -= s20 * 683901; -

4584 s20 = 0; -

4585 -

4586 s7 += s19 * 666643; -

4587 s8 += s19 * 470296; -

4588 s9 += s19 * 654183; -

4589 s10 -= s19 * 997805; -

4590 s11 += s19 * 136657; -

4591 s12 -= s19 * 683901; -

4592 s19 = 0; -

4593 -

4594 s6 += s18 * 666643; -

4595 s7 += s18 * 470296; -

4596 s8 += s18 * 654183; -

4597 s9 -= s18 * 997805; -

4598 s10 += s18 * 136657; -

4599 s11 -= s18 * 683901; -

4600 s18 = 0; -

4601 -

4602 carry6 = (s6 + (1 << 20)) >> 21; -

4603 s7 += carry6; -

4604 s6 -= carry6 * (1 << 21); -

4605 carry8 = (s8 + (1 << 20)) >> 21; -

4606 s9 += carry8; -

4607 s8 -= carry8 * (1 << 21); -

4608 carry10 = (s10 + (1 << 20)) >> 21; -

4609 s11 += carry10; -

4610 s10 -= carry10 * (1 << 21); -

4611 carry12 = (s12 + (1 << 20)) >> 21; -

4612 s13 += carry12; -

4613 s12 -= carry12 * (1 << 21); -

4614 carry14 = (s14 + (1 << 20)) >> 21; -

4615 s15 += carry14; -

4616 s14 -= carry14 * (1 << 21); -

4617 carry16 = (s16 + (1 << 20)) >> 21; -

4618 s17 += carry16; -

4619 s16 -= carry16 * (1 << 21); -

4620 -

4621 carry7 = (s7 + (1 << 20)) >> 21; -

4622 s8 += carry7; -

4623 s7 -= carry7 * (1 << 21); -

4624 carry9 = (s9 + (1 << 20)) >> 21; -

4625 s10 += carry9; -

4626 s9 -= carry9 * (1 << 21); -

4627 carry11 = (s11 + (1 << 20)) >> 21; -

4628 s12 += carry11; -

4629 s11 -= carry11 * (1 << 21); -

4630 carry13 = (s13 + (1 << 20)) >> 21; -

4631 s14 += carry13; -

4632 s13 -= carry13 * (1 << 21); -

4633 carry15 = (s15 + (1 << 20)) >> 21; -

4634 s16 += carry15; -

4635 s15 -= carry15 * (1 << 21); -

4636 -

4637 s5 += s17 * 666643; -

4638 s6 += s17 * 470296; -

4639 s7 += s17 * 654183; -

4640 s8 -= s17 * 997805; -

4641 s9 += s17 * 136657; -

4642 s10 -= s17 * 683901; -

4643 s17 = 0; -

4644 -

4645 s4 += s16 * 666643; -

4646 s5 += s16 * 470296; -

4647 s6 += s16 * 654183; -

4648 s7 -= s16 * 997805; -

4649 s8 += s16 * 136657; -

4650 s9 -= s16 * 683901; -

4651 s16 = 0; -

4652 -

4653 s3 += s15 * 666643; -

4654 s4 += s15 * 470296; -

4655 s5 += s15 * 654183; -

4656 s6 -= s15 * 997805; -

4657 s7 += s15 * 136657; -

4658 s8 -= s15 * 683901; -

4659 s15 = 0; -

4660 -

4661 s2 += s14 * 666643; -

4662 s3 += s14 * 470296; -

4663 s4 += s14 * 654183; -

4664 s5 -= s14 * 997805; -

4665 s6 += s14 * 136657; -

4666 s7 -= s14 * 683901; -

4667 s14 = 0; -

4668 -

4669 s1 += s13 * 666643; -

4670 s2 += s13 * 470296; -

4671 s3 += s13 * 654183; -

4672 s4 -= s13 * 997805; -

4673 s5 += s13 * 136657; -

4674 s6 -= s13 * 683901; -

4675 s13 = 0; -

4676 -

4677 s0 += s12 * 666643; -

4678 s1 += s12 * 470296; -

4679 s2 += s12 * 654183; -

4680 s3 -= s12 * 997805; -

4681 s4 += s12 * 136657; -

4682 s5 -= s12 * 683901; -

4683 s12 = 0; -

4684 -

4685 carry0 = (s0 + (1 << 20)) >> 21; -

4686 s1 += carry0; -

4687 s0 -= carry0 * (1 << 21); -

4688 carry2 = (s2 + (1 << 20)) >> 21; -

4689 s3 += carry2; -

4690 s2 -= carry2 * (1 << 21); -

4691 carry4 = (s4 + (1 << 20)) >> 21; -

4692 s5 += carry4; -

4693 s4 -= carry4 * (1 << 21); -

4694 carry6 = (s6 + (1 << 20)) >> 21; -

4695 s7 += carry6; -

4696 s6 -= carry6 * (1 << 21); -

4697 carry8 = (s8 + (1 << 20)) >> 21; -

4698 s9 += carry8; -

4699 s8 -= carry8 * (1 << 21); -

4700 carry10 = (s10 + (1 << 20)) >> 21; -

4701 s11 += carry10; -

4702 s10 -= carry10 * (1 << 21); -

4703 -

4704 carry1 = (s1 + (1 << 20)) >> 21; -

4705 s2 += carry1; -

4706 s1 -= carry1 * (1 << 21); -

4707 carry3 = (s3 + (1 << 20)) >> 21; -

4708 s4 += carry3; -

4709 s3 -= carry3 * (1 << 21); -

4710 carry5 = (s5 + (1 << 20)) >> 21; -

4711 s6 += carry5; -

4712 s5 -= carry5 * (1 << 21); -

4713 carry7 = (s7 + (1 << 20)) >> 21; -

4714 s8 += carry7; -

4715 s7 -= carry7 * (1 << 21); -

4716 carry9 = (s9 + (1 << 20)) >> 21; -

4717 s10 += carry9; -

4718 s9 -= carry9 * (1 << 21); -

4719 carry11 = (s11 + (1 << 20)) >> 21; -

4720 s12 += carry11; -

4721 s11 -= carry11 * (1 << 21); -

4722 -

4723 s0 += s12 * 666643; -

4724 s1 += s12 * 470296; -

4725 s2 += s12 * 654183; -

4726 s3 -= s12 * 997805; -

4727 s4 += s12 * 136657; -

4728 s5 -= s12 * 683901; -

4729 s12 = 0; -

4730 -

4731 carry0 = s0 >> 21; -

4732 s1 += carry0; -

4733 s0 -= carry0 * (1 << 21); -

4734 carry1 = s1 >> 21; -

4735 s2 += carry1; -

4736 s1 -= carry1 * (1 << 21); -

4737 carry2 = s2 >> 21; -

4738 s3 += carry2; -

4739 s2 -= carry2 * (1 << 21); -

4740 carry3 = s3 >> 21; -

4741 s4 += carry3; -

4742 s3 -= carry3 * (1 << 21); -

4743 carry4 = s4 >> 21; -

4744 s5 += carry4; -

4745 s4 -= carry4 * (1 << 21); -

4746 carry5 = s5 >> 21; -

4747 s6 += carry5; -

4748 s5 -= carry5 * (1 << 21); -

4749 carry6 = s6 >> 21; -

4750 s7 += carry6; -

4751 s6 -= carry6 * (1 << 21); -

4752 carry7 = s7 >> 21; -

4753 s8 += carry7; -

4754 s7 -= carry7 * (1 << 21); -

4755 carry8 = s8 >> 21; -

4756 s9 += carry8; -

4757 s8 -= carry8 * (1 << 21); -

4758 carry9 = s9 >> 21; -

4759 s10 += carry9; -

4760 s9 -= carry9 * (1 << 21); -

4761 carry10 = s10 >> 21; -

4762 s11 += carry10; -

4763 s10 -= carry10 * (1 << 21); -

4764 carry11 = s11 >> 21; -

4765 s12 += carry11; -

4766 s11 -= carry11 * (1 << 21); -

4767 -

4768 s0 += s12 * 666643; -

4769 s1 += s12 * 470296; -

4770 s2 += s12 * 654183; -

4771 s3 -= s12 * 997805; -

4772 s4 += s12 * 136657; -

4773 s5 -= s12 * 683901; -

4774 s12 = 0; -

4775 -

4776 carry0 = s0 >> 21; -

4777 s1 += carry0; -

4778 s0 -= carry0 * (1 << 21); -

4779 carry1 = s1 >> 21; -

4780 s2 += carry1; -

4781 s1 -= carry1 * (1 << 21); -

4782 carry2 = s2 >> 21; -

4783 s3 += carry2; -

4784 s2 -= carry2 * (1 << 21); -

4785 carry3 = s3 >> 21; -

4786 s4 += carry3; -

4787 s3 -= carry3 * (1 << 21); -

4788 carry4 = s4 >> 21; -

4789 s5 += carry4; -

4790 s4 -= carry4 * (1 << 21); -

4791 carry5 = s5 >> 21; -

4792 s6 += carry5; -

4793 s5 -= carry5 * (1 << 21); -

4794 carry6 = s6 >> 21; -

4795 s7 += carry6; -

4796 s6 -= carry6 * (1 << 21); -

4797 carry7 = s7 >> 21; -

4798 s8 += carry7; -

4799 s7 -= carry7 * (1 << 21); -

4800 carry8 = s8 >> 21; -

4801 s9 += carry8; -

4802 s8 -= carry8 * (1 << 21); -

4803 carry9 = s9 >> 21; -

4804 s10 += carry9; -

4805 s9 -= carry9 * (1 << 21); -

4806 carry10 = s10 >> 21; -

4807 s11 += carry10; -

4808 s10 -= carry10 * (1 << 21); -

4809 -

4810 s[0] = (uint8_t)(s0 >> 0); -

4811 s[1] = (uint8_t)(s0 >> 8); -

4812 s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); -

4813 s[3] = (uint8_t)(s1 >> 3); -

4814 s[4] = (uint8_t)(s1 >> 11); -

4815 s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); -

4816 s[6] = (uint8_t)(s2 >> 6); -

4817 s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); -

4818 s[8] = (uint8_t)(s3 >> 1); -

4819 s[9] = (uint8_t)(s3 >> 9); -

4820 s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); -

4821 s[11] = (uint8_t)(s4 >> 4); -

4822 s[12] = (uint8_t)(s4 >> 12); -

4823 s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); -

4824 s[14] = (uint8_t)(s5 >> 7); -

4825 s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); -

4826 s[16] = (uint8_t)(s6 >> 2); -

4827 s[17] = (uint8_t)(s6 >> 10); -

4828 s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); -

4829 s[19] = (uint8_t)(s7 >> 5); -

4830 s[20] = (uint8_t)(s7 >> 13); -

4831 s[21] = (uint8_t)(s8 >> 0); -

4832 s[22] = (uint8_t)(s8 >> 8); -

4833 s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); -

4834 s[24] = (uint8_t)(s9 >> 3); -

4835 s[25] = (uint8_t)(s9 >> 11); -

4836 s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); -

4837 s[27] = (uint8_t)(s10 >> 6); -

4838 s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); -

4839 s[29] = (uint8_t)(s11 >> 1); -

4840 s[30] = (uint8_t)(s11 >> 9); -

4841 s[31] = (uint8_t)(s11 >> 17); -

4842

}

executed 32 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

4843 -

4844 /* Input: -

4845 * a[0]+256*a[1]+...+256^31*a[31] = a -

4846 * b[0]+256*b[1]+...+256^31*b[31] = b -

4847 * c[0]+256*c[1]+...+256^31*c[31] = c -

4848 * -

4849 * Output: -

4850 * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l -

4851 * where l = 2^252 + 27742317777372353535851937790883648493. */ -

4852 static void sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, -

4853 const uint8_t *c) { -

4854 int64_t a0 = 2097151 & load_3(a); -

4855 int64_t a1 = 2097151 & (load_4(a + 2) >> 5); -

4856 int64_t a2 = 2097151 & (load_3(a + 5) >> 2); -

4857 int64_t a3 = 2097151 & (load_4(a + 7) >> 7); -

4858 int64_t a4 = 2097151 & (load_4(a + 10) >> 4); -

4859 int64_t a5 = 2097151 & (load_3(a + 13) >> 1); -

4860 int64_t a6 = 2097151 & (load_4(a + 15) >> 6); -

4861 int64_t a7 = 2097151 & (load_3(a + 18) >> 3); -

4862 int64_t a8 = 2097151 & load_3(a + 21); -

4863 int64_t a9 = 2097151 & (load_4(a + 23) >> 5); -

4864 int64_t a10 = 2097151 & (load_3(a + 26) >> 2); -

4865 int64_t a11 = (load_4(a + 28) >> 7); -

4866 int64_t b0 = 2097151 & load_3(b); -

4867 int64_t b1 = 2097151 & (load_4(b + 2) >> 5); -

4868 int64_t b2 = 2097151 & (load_3(b + 5) >> 2); -

4869 int64_t b3 = 2097151 & (load_4(b + 7) >> 7); -

4870 int64_t b4 = 2097151 & (load_4(b + 10) >> 4); -

4871 int64_t b5 = 2097151 & (load_3(b + 13) >> 1); -

4872 int64_t b6 = 2097151 & (load_4(b + 15) >> 6); -

4873 int64_t b7 = 2097151 & (load_3(b + 18) >> 3); -

4874 int64_t b8 = 2097151 & load_3(b + 21); -

4875 int64_t b9 = 2097151 & (load_4(b + 23) >> 5); -

4876 int64_t b10 = 2097151 & (load_3(b + 26) >> 2); -

4877 int64_t b11 = (load_4(b + 28) >> 7); -

4878 int64_t c0 = 2097151 & load_3(c); -

4879 int64_t c1 = 2097151 & (load_4(c + 2) >> 5); -

4880 int64_t c2 = 2097151 & (load_3(c + 5) >> 2); -

4881 int64_t c3 = 2097151 & (load_4(c + 7) >> 7); -

4882 int64_t c4 = 2097151 & (load_4(c + 10) >> 4); -

4883 int64_t c5 = 2097151 & (load_3(c + 13) >> 1); -

4884 int64_t c6 = 2097151 & (load_4(c + 15) >> 6); -

4885 int64_t c7 = 2097151 & (load_3(c + 18) >> 3); -

4886 int64_t c8 = 2097151 & load_3(c + 21); -

4887 int64_t c9 = 2097151 & (load_4(c + 23) >> 5); -

4888 int64_t c10 = 2097151 & (load_3(c + 26) >> 2); -

4889 int64_t c11 = (load_4(c + 28) >> 7); -

4890 int64_t s0; -

4891 int64_t s1; -

4892 int64_t s2; -

4893 int64_t s3; -

4894 int64_t s4; -

4895 int64_t s5; -

4896 int64_t s6; -

4897 int64_t s7; -

4898 int64_t s8; -

4899 int64_t s9; -

4900 int64_t s10; -

4901 int64_t s11; -

4902 int64_t s12; -

4903 int64_t s13; -

4904 int64_t s14; -

4905 int64_t s15; -

4906 int64_t s16; -

4907 int64_t s17; -

4908 int64_t s18; -

4909 int64_t s19; -

4910 int64_t s20; -

4911 int64_t s21; -

4912 int64_t s22; -

4913 int64_t s23; -

4914 int64_t carry0; -

4915 int64_t carry1; -

4916 int64_t carry2; -

4917 int64_t carry3; -

4918 int64_t carry4; -

4919 int64_t carry5; -

4920 int64_t carry6; -

4921 int64_t carry7; -

4922 int64_t carry8; -

4923 int64_t carry9; -

4924 int64_t carry10; -

4925 int64_t carry11; -

4926 int64_t carry12; -

4927 int64_t carry13; -

4928 int64_t carry14; -

4929 int64_t carry15; -

4930 int64_t carry16; -

4931 int64_t carry17; -

4932 int64_t carry18; -

4933 int64_t carry19; -

4934 int64_t carry20; -

4935 int64_t carry21; -

4936 int64_t carry22; -

4937 -

4938 s0 = c0 + a0 * b0; -

4939 s1 = c1 + a0 * b1 + a1 * b0; -

4940 s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; -

4941 s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; -

4942 s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; -

4943 s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; -

4944 s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; -

4945 s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + -

4946 a6 * b1 + a7 * b0; -

4947 s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + -

4948 a6 * b2 + a7 * b1 + a8 * b0; -

4949 s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + -

4950 a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; -

4951 s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + -

4952 a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; -

4953 s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + -

4954 a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; -

4955 s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + -

4956 a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; -

4957 s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + -

4958 a9 * b4 + a10 * b3 + a11 * b2; -

4959 s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + -

4960 a10 * b4 + a11 * b3; -

4961 s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + -

4962 a11 * b4; -

4963 s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; -

4964 s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; -

4965 s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; -

4966 s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; -

4967 s20 = a9 * b11 + a10 * b10 + a11 * b9; -

4968 s21 = a10 * b11 + a11 * b10; -

4969 s22 = a11 * b11; -

4970 s23 = 0; -

4971 -

4972 carry0 = (s0 + (1 << 20)) >> 21; -

4973 s1 += carry0; -

4974 s0 -= carry0 * (1 << 21); -

4975 carry2 = (s2 + (1 << 20)) >> 21; -

4976 s3 += carry2; -

4977 s2 -= carry2 * (1 << 21); -

4978 carry4 = (s4 + (1 << 20)) >> 21; -

4979 s5 += carry4; -

4980 s4 -= carry4 * (1 << 21); -

4981 carry6 = (s6 + (1 << 20)) >> 21; -

4982 s7 += carry6; -

4983 s6 -= carry6 * (1 << 21); -

4984 carry8 = (s8 + (1 << 20)) >> 21; -

4985 s9 += carry8; -

4986 s8 -= carry8 * (1 << 21); -

4987 carry10 = (s10 + (1 << 20)) >> 21; -

4988 s11 += carry10; -

4989 s10 -= carry10 * (1 << 21); -

4990 carry12 = (s12 + (1 << 20)) >> 21; -

4991 s13 += carry12; -

4992 s12 -= carry12 * (1 << 21); -

4993 carry14 = (s14 + (1 << 20)) >> 21; -

4994 s15 += carry14; -

4995 s14 -= carry14 * (1 << 21); -

4996 carry16 = (s16 + (1 << 20)) >> 21; -

4997 s17 += carry16; -

4998 s16 -= carry16 * (1 << 21); -

4999 carry18 = (s18 + (1 << 20)) >> 21; -

5000 s19 += carry18; -

5001 s18 -= carry18 * (1 << 21); -

5002 carry20 = (s20 + (1 << 20)) >> 21; -

5003 s21 += carry20; -

5004 s20 -= carry20 * (1 << 21); -

5005 carry22 = (s22 + (1 << 20)) >> 21; -

5006 s23 += carry22; -

5007 s22 -= carry22 * (1 << 21); -

5008 -

5009 carry1 = (s1 + (1 << 20)) >> 21; -

5010 s2 += carry1; -

5011 s1 -= carry1 * (1 << 21); -

5012 carry3 = (s3 + (1 << 20)) >> 21; -

5013 s4 += carry3; -

5014 s3 -= carry3 * (1 << 21); -

5015 carry5 = (s5 + (1 << 20)) >> 21; -

5016 s6 += carry5; -

5017 s5 -= carry5 * (1 << 21); -

5018 carry7 = (s7 + (1 << 20)) >> 21; -

5019 s8 += carry7; -

5020 s7 -= carry7 * (1 << 21); -

5021 carry9 = (s9 + (1 << 20)) >> 21; -

5022 s10 += carry9; -

5023 s9 -= carry9 * (1 << 21); -

5024 carry11 = (s11 + (1 << 20)) >> 21; -

5025 s12 += carry11; -

5026 s11 -= carry11 * (1 << 21); -

5027 carry13 = (s13 + (1 << 20)) >> 21; -

5028 s14 += carry13; -

5029 s13 -= carry13 * (1 << 21); -

5030 carry15 = (s15 + (1 << 20)) >> 21; -

5031 s16 += carry15; -

5032 s15 -= carry15 * (1 << 21); -

5033 carry17 = (s17 + (1 << 20)) >> 21; -

5034 s18 += carry17; -

5035 s17 -= carry17 * (1 << 21); -

5036 carry19 = (s19 + (1 << 20)) >> 21; -

5037 s20 += carry19; -

5038 s19 -= carry19 * (1 << 21); -

5039 carry21 = (s21 + (1 << 20)) >> 21; -

5040 s22 += carry21; -

5041 s21 -= carry21 * (1 << 21); -

5042 -

5043 s11 += s23 * 666643; -

5044 s12 += s23 * 470296; -

5045 s13 += s23 * 654183; -

5046 s14 -= s23 * 997805; -

5047 s15 += s23 * 136657; -

5048 s16 -= s23 * 683901; -

5049 s23 = 0; -

5050 -

5051 s10 += s22 * 666643; -

5052 s11 += s22 * 470296; -

5053 s12 += s22 * 654183; -

5054 s13 -= s22 * 997805; -

5055 s14 += s22 * 136657; -

5056 s15 -= s22 * 683901; -

5057 s22 = 0; -

5058 -

5059 s9 += s21 * 666643; -

5060 s10 += s21 * 470296; -

5061 s11 += s21 * 654183; -

5062 s12 -= s21 * 997805; -

5063 s13 += s21 * 136657; -

5064 s14 -= s21 * 683901; -

5065 s21 = 0; -

5066 -

5067 s8 += s20 * 666643; -

5068 s9 += s20 * 470296; -

5069 s10 += s20 * 654183; -

5070 s11 -= s20 * 997805; -

5071 s12 += s20 * 136657; -

5072 s13 -= s20 * 683901; -

5073 s20 = 0; -

5074 -

5075 s7 += s19 * 666643; -

5076 s8 += s19 * 470296; -

5077 s9 += s19 * 654183; -

5078 s10 -= s19 * 997805; -

5079 s11 += s19 * 136657; -

5080 s12 -= s19 * 683901; -

5081 s19 = 0; -

5082 -

5083 s6 += s18 * 666643; -

5084 s7 += s18 * 470296; -

5085 s8 += s18 * 654183; -

5086 s9 -= s18 * 997805; -

5087 s10 += s18 * 136657; -

5088 s11 -= s18 * 683901; -

5089 s18 = 0; -

5090 -

5091 carry6 = (s6 + (1 << 20)) >> 21; -

5092 s7 += carry6; -

5093 s6 -= carry6 * (1 << 21); -

5094 carry8 = (s8 + (1 << 20)) >> 21; -

5095 s9 += carry8; -

5096 s8 -= carry8 * (1 << 21); -

5097 carry10 = (s10 + (1 << 20)) >> 21; -

5098 s11 += carry10; -

5099 s10 -= carry10 * (1 << 21); -

5100 carry12 = (s12 + (1 << 20)) >> 21; -

5101 s13 += carry12; -

5102 s12 -= carry12 * (1 << 21); -

5103 carry14 = (s14 + (1 << 20)) >> 21; -

5104 s15 += carry14; -

5105 s14 -= carry14 * (1 << 21); -

5106 carry16 = (s16 + (1 << 20)) >> 21; -

5107 s17 += carry16; -

5108 s16 -= carry16 * (1 << 21); -

5109 -

5110 carry7 = (s7 + (1 << 20)) >> 21; -

5111 s8 += carry7; -

5112 s7 -= carry7 * (1 << 21); -

5113 carry9 = (s9 + (1 << 20)) >> 21; -

5114 s10 += carry9; -

5115 s9 -= carry9 * (1 << 21); -

5116 carry11 = (s11 + (1 << 20)) >> 21; -

5117 s12 += carry11; -

5118 s11 -= carry11 * (1 << 21); -

5119 carry13 = (s13 + (1 << 20)) >> 21; -

5120 s14 += carry13; -

5121 s13 -= carry13 * (1 << 21); -

5122 carry15 = (s15 + (1 << 20)) >> 21; -

5123 s16 += carry15; -

5124 s15 -= carry15 * (1 << 21); -

5125 -

5126 s5 += s17 * 666643; -

5127 s6 += s17 * 470296; -

5128 s7 += s17 * 654183; -

5129 s8 -= s17 * 997805; -

5130 s9 += s17 * 136657; -

5131 s10 -= s17 * 683901; -

5132 s17 = 0; -

5133 -

5134 s4 += s16 * 666643; -

5135 s5 += s16 * 470296; -

5136 s6 += s16 * 654183; -

5137 s7 -= s16 * 997805; -

5138 s8 += s16 * 136657; -

5139 s9 -= s16 * 683901; -

5140 s16 = 0; -

5141 -

5142 s3 += s15 * 666643; -

5143 s4 += s15 * 470296; -

5144 s5 += s15 * 654183; -

5145 s6 -= s15 * 997805; -

5146 s7 += s15 * 136657; -

5147 s8 -= s15 * 683901; -

5148 s15 = 0; -

5149 -

5150 s2 += s14 * 666643; -

5151 s3 += s14 * 470296; -

5152 s4 += s14 * 654183; -

5153 s5 -= s14 * 997805; -

5154 s6 += s14 * 136657; -

5155 s7 -= s14 * 683901; -

5156 s14 = 0; -

5157 -

5158 s1 += s13 * 666643; -

5159 s2 += s13 * 470296; -

5160 s3 += s13 * 654183; -

5161 s4 -= s13 * 997805; -

5162 s5 += s13 * 136657; -

5163 s6 -= s13 * 683901; -

5164 s13 = 0; -

5165 -

5166 s0 += s12 * 666643; -

5167 s1 += s12 * 470296; -

5168 s2 += s12 * 654183; -

5169 s3 -= s12 * 997805; -

5170 s4 += s12 * 136657; -

5171 s5 -= s12 * 683901; -

5172 s12 = 0; -

5173 -

5174 carry0 = (s0 + (1 << 20)) >> 21; -

5175 s1 += carry0; -

5176 s0 -= carry0 * (1 << 21); -

5177 carry2 = (s2 + (1 << 20)) >> 21; -

5178 s3 += carry2; -

5179 s2 -= carry2 * (1 << 21); -

5180 carry4 = (s4 + (1 << 20)) >> 21; -

5181 s5 += carry4; -

5182 s4 -= carry4 * (1 << 21); -

5183 carry6 = (s6 + (1 << 20)) >> 21; -

5184 s7 += carry6; -

5185 s6 -= carry6 * (1 << 21); -

5186 carry8 = (s8 + (1 << 20)) >> 21; -

5187 s9 += carry8; -

5188 s8 -= carry8 * (1 << 21); -

5189 carry10 = (s10 + (1 << 20)) >> 21; -

5190 s11 += carry10; -

5191 s10 -= carry10 * (1 << 21); -

5192 -

5193 carry1 = (s1 + (1 << 20)) >> 21; -

5194 s2 += carry1; -

5195 s1 -= carry1 * (1 << 21); -

5196 carry3 = (s3 + (1 << 20)) >> 21; -

5197 s4 += carry3; -

5198 s3 -= carry3 * (1 << 21); -

5199 carry5 = (s5 + (1 << 20)) >> 21; -

5200 s6 += carry5; -

5201 s5 -= carry5 * (1 << 21); -

5202 carry7 = (s7 + (1 << 20)) >> 21; -

5203 s8 += carry7; -

5204 s7 -= carry7 * (1 << 21); -

5205 carry9 = (s9 + (1 << 20)) >> 21; -

5206 s10 += carry9; -

5207 s9 -= carry9 * (1 << 21); -

5208 carry11 = (s11 + (1 << 20)) >> 21; -

5209 s12 += carry11; -

5210 s11 -= carry11 * (1 << 21); -

5211 -

5212 s0 += s12 * 666643; -

5213 s1 += s12 * 470296; -

5214 s2 += s12 * 654183; -

5215 s3 -= s12 * 997805; -

5216 s4 += s12 * 136657; -

5217 s5 -= s12 * 683901; -

5218 s12 = 0; -

5219 -

5220 carry0 = s0 >> 21; -

5221 s1 += carry0; -

5222 s0 -= carry0 * (1 << 21); -

5223 carry1 = s1 >> 21; -

5224 s2 += carry1; -

5225 s1 -= carry1 * (1 << 21); -

5226 carry2 = s2 >> 21; -

5227 s3 += carry2; -

5228 s2 -= carry2 * (1 << 21); -

5229 carry3 = s3 >> 21; -

5230 s4 += carry3; -

5231 s3 -= carry3 * (1 << 21); -

5232 carry4 = s4 >> 21; -

5233 s5 += carry4; -

5234 s4 -= carry4 * (1 << 21); -

5235 carry5 = s5 >> 21; -

5236 s6 += carry5; -

5237 s5 -= carry5 * (1 << 21); -

5238 carry6 = s6 >> 21; -

5239 s7 += carry6; -

5240 s6 -= carry6 * (1 << 21); -

5241 carry7 = s7 >> 21; -

5242 s8 += carry7; -

5243 s7 -= carry7 * (1 << 21); -

5244 carry8 = s8 >> 21; -

5245 s9 += carry8; -

5246 s8 -= carry8 * (1 << 21); -

5247 carry9 = s9 >> 21; -

5248 s10 += carry9; -

5249 s9 -= carry9 * (1 << 21); -

5250 carry10 = s10 >> 21; -

5251 s11 += carry10; -

5252 s10 -= carry10 * (1 << 21); -

5253 carry11 = s11 >> 21; -

5254 s12 += carry11; -

5255 s11 -= carry11 * (1 << 21); -

5256 -

5257 s0 += s12 * 666643; -

5258 s1 += s12 * 470296; -

5259 s2 += s12 * 654183; -

5260 s3 -= s12 * 997805; -

5261 s4 += s12 * 136657; -

5262 s5 -= s12 * 683901; -

5263 s12 = 0; -

5264 -

5265 carry0 = s0 >> 21; -

5266 s1 += carry0; -

5267 s0 -= carry0 * (1 << 21); -

5268 carry1 = s1 >> 21; -

5269 s2 += carry1; -

5270 s1 -= carry1 * (1 << 21); -

5271 carry2 = s2 >> 21; -

5272 s3 += carry2; -

5273 s2 -= carry2 * (1 << 21); -

5274 carry3 = s3 >> 21; -

5275 s4 += carry3; -

5276 s3 -= carry3 * (1 << 21); -

5277 carry4 = s4 >> 21; -

5278 s5 += carry4; -

5279 s4 -= carry4 * (1 << 21); -

5280 carry5 = s5 >> 21; -

5281 s6 += carry5; -

5282 s5 -= carry5 * (1 << 21); -

5283 carry6 = s6 >> 21; -

5284 s7 += carry6; -

5285 s6 -= carry6 * (1 << 21); -

5286 carry7 = s7 >> 21; -

5287 s8 += carry7; -

5288 s7 -= carry7 * (1 << 21); -

5289 carry8 = s8 >> 21; -

5290 s9 += carry8; -

5291 s8 -= carry8 * (1 << 21); -

5292 carry9 = s9 >> 21; -

5293 s10 += carry9; -

5294 s9 -= carry9 * (1 << 21); -

5295 carry10 = s10 >> 21; -

5296 s11 += carry10; -

5297 s10 -= carry10 * (1 << 21); -

5298 -

5299 s[0] = (uint8_t)(s0 >> 0); -

5300 s[1] = (uint8_t)(s0 >> 8); -

5301 s[2] = (uint8_t)((s0 >> 16) | (s1 << 5)); -

5302 s[3] = (uint8_t)(s1 >> 3); -

5303 s[4] = (uint8_t)(s1 >> 11); -

5304 s[5] = (uint8_t)((s1 >> 19) | (s2 << 2)); -

5305 s[6] = (uint8_t)(s2 >> 6); -

5306 s[7] = (uint8_t)((s2 >> 14) | (s3 << 7)); -

5307 s[8] = (uint8_t)(s3 >> 1); -

5308 s[9] = (uint8_t)(s3 >> 9); -

5309 s[10] = (uint8_t)((s3 >> 17) | (s4 << 4)); -

5310 s[11] = (uint8_t)(s4 >> 4); -

5311 s[12] = (uint8_t)(s4 >> 12); -

5312 s[13] = (uint8_t)((s4 >> 20) | (s5 << 1)); -

5313 s[14] = (uint8_t)(s5 >> 7); -

5314 s[15] = (uint8_t)((s5 >> 15) | (s6 << 6)); -

5315 s[16] = (uint8_t)(s6 >> 2); -

5316 s[17] = (uint8_t)(s6 >> 10); -

5317 s[18] = (uint8_t)((s6 >> 18) | (s7 << 3)); -

5318 s[19] = (uint8_t)(s7 >> 5); -

5319 s[20] = (uint8_t)(s7 >> 13); -

5320 s[21] = (uint8_t)(s8 >> 0); -

5321 s[22] = (uint8_t)(s8 >> 8); -

5322 s[23] = (uint8_t)((s8 >> 16) | (s9 << 5)); -

5323 s[24] = (uint8_t)(s9 >> 3); -

5324 s[25] = (uint8_t)(s9 >> 11); -

5325 s[26] = (uint8_t)((s9 >> 19) | (s10 << 2)); -

5326 s[27] = (uint8_t)(s10 >> 6); -

5327 s[28] = (uint8_t)((s10 >> 14) | (s11 << 7)); -

5328 s[29] = (uint8_t)(s11 >> 1); -

5329 s[30] = (uint8_t)(s11 >> 9); -

5330 s[31] = (uint8_t)(s11 >> 17); -

5331

}

executed 11 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

5332 -

5333 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, -

5334 const uint8_t public_key[32], const uint8_t private_key[32]) { -

5335 uint8_t az[SHA512_DIGEST_LENGTH]; -

5336 uint8_t nonce[SHA512_DIGEST_LENGTH]; -

5337 ge_p3 R; -

5338 uint8_t hram[SHA512_DIGEST_LENGTH]; -

5339 SHA512_CTX hash_ctx; -

5340 -

5341 SHA512_Init(&hash_ctx); -

5342 SHA512_Update(&hash_ctx, private_key, 32); -

5343 SHA512_Final(az, &hash_ctx); -

5344 -

5345 az[0] &= 248; -

5346 az[31] &= 63; -

5347 az[31] |= 64; -

5348 -

5349 SHA512_Init(&hash_ctx); -

5350 SHA512_Update(&hash_ctx, az + 32, 32); -

5351 SHA512_Update(&hash_ctx, message, message_len); -

5352 SHA512_Final(nonce, &hash_ctx); -

5353 -

5354 x25519_sc_reduce(nonce); -

5355 ge_scalarmult_base(&R, nonce); -

5356 ge_p3_tobytes(out_sig, &R); -

5357 -

5358 SHA512_Init(&hash_ctx); -

5359 SHA512_Update(&hash_ctx, out_sig, 32); -

5360 SHA512_Update(&hash_ctx, public_key, 32); -

5361 SHA512_Update(&hash_ctx, message, message_len); -

5362 SHA512_Final(hram, &hash_ctx); -

5363 -

5364 x25519_sc_reduce(hram); -

5365 sc_muladd(out_sig + 32, hram, az, nonce); -

5366 -

5367 OPENSSL_cleanse(&hash_ctx, sizeof(hash_ctx)); -

5368 OPENSSL_cleanse(nonce, sizeof(nonce)); -

5369 OPENSSL_cleanse(az, sizeof(az)); -

5370 -

5371

return 1;

executed 11 times by 1 test: return 1;

Executed by:

libcrypto.so.1.1

5372 } -

5373 -

5374 int ED25519_verify(const uint8_t *message, size_t message_len, -

5375 const uint8_t signature[64], const uint8_t public_key[32]) { -

5376 ge_p3 A; -

5377 uint8_t rcopy[32]; -

5378 uint8_t scopy[32]; -

5379 SHA512_CTX hash_ctx; -

5380 ge_p2 R; -

5381 uint8_t rcheck[32]; -

5382 uint8_t h[SHA512_DIGEST_LENGTH]; -

5383 -

5384

if ((signature[63] & 224) != 0 ||

(signature[63] & 224) != 0	Description
TRUE	never evaluated
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

0-10

5385

ge_frombytes_vartime(&A, public_key) != 0) {

ge_frombytes_v...blic_key) != 0	Description
TRUE	never evaluated
FALSE	evaluated 10 times by 1 test Evaluated by: libcrypto.so.1.1

0-10

5386

return 0;

never executed: return 0;

5387 } -

5388 -

5389 fe_neg(A.X, A.X); -

5390 fe_neg(A.T, A.T); -

5391 -

5392 memcpy(rcopy, signature, 32); -

5393 memcpy(scopy, signature + 32, 32); -

5394 -

5395 SHA512_Init(&hash_ctx); -

5396 SHA512_Update(&hash_ctx, signature, 32); -

5397 SHA512_Update(&hash_ctx, public_key, 32); -

5398 SHA512_Update(&hash_ctx, message, message_len); -

5399 SHA512_Final(h, &hash_ctx); -

5400 -

5401 x25519_sc_reduce(h); -

5402 -

5403 ge_double_scalarmult_vartime(&R, h, &A, scopy); -

5404 -

5405 ge_tobytes(rcheck, &R); -

5406 -

5407

return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;

executed 10 times by 1 test: return CRYPTO_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0;

Executed by:

libcrypto.so.1.1

5408 } -

5409 -

5410 void ED25519_public_from_private(uint8_t out_public_key[32], -

5411 const uint8_t private_key[32]) { -

5412 uint8_t az[SHA512_DIGEST_LENGTH]; -

5413 ge_p3 A; -

5414 -

5415 SHA512(private_key, 32, az); -

5416 -

5417 az[0] &= 248; -

5418 az[31] &= 63; -

5419 az[31] |= 64; -

5420 -

5421 ge_scalarmult_base(&A, az); -

5422 ge_p3_tobytes(out_public_key, &A); -

5423 -

5424 OPENSSL_cleanse(az, sizeof(az)); -

5425

}

executed 35 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

5426 -

5427 int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32], -

5428 const uint8_t peer_public_value[32]) { -

5429 static const uint8_t kZeros[32] = {0}; -

5430 x25519_scalar_mult(out_shared_key, private_key, peer_public_value); -

5431 /* The all-zero output results when the input is a point of small order. */ -

5432

return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;

executed 2916 times by 1 test: return CRYPTO_memcmp(kZeros, out_shared_key, 32) != 0;

Executed by:

libcrypto.so.1.1

2916

5433 } -

5434 -

5435 void X25519_public_from_private(uint8_t out_public_value[32], -

5436 const uint8_t private_key[32]) { -

5437 uint8_t e[32]; -

5438 ge_p3 A; -

5439 fe zplusy, zminusy, zminusy_inv; -

5440 -

5441 memcpy(e, private_key, 32); -

5442 e[0] &= 248; -

5443 e[31] &= 127; -

5444 e[31] |= 64; -

5445 -

5446 ge_scalarmult_base(&A, e); -

5447 -

5448 /* We only need the u-coordinate of the curve25519 point. The map is -

5449 * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ -

5450 fe_add(zplusy, A.Z, A.Y); -

5451 fe_sub(zminusy, A.Z, A.Y); -

5452 fe_invert(zminusy_inv, zminusy); -

5453 fe_mul(zplusy, zplusy, zminusy_inv); -

5454 fe_tobytes(out_public_value, zplusy); -

5455 -

5456 OPENSSL_cleanse(e, sizeof(e)); -

5457

}

executed 6229 times by 1 test: end of block

Executed by:

libcrypto.so.1.1

6229

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