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curve25519.c

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/home/opencoverage/opencoverage/guest-scripts/libressl/src/crypto/curve25519/curve25519.c

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1 /* -

3 * -

4 * Permission to use, copy, modify, and/or distribute this software for any -

5 * purpose with or without fee is hereby granted, provided that the above -

6 * copyright notice and this permission notice appear in all copies. -

7 * -

8 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES -

9 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF -

10 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY -

11 * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES -

12 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION -

13 * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN -

14 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. -

15 */ -

16 -

17 /* -

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

19 * 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as -

20 * public domain but this file has the ISC license just to keep licencing -

21 * simple. -

22 * -

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

24 */ -

25 -

26 #include <stdlib.h> -

27 #include <string.h> -

28 -

29 #include <openssl/curve25519.h> -

30 -

31 #ifdef ED25519 -

32 #include <openssl/sha.h> -

33 #endif -

34 -

35 #include "curve25519_internal.h" -

36 -

37 static const int64_t kBottom25Bits = 0x1ffffffLL; -

38 static const int64_t kBottom26Bits = 0x3ffffffLL; -

39 static const int64_t kTop39Bits = 0xfffffffffe000000LL; -

40 static const int64_t kTop38Bits = 0xfffffffffc000000LL; -

41 -

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

43 uint64_t result; -

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

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

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

return result;

executed 8184 times by 3 tests: return result;

Executed by:

ssltest
tlstest
x25519test

8184

48 } -

49 -

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

51 uint64_t result; -

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

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

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

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

return result;

executed 2046 times by 3 tests: return result;

Executed by:

ssltest
tlstest
x25519test

2046

57 } -

58 -

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

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

61 int64_t h0 = load_4(s); -

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

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

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

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

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

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

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

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

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

71 int64_t carry0; -

72 int64_t carry1; -

73 int64_t carry2; -

74 int64_t carry3; -

75 int64_t carry4; -

76 int64_t carry5; -

77 int64_t carry6; -

78 int64_t carry7; -

79 int64_t carry8; -

80 int64_t carry9; -

81 -

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

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

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

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

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

87 -

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

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

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

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

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

93 -

94 h[0] = h0; -

95 h[1] = h1; -

96 h[2] = h2; -

97 h[3] = h3; -

98 h[4] = h4; -

99 h[5] = h5; -

100 h[6] = h6; -

101 h[7] = h7; -

102 h[8] = h8; -

103 h[9] = h9; -

104

}

executed 1023 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1023

105 -

106 /* Preconditions: -

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

108 * -

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

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

111 * -

112 * Proof: -

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

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

115 * -

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

117 * Then 0<y<1. -

118 * -

119 * Write r=h-pq. -

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

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

122 * -

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

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

125 * -

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

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

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

129 int32_t h0 = h[0]; -

130 int32_t h1 = h[1]; -

131 int32_t h2 = h[2]; -

132 int32_t h3 = h[3]; -

133 int32_t h4 = h[4]; -

134 int32_t h5 = h[5]; -

135 int32_t h6 = h[6]; -

136 int32_t h7 = h[7]; -

137 int32_t h8 = h[8]; -

138 int32_t h9 = h[9]; -

139 int32_t q; -

140 -

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

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

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

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

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

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

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

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

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

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

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

152 -

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

154 h0 += 19 * q; -

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

156 -

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

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

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

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

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

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

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

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

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

166 h9 &= kBottom25Bits; -

167 /* h10 = carry9 */ -

168 -

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

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

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

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

173 -

174 s[0] = h0 >> 0; -

175 s[1] = h0 >> 8; -

176 s[2] = h0 >> 16; -

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

178 s[4] = h1 >> 6; -

179 s[5] = h1 >> 14; -

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

181 s[7] = h2 >> 5; -

182 s[8] = h2 >> 13; -

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

184 s[10] = h3 >> 3; -

185 s[11] = h3 >> 11; -

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

187 s[13] = h4 >> 2; -

188 s[14] = h4 >> 10; -

189 s[15] = h4 >> 18; -

190 s[16] = h5 >> 0; -

191 s[17] = h5 >> 8; -

192 s[18] = h5 >> 16; -

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

194 s[20] = h6 >> 7; -

195 s[21] = h6 >> 15; -

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

197 s[23] = h7 >> 5; -

198 s[24] = h7 >> 13; -

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

200 s[26] = h8 >> 4; -

201 s[27] = h8 >> 12; -

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

203 s[29] = h9 >> 2; -

204 s[30] = h9 >> 10; -

205 s[31] = h9 >> 18; -

206

}

executed 1023 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1023

207 -

208 /* h = f */ -

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

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

211

}

executed 1023 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1023

212 -

213 /* h = 0 */ -

214

static

executed 1023 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

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

executed 1023 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1023

215 -

216 /* h = 1 */ -

217 static void fe_1(fe h) { -

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

219 h[0] = 1; -

220

}

executed 2046 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

2046

221 -

222 /* h = f + g -

223 * Can overlap h with f or g. -

224 * -

225 * Preconditions: -

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

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

228 * -

229 * Postconditions: -

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

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

232 unsigned i; -

233

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

i < 10	Description
TRUE	evaluated 10434600 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1043460 times by 3 tests Evaluated by: ssltest tlstest x25519test

1043460-10434600

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

235

}

executed 10434600 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

10434600

236

}

executed 1043460 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1043460

237 -

238 /* h = f - g -

239 * Can overlap h with f or g. -

240 * -

241 * Preconditions: -

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

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

244 * -

245 * Postconditions: -

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

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

248 unsigned i; -

249

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

i < 10	Description
TRUE	evaluated 10434600 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1043460 times by 3 tests Evaluated by: ssltest tlstest x25519test

1043460-10434600

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

251

}

executed 10434600 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

10434600

252

}

executed 1043460 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1043460

253 -

254 /* h = f * g -

255 * Can overlap h with f or g. -

256 * -

257 * Preconditions: -

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

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

260 * -

261 * Postconditions: -

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

263 * -

264 * Notes on implementation strategy: -

265 * -

266 * Using schoolbook multiplication. -

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

268 * -

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

270 * cheaper than 64-bit postcomputations. -

271 * -

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

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

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

275 * -

276 * There are 12 carries below. -

277 * 10 of them are 2-way parallelizable and vectorizable. -

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

279 * -

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

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

282 int32_t f0 = f[0]; -

283 int32_t f1 = f[1]; -

284 int32_t f2 = f[2]; -

285 int32_t f3 = f[3]; -

286 int32_t f4 = f[4]; -

287 int32_t f5 = f[5]; -

288 int32_t f6 = f[6]; -

289 int32_t f7 = f[7]; -

290 int32_t f8 = f[8]; -

291 int32_t f9 = f[9]; -

292 int32_t g0 = g[0]; -

293 int32_t g1 = g[1]; -

294 int32_t g2 = g[2]; -

295 int32_t g3 = g[3]; -

296 int32_t g4 = g[4]; -

297 int32_t g5 = g[5]; -

298 int32_t g6 = g[6]; -

299 int32_t g7 = g[7]; -

300 int32_t g8 = g[8]; -

301 int32_t g9 = g[9]; -

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

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

304 int32_t g3_19 = 19 * g3; -

305 int32_t g4_19 = 19 * g4; -

306 int32_t g5_19 = 19 * g5; -

307 int32_t g6_19 = 19 * g6; -

308 int32_t g7_19 = 19 * g7; -

309 int32_t g8_19 = 19 * g8; -

310 int32_t g9_19 = 19 * g9; -

311 int32_t f1_2 = 2 * f1; -

312 int32_t f3_2 = 2 * f3; -

313 int32_t f5_2 = 2 * f5; -

314 int32_t f7_2 = 2 * f7; -

315 int32_t f9_2 = 2 * f9; -

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

426 int64_t carry0; -

427 int64_t carry1; -

428 int64_t carry2; -

429 int64_t carry3; -

430 int64_t carry4; -

431 int64_t carry5; -

432 int64_t carry6; -

433 int64_t carry7; -

434 int64_t carry8; -

435 int64_t carry9; -

436 -

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

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

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

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

441 -

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

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

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

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

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

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

448 -

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

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

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

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

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

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

455 -

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

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

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

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

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

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

462 -

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

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

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

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

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

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

469 -

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

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

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

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

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

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

476 -

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

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

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

480 -

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

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

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

484 -

485 h[0] = h0; -

486 h[1] = h1; -

487 h[2] = h2; -

488 h[3] = h3; -

489 h[4] = h4; -

490 h[5] = h5; -

491 h[6] = h6; -

492 h[7] = h7; -

493 h[8] = h8; -

494 h[9] = h9; -

495

}

executed 1316601 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1316601

496 -

497 /* h = f * f -

498 * Can overlap h with f. -

499 * -

500 * Preconditions: -

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

502 * -

503 * Postconditions: -

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

505 * -

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

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

508 int32_t f0 = f[0]; -

509 int32_t f1 = f[1]; -

510 int32_t f2 = f[2]; -

511 int32_t f3 = f[3]; -

512 int32_t f4 = f[4]; -

513 int32_t f5 = f[5]; -

514 int32_t f6 = f[6]; -

515 int32_t f7 = f[7]; -

516 int32_t f8 = f[8]; -

517 int32_t f9 = f[9]; -

518 int32_t f0_2 = 2 * f0; -

519 int32_t f1_2 = 2 * f1; -

520 int32_t f2_2 = 2 * f2; -

521 int32_t f3_2 = 2 * f3; -

522 int32_t f4_2 = 2 * f4; -

523 int32_t f5_2 = 2 * f5; -

524 int32_t f6_2 = 2 * f6; -

525 int32_t f7_2 = 2 * f7; -

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

596 int64_t carry0; -

597 int64_t carry1; -

598 int64_t carry2; -

599 int64_t carry3; -

600 int64_t carry4; -

601 int64_t carry5; -

602 int64_t carry6; -

603 int64_t carry7; -

604 int64_t carry8; -

605 int64_t carry9; -

606 -

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

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

609 -

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

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

612 -

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

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

615 -

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

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

618 -

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

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

621 -

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

623 -

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

625 -

626 h[0] = h0; -

627 h[1] = h1; -

628 h[2] = h2; -

629 h[3] = h3; -

630 h[4] = h4; -

631 h[5] = h5; -

632 h[6] = h6; -

633 h[7] = h7; -

634 h[8] = h8; -

635 h[9] = h9; -

636

}

executed 1303302 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1303302

637 -

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

639 fe t0; -

640 fe t1; -

641 fe t2; -

642 fe t3; -

643 int i; -

644 -

645 fe_sq(t0, z); -

646

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

i < 1	Description
TRUE	never evaluated
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

0-1023

647 fe_sq(t0, t0); -

648

}

never executed: end of block

649 fe_sq(t1, t0); -

650

for (i = 1; i < 2; ++i) {

i < 2	Description
TRUE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023

651 fe_sq(t1, t1); -

652

}

executed 1023 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1023

653 fe_mul(t1, z, t1); -

654 fe_mul(t0, t0, t1); -

655 fe_sq(t2, t0); -

656

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

i < 1	Description
TRUE	never evaluated
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

0-1023

657 fe_sq(t2, t2); -

658

}

never executed: end of block

659 fe_mul(t1, t1, t2); -

660 fe_sq(t2, t1); -

661

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

i < 5	Description
TRUE	evaluated 4092 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-4092

662 fe_sq(t2, t2); -

663

}

executed 4092 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

4092

664 fe_mul(t1, t2, t1); -

665 fe_sq(t2, t1); -

666

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

i < 10	Description
TRUE	evaluated 9207 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-9207

667 fe_sq(t2, t2); -

668

}

executed 9207 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

9207

669 fe_mul(t2, t2, t1); -

670 fe_sq(t3, t2); -

671

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

i < 20	Description
TRUE	evaluated 19437 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-19437

672 fe_sq(t3, t3); -

673

}

executed 19437 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

19437

674 fe_mul(t2, t3, t2); -

675 fe_sq(t2, t2); -

676

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

i < 10	Description
TRUE	evaluated 9207 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-9207

677 fe_sq(t2, t2); -

678

}

executed 9207 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

9207

679 fe_mul(t1, t2, t1); -

680 fe_sq(t2, t1); -

681

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

i < 50	Description
TRUE	evaluated 50127 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-50127

682 fe_sq(t2, t2); -

683

}

executed 50127 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

50127

684 fe_mul(t2, t2, t1); -

685 fe_sq(t3, t2); -

686

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

i < 100	Description
TRUE	evaluated 101277 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-101277

687 fe_sq(t3, t3); -

688

}

executed 101277 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

101277

689 fe_mul(t2, t3, t2); -

690 fe_sq(t2, t2); -

691

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

i < 50	Description
TRUE	evaluated 50127 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-50127

692 fe_sq(t2, t2); -

693

}

executed 50127 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

50127

694 fe_mul(t1, t2, t1); -

695 fe_sq(t1, t1); -

696

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

i < 5	Description
TRUE	evaluated 4092 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-4092

697 fe_sq(t1, t1); -

698

}

executed 4092 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

4092

699 fe_mul(out, t1, t0); -

700

}

executed 1023 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1023

701 -

702 /* h = -f -

703 * -

704 * Preconditions: -

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

706 * -

707 * Postconditions: -

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

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

710 unsigned i; -

711

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

i < 10	Description
TRUE	never evaluated
FALSE	never evaluated

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

713

}

never executed: end of block

714

}

never executed: end of block

715 -

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

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

718 * -

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

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

721 b = 0-b; -

722 unsigned i; -

723

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

i < 10	Description
TRUE	never evaluated
FALSE	never evaluated

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

725 x &= b; -

726 f[i] ^= x; -

727

}

never executed: end of block

728

}

never executed: end of block

729 -

730 /* return 0 if f == 0 -

731 * return 1 if f != 0 -

732 * -

733 * Preconditions: -

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

735 static int fe_isnonzero(const fe f) { -

736 uint8_t s[32]; -

737 fe_tobytes(s, f); -

738 -

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

740

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

never executed: return timingsafe_memcmp(s, zero, sizeof(zero)) != 0;

741 } -

742 -

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

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

745 * -

746 * Preconditions: -

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

748 static int fe_isnegative(const fe f) { -

749 uint8_t s[32]; -

750 fe_tobytes(s, f); -

751

return s[0] & 1;

never executed: return s[0] & 1;

752 } -

753 -

754 /* h = 2 * f * f -

755 * Can overlap h with f. -

756 * -

757 * Preconditions: -

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

759 * -

760 * Postconditions: -

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

762 * -

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

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

765 int32_t f0 = f[0]; -

766 int32_t f1 = f[1]; -

767 int32_t f2 = f[2]; -

768 int32_t f3 = f[3]; -

769 int32_t f4 = f[4]; -

770 int32_t f5 = f[5]; -

771 int32_t f6 = f[6]; -

772 int32_t f7 = f[7]; -

773 int32_t f8 = f[8]; -

774 int32_t f9 = f[9]; -

775 int32_t f0_2 = 2 * f0; -

776 int32_t f1_2 = 2 * f1; -

777 int32_t f2_2 = 2 * f2; -

778 int32_t f3_2 = 2 * f3; -

779 int32_t f4_2 = 2 * f4; -

780 int32_t f5_2 = 2 * f5; -

781 int32_t f6_2 = 2 * f6; -

782 int32_t f7_2 = 2 * f7; -

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

853 int64_t carry0; -

854 int64_t carry1; -

855 int64_t carry2; -

856 int64_t carry3; -

857 int64_t carry4; -

858 int64_t carry5; -

859 int64_t carry6; -

860 int64_t carry7; -

861 int64_t carry8; -

862 int64_t carry9; -

863 -

864 h0 += h0; -

865 h1 += h1; -

866 h2 += h2; -

867 h3 += h3; -

868 h4 += h4; -

869 h5 += h5; -

870 h6 += h6; -

871 h7 += h7; -

872 h8 += h8; -

873 h9 += h9; -

874 -

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

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

877 -

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

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

880 -

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

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

883 -

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

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

886 -

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

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

889 -

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

891 -

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

893 -

894 h[0] = h0; -

895 h[1] = h1; -

896 h[2] = h2; -

897 h[3] = h3; -

898 h[4] = h4; -

899 h[5] = h5; -

900 h[6] = h6; -

901 h[7] = h7; -

902 h[8] = h8; -

903 h[9] = h9; -

904

}

never executed: end of block

905 -

906 static void fe_pow22523(fe out, const fe z) { -

907 fe t0; -

908 fe t1; -

909 fe t2; -

910 int i; -

911 -

912 fe_sq(t0, z); -

913

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

i < 1	Description
TRUE	never evaluated
FALSE	never evaluated

914 fe_sq(t0, t0); -

915

}

never executed: end of block

916 fe_sq(t1, t0); -

917

for (i = 1; i < 2; ++i) {

i < 2	Description
TRUE	never evaluated
FALSE	never evaluated

918 fe_sq(t1, t1); -

919

}

never executed: end of block

920 fe_mul(t1, z, t1); -

921 fe_mul(t0, t0, t1); -

922 fe_sq(t0, t0); -

923

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

i < 1	Description
TRUE	never evaluated
FALSE	never evaluated

924 fe_sq(t0, t0); -

925

}

never executed: end of block

926 fe_mul(t0, t1, t0); -

927 fe_sq(t1, t0); -

928

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

i < 5	Description
TRUE	never evaluated
FALSE	never evaluated

929 fe_sq(t1, t1); -

930

}

never executed: end of block

931 fe_mul(t0, t1, t0); -

932 fe_sq(t1, t0); -

933

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

i < 10	Description
TRUE	never evaluated
FALSE	never evaluated

934 fe_sq(t1, t1); -

935

}

never executed: end of block

936 fe_mul(t1, t1, t0); -

937 fe_sq(t2, t1); -

938

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

i < 20	Description
TRUE	never evaluated
FALSE	never evaluated

939 fe_sq(t2, t2); -

940

}

never executed: end of block

941 fe_mul(t1, t2, t1); -

942 fe_sq(t1, t1); -

943

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

i < 10	Description
TRUE	never evaluated
FALSE	never evaluated

944 fe_sq(t1, t1); -

945

}

never executed: end of block

946 fe_mul(t0, t1, t0); -

947 fe_sq(t1, t0); -

948

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

i < 50	Description
TRUE	never evaluated
FALSE	never evaluated

949 fe_sq(t1, t1); -

950

}

never executed: end of block

951 fe_mul(t1, t1, t0); -

952 fe_sq(t2, t1); -

953

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

i < 100	Description
TRUE	never evaluated
FALSE	never evaluated

954 fe_sq(t2, t2); -

955

}

never executed: end of block

956 fe_mul(t1, t2, t1); -

957 fe_sq(t1, t1); -

958

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

i < 50	Description
TRUE	never evaluated
FALSE	never evaluated

959 fe_sq(t1, t1); -

960

}

never executed: end of block

961 fe_mul(t0, t1, t0); -

962 fe_sq(t0, t0); -

963

for (i = 1; i < 2; ++i) {

i < 2	Description
TRUE	never evaluated
FALSE	never evaluated

964 fe_sq(t0, t0); -

965

}

never executed: end of block

966 fe_mul(out, t0, z); -

967

}

never executed: end of block

968 -

969 void x25519_ge_tobytes(uint8_t *s, const ge_p2 *h) { -

970 fe recip; -

971 fe x; -

972 fe y; -

973 -

974 fe_invert(recip, h->Z); -

975 fe_mul(x, h->X, recip); -

976 fe_mul(y, h->Y, recip); -

977 fe_tobytes(s, y); -

978 s[31] ^= fe_isnegative(x) << 7; -

979

}

never executed: end of block

980 -

981 #ifdef ED25519 -

982 static void ge_p3_tobytes(uint8_t *s, const ge_p3 *h) { -

983 fe recip; -

984 fe x; -

985 fe y; -

986 -

987 fe_invert(recip, h->Z); -

988 fe_mul(x, h->X, recip); -

989 fe_mul(y, h->Y, recip); -

990 fe_tobytes(s, y); -

991 s[31] ^= fe_isnegative(x) << 7; -

992 } -

993 #endif -

994 -

995 static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, -

996 -8787816, -6275908, -3247719, -18696448, -12055116}; -

997 -

998 static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, -

999 -272473, -25146209, -2005654, 326686, 11406482}; -

1000 -

1001 int x25519_ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { -

1002 fe u; -

1003 fe v; -

1004 fe v3; -

1005 fe vxx; -

1006 fe check; -

1007 -

1008 fe_frombytes(h->Y, s); -

1009 fe_1(h->Z); -

1010 fe_sq(u, h->Y); -

1011 fe_mul(v, u, d); -

1012 fe_sub(u, u, h->Z); /* u = y^2-1 */ -

1013 fe_add(v, v, h->Z); /* v = dy^2+1 */ -

1014 -

1015 fe_sq(v3, v); -

1016 fe_mul(v3, v3, v); /* v3 = v^3 */ -

1017 fe_sq(h->X, v3); -

1018 fe_mul(h->X, h->X, v); -

1019 fe_mul(h->X, h->X, u); /* x = uv^7 */ -

1020 -

1021 fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ -

1022 fe_mul(h->X, h->X, v3); -

1023 fe_mul(h->X, h->X, u); /* x = uv^3(uv^7)^((q-5)/8) */ -

1024 -

1025 fe_sq(vxx, h->X); -

1026 fe_mul(vxx, vxx, v); -

1027 fe_sub(check, vxx, u); /* vx^2-u */ -

1028

if (fe_isnonzero(check)) {

fe_isnonzero(check)	Description
TRUE	never evaluated
FALSE	never evaluated

1029 fe_add(check, vxx, u); /* vx^2+u */ -

1030

if (fe_isnonzero(check)) {

fe_isnonzero(check)	Description
TRUE	never evaluated
FALSE	never evaluated

1031

return -1;

never executed: return -1;

1032 } -

1033 fe_mul(h->X, h->X, sqrtm1); -

1034

}

never executed: end of block

1035 -

1036

if (fe_isnegative(h->X) != (s[31] >> 7)) {

fe_isnegative(...= (s[31] >> 7)	Description
TRUE	never evaluated
FALSE	never evaluated

1037 fe_neg(h->X, h->X); -

1038

}

never executed: end of block

1039 -

1040 fe_mul(h->T, h->X, h->Y); -

1041

return 0;

never executed: return 0;

1042 } -

1043 -

1044 static void ge_p2_0(ge_p2 *h) { -

1045 fe_0(h->X); -

1046 fe_1(h->Y); -

1047 fe_1(h->Z); -

1048

}

never executed: end of block

1049 -

1050 static void ge_p3_0(ge_p3 *h) { -

1051 fe_0(h->X); -

1052 fe_1(h->Y); -

1053 fe_1(h->Z); -

1054 fe_0(h->T); -

1055

}

never executed: end of block

1056 -

1057 static void ge_cached_0(ge_cached *h) { -

1058 fe_1(h->YplusX); -

1059 fe_1(h->YminusX); -

1060 fe_1(h->Z); -

1061 fe_0(h->T2d); -

1062

}

never executed: end of block

1063 -

1064 static void ge_precomp_0(ge_precomp *h) { -

1065 fe_1(h->yplusx); -

1066 fe_1(h->yminusx); -

1067 fe_0(h->xy2d); -

1068

}

never executed: end of block

1069 -

1070 /* r = p */ -

1071 static void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { -

1072 fe_copy(r->X, p->X); -

1073 fe_copy(r->Y, p->Y); -

1074 fe_copy(r->Z, p->Z); -

1075

}

never executed: end of block

1076 -

1077 static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, -

1078 15978800, -12551817, -6495438, 29715968, 9444199}; -

1079 -

1080 /* r = p */ -

1081 void x25519_ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { -

1082 fe_add(r->YplusX, p->Y, p->X); -

1083 fe_sub(r->YminusX, p->Y, p->X); -

1084 fe_copy(r->Z, p->Z); -

1085 fe_mul(r->T2d, p->T, d2); -

1086

}

never executed: end of block

1087 -

1088 /* r = p */ -

1089 void x25519_ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { -

1090 fe_mul(r->X, p->X, p->T); -

1091 fe_mul(r->Y, p->Y, p->Z); -

1092 fe_mul(r->Z, p->Z, p->T); -

1093

}

never executed: end of block

1094 -

1095 /* r = p */ -

1096 void x25519_ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { -

1097 fe_mul(r->X, p->X, p->T); -

1098 fe_mul(r->Y, p->Y, p->Z); -

1099 fe_mul(r->Z, p->Z, p->T); -

1100 fe_mul(r->T, p->X, p->Y); -

1101

}

never executed: end of block

1102 -

1103 /* r = p */ -

1104 static void ge_p1p1_to_cached(ge_cached *r, const ge_p1p1 *p) { -

1105 ge_p3 t; -

1106 x25519_ge_p1p1_to_p3(&t, p); -

1107 x25519_ge_p3_to_cached(r, &t); -

1108

}

never executed: end of block

1109 -

1110 /* r = 2 * p */ -

1111 static void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { -

1112 fe t0; -

1113 -

1114 fe_sq(r->X, p->X); -

1115 fe_sq(r->Z, p->Y); -

1116 fe_sq2(r->T, p->Z); -

1117 fe_add(r->Y, p->X, p->Y); -

1118 fe_sq(t0, r->Y); -

1119 fe_add(r->Y, r->Z, r->X); -

1120 fe_sub(r->Z, r->Z, r->X); -

1121 fe_sub(r->X, t0, r->Y); -

1122 fe_sub(r->T, r->T, r->Z); -

1123

}

never executed: end of block

1124 -

1125 /* r = 2 * p */ -

1126 static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { -

1127 ge_p2 q; -

1128 ge_p3_to_p2(&q, p); -

1129 ge_p2_dbl(r, &q); -

1130

}

never executed: end of block

1131 -

1132 /* r = p + q */ -

1133 static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { -

1134 fe t0; -

1135 -

1136 fe_add(r->X, p->Y, p->X); -

1137 fe_sub(r->Y, p->Y, p->X); -

1138 fe_mul(r->Z, r->X, q->yplusx); -

1139 fe_mul(r->Y, r->Y, q->yminusx); -

1140 fe_mul(r->T, q->xy2d, p->T); -

1141 fe_add(t0, p->Z, p->Z); -

1142 fe_sub(r->X, r->Z, r->Y); -

1143 fe_add(r->Y, r->Z, r->Y); -

1144 fe_add(r->Z, t0, r->T); -

1145 fe_sub(r->T, t0, r->T); -

1146

}

never executed: end of block

1147 -

1148 #ifdef ED25519 -

1149 /* r = p - q */ -

1150 static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { -

1151 fe t0; -

1152 -

1153 fe_add(r->X, p->Y, p->X); -

1154 fe_sub(r->Y, p->Y, p->X); -

1155 fe_mul(r->Z, r->X, q->yminusx); -

1156 fe_mul(r->Y, r->Y, q->yplusx); -

1157 fe_mul(r->T, q->xy2d, p->T); -

1158 fe_add(t0, p->Z, p->Z); -

1159 fe_sub(r->X, r->Z, r->Y); -

1160 fe_add(r->Y, r->Z, r->Y); -

1161 fe_sub(r->Z, t0, r->T); -

1162 fe_add(r->T, t0, r->T); -

1163 } -

1164 #endif -

1165 -

1166 /* r = p + q */ -

1167 void x25519_ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { -

1168 fe t0; -

1169 -

1170 fe_add(r->X, p->Y, p->X); -

1171 fe_sub(r->Y, p->Y, p->X); -

1172 fe_mul(r->Z, r->X, q->YplusX); -

1173 fe_mul(r->Y, r->Y, q->YminusX); -

1174 fe_mul(r->T, q->T2d, p->T); -

1175 fe_mul(r->X, p->Z, q->Z); -

1176 fe_add(t0, r->X, r->X); -

1177 fe_sub(r->X, r->Z, r->Y); -

1178 fe_add(r->Y, r->Z, r->Y); -

1179 fe_add(r->Z, t0, r->T); -

1180 fe_sub(r->T, t0, r->T); -

1181

}

never executed: end of block

1182 -

1183 /* r = p - q */ -

1184 void x25519_ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { -

1185 fe t0; -

1186 -

1187 fe_add(r->X, p->Y, p->X); -

1188 fe_sub(r->Y, p->Y, p->X); -

1189 fe_mul(r->Z, r->X, q->YminusX); -

1190 fe_mul(r->Y, r->Y, q->YplusX); -

1191 fe_mul(r->T, q->T2d, p->T); -

1192 fe_mul(r->X, p->Z, q->Z); -

1193 fe_add(t0, r->X, r->X); -

1194 fe_sub(r->X, r->Z, r->Y); -

1195 fe_add(r->Y, r->Z, r->Y); -

1196 fe_sub(r->Z, t0, r->T); -

1197 fe_add(r->T, t0, r->T); -

1198

}

never executed: end of block

1199 -

1200 static uint8_t equal(signed char b, signed char c) { -

1201 uint8_t ub = b; -

1202 uint8_t uc = c; -

1203 uint8_t x = ub ^ uc; /* 0: yes; 1..255: no */ -

1204 uint32_t y = x; /* 0: yes; 1..255: no */ -

1205 y -= 1; /* 4294967295: yes; 0..254: no */ -

1206 y >>= 31; /* 1: yes; 0: no */ -

1207

return y;

never executed: return y;

1208 } -

1209 -

1210 static void cmov(ge_precomp *t, const ge_precomp *u, uint8_t b) { -

1211 fe_cmov(t->yplusx, u->yplusx, b); -

1212 fe_cmov(t->yminusx, u->yminusx, b); -

1213 fe_cmov(t->xy2d, u->xy2d, b); -

1214

}

never executed: end of block

1215 -

1216 void x25519_ge_scalarmult_small_precomp( -

1217 ge_p3 *h, const uint8_t a[32], const uint8_t precomp_table[15 * 2 * 32]) { -

1218 /* precomp_table is first expanded into matching |ge_precomp| -

1219 * elements. */ -

1220 ge_precomp multiples[15]; -

1221 -

1222 unsigned i; -

1223

for (i = 0; i < 15; i++) {

i < 15	Description
TRUE	never evaluated
FALSE	never evaluated

1224 const uint8_t *bytes = &precomp_table[i*(2 * 32)]; -

1225 fe x, y; -

1226 fe_frombytes(x, bytes); -

1227 fe_frombytes(y, bytes + 32); -

1228 -

1229 ge_precomp *out = &multiples[i]; -

1230 fe_add(out->yplusx, y, x); -

1231 fe_sub(out->yminusx, y, x); -

1232 fe_mul(out->xy2d, x, y); -

1233 fe_mul(out->xy2d, out->xy2d, d2); -

1234

}

never executed: end of block

1235 -

1236 /* See the comment above |k25519SmallPrecomp| about the structure of the -

1237 * precomputed elements. This loop does 64 additions and 64 doublings to -

1238 * calculate the result. */ -

1239 ge_p3_0(h); -

1240 -

1241

for (i = 63; i < 64; i--) {

i < 64	Description
TRUE	never evaluated
FALSE	never evaluated

1242 unsigned j; -

1243 signed char index = 0; -

1244 -

1245

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

j < 4	Description
TRUE	never evaluated
FALSE	never evaluated

1246 const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7)); -

1247 index |= (bit << j); -

1248

}

never executed: end of block

1249 -

1250 ge_precomp e; -

1251 ge_precomp_0(&e); -

1252 -

1253

for (j = 1; j < 16; j++) {

j < 16	Description
TRUE	never evaluated
FALSE	never evaluated

1254 cmov(&e, &multiples[j-1], equal(index, j)); -

1255

}

never executed: end of block

1256 -

1257 ge_cached cached; -

1258 ge_p1p1 r; -

1259 x25519_ge_p3_to_cached(&cached, h); -

1260 x25519_ge_add(&r, h, &cached); -

1261 x25519_ge_p1p1_to_p3(h, &r); -

1262 -

1263 ge_madd(&r, h, &e); -

1264 x25519_ge_p1p1_to_p3(h, &r); -

1265

}

never executed: end of block

1266

}

never executed: end of block

1267 -

1268 #if defined(OPENSSL_SMALL) -

1269 -

1270 /* This block of code replaces the standard base-point table with a much smaller -

1271 * one. The standard table is 30,720 bytes while this one is just 960. -

1272 * -

1273 * This table contains 15 pairs of group elements, (x, y), where each field -

1274 * element is serialised with |fe_tobytes|. If |i| is the index of the group -

1275 * element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀ -

1276 * is the most significant bit). The value of the group element is then: -

1277 * (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */ -

1278 static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = { -

1279 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, -

1280 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, -

1281 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66, -

1282 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, -

1283 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, -

1284 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e, -

1285 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4, -

1286 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62, -

1287 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba, -

1288 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd, -

1289 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61, -

1290 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c, -

1291 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c, -

1292 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5, -

1293 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3, -

1294 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18, -

1295 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2, -

1296 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95, -

1297 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b, -

1298 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90, -

1299 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52, -

1300 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb, -

1301 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c, -

1302 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e, -

1303 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e, -

1304 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a, -

1305 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43, -

1306 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53, -

1307 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8, -

1308 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89, -

1309 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef, -

1310 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60, -

1311 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a, -

1312 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8, -

1313 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54, -

1314 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b, -

1315 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd, -

1316 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb, -

1317 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c, -

1318 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b, -

1319 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63, -

1320 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a, -

1321 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07, -

1322 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa, -

1323 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a, -

1324 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84, -

1325 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc, -

1326 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42, -

1327 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0, -

1328 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0, -

1329 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a, -

1330 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5, -

1331 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c, -

1332 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27, -

1333 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31, -

1334 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c, -

1335 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87, -

1336 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0, -

1337 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23, -

1338 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2, -

1339 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87, -

1340 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d, -

1341 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b, -

1342 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d, -

1343 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6, -

1344 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84, -

1345 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04, -

1346 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19, -

1347 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b, -

1348 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a, -

1349 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea, -

1350 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30, -

1351 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7, -

1352 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa, -

1353 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5, -

1354 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71, -

1355 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab, -

1356 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb, -

1357 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c, -

1358 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25, -

1359 }; -

1360 -

1361 void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { -

1362 x25519_ge_scalarmult_small_precomp(h, a, k25519SmallPrecomp); -

1363 } -

1364 -

1365 #else -

1366 -

1367 /* k25519Precomp[i][j] = (j+1)*256^i*B */ -

1368 static const ge_precomp k25519Precomp[32][8] = { -

1369 { -

1370 { -

1371 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, -

1372 27544626, -11754271, -6079156, 2047605}, -

1373 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, -

1374 5043384, 19500929, -15469378}, -

1375 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, -

1376 29287919, 11864899, -24514362, -4438546}, -

1377 }, -

1378 { -

1379 {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -

1380 -11717903, -3814571, -358445, -10211303}, -

1381 {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -

1382 -15616551, 11189268, -26829678, -5319081}, -

1383 {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -

1384 -3128826, -9541118, -15472047, -4166697}, -

1385 }, -

1386 { -

1387 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, -

1388 27787600, -14772189, 28944400, -1550024}, -

1389 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, -

1390 16354577, -11775962, 7689662, 11199574}, -

1391 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, -

1392 7512774, 10017326, -17749093, -9920357}, -

1393 }, -

1394 { -

1395 {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -

1396 -28926210, 15006023, 3284568, -6276540}, -

1397 {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, -

1398 7464579, 9656445, 13059162, 10374397}, -

1399 {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -

1400 -3839045, -641708, -101325}, -

1401 }, -

1402 { -

1403 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, -

1404 32867885, 14515107, -15438304, 10819380}, -

1405 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, -

1406 12483688, -12668491, 5581306}, -

1407 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, -

1408 28542350, 13850243, -23678021, -15815942}, -

1409 }, -

1410 { -

1411 {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -

1412 -19188627, -15224819, -9818940, -12085777}, -

1413 {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -

1414 -15689887, 1762328, 14866737}, -

1415 {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -

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1778 28311253, 5358056, -23319780, 541964}, -

1779 {16259219, 3261970, 2309254, -15534474, -16885711, -4581916, -

1780 24134070, -16705829, -13337066, -13552195}, -

1781 }, -

1782 { -

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1784 -2399684, -717351, 690426, 14876244}, -

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1786 -13068804, -12297348, -22380984, 6618999}, -

1787 {-1538174, 11685646, 12944378, 13682314, -24389511, -14413193, -

1788 8044829, -13817328, 32239829, -5652762}, -

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1790 { -

1791 {-18603066, 4762990, -926250, 8885304, -28412480, -3187315, 9781647, -

1792 -10350059, 32779359, 5095274}, -

1793 {-33008130, -5214506, -32264887, -3685216, 9460461, -9327423, -

1794 -24601656, 14506724, 21639561, -2630236}, -

1795 {-16400943, -13112215, 25239338, 15531969, 3987758, -4499318, -

1796 -1289502, -6863535, 17874574, 558605}, -

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1798 { -

1799 {-13600129, 10240081, 9171883, 16131053, -20869254, 9599700, -

1800 33499487, 5080151, 2085892, 5119761}, -

1801 {-22205145, -2519528, -16381601, 414691, -25019550, 2170430, -

1802 30634760, -8363614, -31999993, -5759884}, -

1803 {-6845704, 15791202, 8550074, -1312654, 29928809, -12092256, -

1804 27534430, -7192145, -22351378, 12961482}, -

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1806 { -

1807 {-24492060, -9570771, 10368194, 11582341, -23397293, -2245287, -

1808 16533930, 8206996, -30194652, -5159638}, -

1809 {-11121496, -3382234, 2307366, 6362031, -135455, 8868177, -16835630, -

1810 7031275, 7589640, 8945490}, -

1811 {-32152748, 8917967, 6661220, -11677616, -1192060, -15793393, -

1812 7251489, -11182180, 24099109, -14456170}, -

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1814 { -

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1816 -19118182, -13289025, -6231896, -10280736}, -

1817 {10853594, 10721687, 26480089, 5861829, -22995819, 1972175, -

1818 -1866647, -10557898, -3363451, -6441124}, -

1819 {-17002408, 5906790, 221599, -6563147, 7828208, -13248918, 24362661, -

1820 -2008168, -13866408, 7421392}, -

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1822 { -

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1824 -21175108, 15441252, 28826358, -4123029}, -

1825 {6267086, 9695052, 7709135, -16603597, -32869068, -1886135, -

1826 14795160, -7840124, 13746021, -1742048}, -

1827 {28584902, 7787108, -6732942, -15050729, 22846041, -7571236, -

1828 -3181936, -363524, 4771362, -8419958}, -

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1830 }, -

1831 { -

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1834 33543569, -12141695, 3569627, 11342593}, -

1835 {26514989, 4740088, 27912651, 3697550, 19331575, -11472339, 6809886, -

1836 4608608, 7325975, -14801071}, -

1837 {-11618399, -14554430, -24321212, 7655128, -1369274, 5214312, -

1838 -27400540, 10258390, -17646694, -8186692}, -

1839 }, -

1840 { -

1841 {11431204, 15823007, 26570245, 14329124, 18029990, 4796082, -

1842 -31446179, 15580664, 9280358, -3973687}, -

1843 {-160783, -10326257, -22855316, -4304997, -20861367, -13621002, -

1844 -32810901, -11181622, -15545091, 4387441}, -

1845 {-20799378, 12194512, 3937617, -5805892, -27154820, 9340370, -

1846 -24513992, 8548137, 20617071, -7482001}, -

1847 }, -

1848 { -

1849 {-938825, -3930586, -8714311, 16124718, 24603125, -6225393, -

1850 -13775352, -11875822, 24345683, 10325460}, -

1851 {-19855277, -1568885, -22202708, 8714034, 14007766, 6928528, -

1852 16318175, -1010689, 4766743, 3552007}, -

1853 {-21751364, -16730916, 1351763, -803421, -4009670, 3950935, 3217514, -

1854 14481909, 10988822, -3994762}, -

1855 }, -

1856 { -

1857 {15564307, -14311570, 3101243, 5684148, 30446780, -8051356, -

1858 12677127, -6505343, -8295852, 13296005}, -

1859 {-9442290, 6624296, -30298964, -11913677, -4670981, -2057379, -

1860 31521204, 9614054, -30000824, 12074674}, -

1861 {4771191, -135239, 14290749, -13089852, 27992298, 14998318, -

1862 -1413936, -1556716, 29832613, -16391035}, -

1863 }, -

1864 { -

1865 {7064884, -7541174, -19161962, -5067537, -18891269, -2912736, -

1866 25825242, 5293297, -27122660, 13101590}, -

1867 {-2298563, 2439670, -7466610, 1719965, -27267541, -16328445, -

1868 32512469, -5317593, -30356070, -4190957}, -

1869 {-30006540, 10162316, -33180176, 3981723, -16482138, -13070044, -

1870 14413974, 9515896, 19568978, 9628812}, -

1871 }, -

1872 { -

1873 {33053803, 199357, 15894591, 1583059, 27380243, -4580435, -17838894, -

1874 -6106839, -6291786, 3437740}, -

1875 {-18978877, 3884493, 19469877, 12726490, 15913552, 13614290, -

1876 -22961733, 70104, 7463304, 4176122}, -

1877 {-27124001, 10659917, 11482427, -16070381, 12771467, -6635117, -

1878 -32719404, -5322751, 24216882, 5944158}, -

1879 }, -

1880 { -

1881 {8894125, 7450974, -2664149, -9765752, -28080517, -12389115, -

1882 19345746, 14680796, 11632993, 5847885}, -

1883 {26942781, -2315317, 9129564, -4906607, 26024105, 11769399, -

1884 -11518837, 6367194, -9727230, 4782140}, -

1885 {19916461, -4828410, -22910704, -11414391, 25606324, -5972441, -

1886 33253853, 8220911, 6358847, -1873857}, -

1887 }, -

1888 { -

1889 {801428, -2081702, 16569428, 11065167, 29875704, 96627, 7908388, -

1890 -4480480, -13538503, 1387155}, -

1891 {19646058, 5720633, -11416706, 12814209, 11607948, 12749789, -

1892 14147075, 15156355, -21866831, 11835260}, -

1893 {19299512, 1155910, 28703737, 14890794, 2925026, 7269399, 26121523, -

1894 15467869, -26560550, 5052483}, -

1895 }, -

1896 }, -

1897 { -

1898 { -

1899 {-3017432, 10058206, 1980837, 3964243, 22160966, 12322533, -6431123, -

1900 -12618185, 12228557, -7003677}, -

1901 {32944382, 14922211, -22844894, 5188528, 21913450, -8719943, -

1902 4001465, 13238564, -6114803, 8653815}, -

1903 {22865569, -4652735, 27603668, -12545395, 14348958, 8234005, -

1904 24808405, 5719875, 28483275, 2841751}, -

1905 }, -

1906 { -

1907 {-16420968, -1113305, -327719, -12107856, 21886282, -15552774, -

1908 -1887966, -315658, 19932058, -12739203}, -

1909 {-11656086, 10087521, -8864888, -5536143, -19278573, -3055912, -

1910 3999228, 13239134, -4777469, -13910208}, -

1911 {1382174, -11694719, 17266790, 9194690, -13324356, 9720081, -

1912 20403944, 11284705, -14013818, 3093230}, -

1913 }, -

1914 { -

1915 {16650921, -11037932, -1064178, 1570629, -8329746, 7352753, -302424, -

1916 16271225, -24049421, -6691850}, -

1917 {-21911077, -5927941, -4611316, -5560156, -31744103, -10785293, -

1918 24123614, 15193618, -21652117, -16739389}, -

1919 {-9935934, -4289447, -25279823, 4372842, 2087473, 10399484, -

1920 31870908, 14690798, 17361620, 11864968}, -

1921 }, -

1922 { -

1923 {-11307610, 6210372, 13206574, 5806320, -29017692, -13967200, -

1924 -12331205, -7486601, -25578460, -16240689}, -

1925 {14668462, -12270235, 26039039, 15305210, 25515617, 4542480, -

1926 10453892, 6577524, 9145645, -6443880}, -

1927 {5974874, 3053895, -9433049, -10385191, -31865124, 3225009, -

1928 -7972642, 3936128, -5652273, -3050304}, -

1929 }, -

1930 { -

1931 {30625386, -4729400, -25555961, -12792866, -20484575, 7695099, -

1932 17097188, -16303496, -27999779, 1803632}, -

1933 {-3553091, 9865099, -5228566, 4272701, -5673832, -16689700, -

1934 14911344, 12196514, -21405489, 7047412}, -

1935 {20093277, 9920966, -11138194, -5343857, 13161587, 12044805, -

1936 -32856851, 4124601, -32343828, -10257566}, -

1937 }, -

1938 { -

1939 {-20788824, 14084654, -13531713, 7842147, 19119038, -13822605, -

1940 4752377, -8714640, -21679658, 2288038}, -

1941 {-26819236, -3283715, 29965059, 3039786, -14473765, 2540457, -

1942 29457502, 14625692, -24819617, 12570232}, -

1943 {-1063558, -11551823, 16920318, 12494842, 1278292, -5869109, -

1944 -21159943, -3498680, -11974704, 4724943}, -

1945 }, -

1946 { -

1947 {17960970, -11775534, -4140968, -9702530, -8876562, -1410617, -

1948 -12907383, -8659932, -29576300, 1903856}, -

1949 {23134274, -14279132, -10681997, -1611936, 20684485, 15770816, -

1950 -12989750, 3190296, 26955097, 14109738}, -

1951 {15308788, 5320727, -30113809, -14318877, 22902008, 7767164, -

1952 29425325, -11277562, 31960942, 11934971}, -

1953 }, -

1954 { -

1955 {-27395711, 8435796, 4109644, 12222639, -24627868, 14818669, -

1956 20638173, 4875028, 10491392, 1379718}, -

1957 {-13159415, 9197841, 3875503, -8936108, -1383712, -5879801, -

1958 33518459, 16176658, 21432314, 12180697}, -

1959 {-11787308, 11500838, 13787581, -13832590, -22430679, 10140205, -

1960 1465425, 12689540, -10301319, -13872883}, -

1961 }, -

1962 }, -

1963 { -

1964 { -

1965 {5414091, -15386041, -21007664, 9643570, 12834970, 1186149, -

1966 -2622916, -1342231, 26128231, 6032912}, -

1967 {-26337395, -13766162, 32496025, -13653919, 17847801, -12669156, -

1968 3604025, 8316894, -25875034, -10437358}, -

1969 {3296484, 6223048, 24680646, -12246460, -23052020, 5903205, -

1970 -8862297, -4639164, 12376617, 3188849}, -

1971 }, -

1972 { -

1973 {29190488, -14659046, 27549113, -1183516, 3520066, -10697301, -

1974 32049515, -7309113, -16109234, -9852307}, -

1975 {-14744486, -9309156, 735818, -598978, -20407687, -5057904, -

1976 25246078, -15795669, 18640741, -960977}, -

1977 {-6928835, -16430795, 10361374, 5642961, 4910474, 12345252, -

1978 -31638386, -494430, 10530747, 1053335}, -

1979 }, -

1980 { -

1981 {-29265967, -14186805, -13538216, -12117373, -19457059, -10655384, -

1982 -31462369, -2948985, 24018831, 15026644}, -

1983 {-22592535, -3145277, -2289276, 5953843, -13440189, 9425631, -

1984 25310643, 13003497, -2314791, -15145616}, -

1985 {-27419985, -603321, -8043984, -1669117, -26092265, 13987819, -

1986 -27297622, 187899, -23166419, -2531735}, -

1987 }, -

1988 { -

1989 {-21744398, -13810475, 1844840, 5021428, -10434399, -15911473, -

1990 9716667, 16266922, -5070217, 726099}, -

1991 {29370922, -6053998, 7334071, -15342259, 9385287, 2247707, -

1992 -13661962, -4839461, 30007388, -15823341}, -

1993 {-936379, 16086691, 23751945, -543318, -1167538, -5189036, 9137109, -

1994 730663, 9835848, 4555336}, -

1995 }, -

1996 { -

1997 {-23376435, 1410446, -22253753, -12899614, 30867635, 15826977, -

1998 17693930, 544696, -11985298, 12422646}, -

1999 {31117226, -12215734, -13502838, 6561947, -9876867, -12757670, -

2000 -5118685, -4096706, 29120153, 13924425}, -

2001 {-17400879, -14233209, 19675799, -2734756, -11006962, -5858820, -

2002 -9383939, -11317700, 7240931, -237388}, -

2003 }, -

2004 { -

2005 {-31361739, -11346780, -15007447, -5856218, -22453340, -12152771, -

2006 1222336, 4389483, 3293637, -15551743}, -

2007 {-16684801, -14444245, 11038544, 11054958, -13801175, -3338533, -

2008 -24319580, 7733547, 12796905, -6335822}, -

2009 {-8759414, -10817836, -25418864, 10783769, -30615557, -9746811, -

2010 -28253339, 3647836, 3222231, -11160462}, -

2011 }, -

2012 { -

2013 {18606113, 1693100, -25448386, -15170272, 4112353, 10045021, -

2014 23603893, -2048234, -7550776, 2484985}, -

2015 {9255317, -3131197, -12156162, -1004256, 13098013, -9214866, -

2016 16377220, -2102812, -19802075, -3034702}, -

2017 {-22729289, 7496160, -5742199, 11329249, 19991973, -3347502, -

2018 -31718148, 9936966, -30097688, -10618797}, -

2019 }, -

2020 { -

2021 {21878590, -5001297, 4338336, 13643897, -3036865, 13160960, -

2022 19708896, 5415497, -7360503, -4109293}, -

2023 {27736861, 10103576, 12500508, 8502413, -3413016, -9633558, -

2024 10436918, -1550276, -23659143, -8132100}, -

2025 {19492550, -12104365, -29681976, -852630, -3208171, 12403437, -

2026 30066266, 8367329, 13243957, 8709688}, -

2027 }, -

2028 }, -

2029 { -

2030 { -

2031 {12015105, 2801261, 28198131, 10151021, 24818120, -4743133, -

2032 -11194191, -5645734, 5150968, 7274186}, -

2033 {2831366, -12492146, 1478975, 6122054, 23825128, -12733586, -

2034 31097299, 6083058, 31021603, -9793610}, -

2035 {-2529932, -2229646, 445613, 10720828, -13849527, -11505937, -

2036 -23507731, 16354465, 15067285, -14147707}, -

2037 }, -

2038 { -

2039 {7840942, 14037873, -33364863, 15934016, -728213, -3642706, -

2040 21403988, 1057586, -19379462, -12403220}, -

2041 {915865, -16469274, 15608285, -8789130, -24357026, 6060030, -

2042 -17371319, 8410997, -7220461, 16527025}, -

2043 {32922597, -556987, 20336074, -16184568, 10903705, -5384487, -

2044 16957574, 52992, 23834301, 6588044}, -

2045 }, -

2046 { -

2047 {32752030, 11232950, 3381995, -8714866, 22652988, -10744103, -

2048 17159699, 16689107, -20314580, -1305992}, -

2049 {-4689649, 9166776, -25710296, -10847306, 11576752, 12733943, -

2050 7924251, -2752281, 1976123, -7249027}, -

2051 {21251222, 16309901, -2983015, -6783122, 30810597, 12967303, 156041, -

2052 -3371252, 12331345, -8237197}, -

2053 }, -

2054 { -

2055 {8651614, -4477032, -16085636, -4996994, 13002507, 2950805, -

2056 29054427, -5106970, 10008136, -4667901}, -

2057 {31486080, 15114593, -14261250, 12951354, 14369431, -7387845, -

2058 16347321, -13662089, 8684155, -10532952}, -

2059 {19443825, 11385320, 24468943, -9659068, -23919258, 2187569, -

2060 -26263207, -6086921, 31316348, 14219878}, -

2061 }, -

2062 { -

2063 {-28594490, 1193785, 32245219, 11392485, 31092169, 15722801, -

2064 27146014, 6992409, 29126555, 9207390}, -

2065 {32382935, 1110093, 18477781, 11028262, -27411763, -7548111, -

2066 -4980517, 10843782, -7957600, -14435730}, -

2067 {2814918, 7836403, 27519878, -7868156, -20894015, -11553689, -

2068 -21494559, 8550130, 28346258, 1994730}, -

2069 }, -

2070 { -

2071 {-19578299, 8085545, -14000519, -3948622, 2785838, -16231307, -

2072 -19516951, 7174894, 22628102, 8115180}, -

2073 {-30405132, 955511, -11133838, -15078069, -32447087, -13278079, -

2074 -25651578, 3317160, -9943017, 930272}, -

2075 {-15303681, -6833769, 28856490, 1357446, 23421993, 1057177, -

2076 24091212, -1388970, -22765376, -10650715}, -

2077 }, -

2078 { -

2079 {-22751231, -5303997, -12907607, -12768866, -15811511, -7797053, -

2080 -14839018, -16554220, -1867018, 8398970}, -

2081 {-31969310, 2106403, -4736360, 1362501, 12813763, 16200670, -

2082 22981545, -6291273, 18009408, -15772772}, -

2083 {-17220923, -9545221, -27784654, 14166835, 29815394, 7444469, -

2084 29551787, -3727419, 19288549, 1325865}, -

2085 }, -

2086 { -

2087 {15100157, -15835752, -23923978, -1005098, -26450192, 15509408, -

2088 12376730, -3479146, 33166107, -8042750}, -

2089 {20909231, 13023121, -9209752, 16251778, -5778415, -8094914, -

2090 12412151, 10018715, 2213263, -13878373}, -

2091 {32529814, -11074689, 30361439, -16689753, -9135940, 1513226, -

2092 22922121, 6382134, -5766928, 8371348}, -

2093 }, -

2094 }, -

2095 { -

2096 { -

2097 {9923462, 11271500, 12616794, 3544722, -29998368, -1721626, -

2098 12891687, -8193132, -26442943, 10486144}, -

2099 {-22597207, -7012665, 8587003, -8257861, 4084309, -12970062, 361726, -

2100 2610596, -23921530, -11455195}, -

2101 {5408411, -1136691, -4969122, 10561668, 24145918, 14240566, -

2102 31319731, -4235541, 19985175, -3436086}, -

2103 }, -

2104 { -

2105 {-13994457, 16616821, 14549246, 3341099, 32155958, 13648976, -

2106 -17577068, 8849297, 65030, 8370684}, -

2107 {-8320926, -12049626, 31204563, 5839400, -20627288, -1057277, -

2108 -19442942, 6922164, 12743482, -9800518}, -

2109 {-2361371, 12678785, 28815050, 4759974, -23893047, 4884717, -

2110 23783145, 11038569, 18800704, 255233}, -

2111 }, -

2112 { -

2113 {-5269658, -1773886, 13957886, 7990715, 23132995, 728773, 13393847, -

2114 9066957, 19258688, -14753793}, -

2115 {-2936654, -10827535, -10432089, 14516793, -3640786, 4372541, -

2116 -31934921, 2209390, -1524053, 2055794}, -

2117 {580882, 16705327, 5468415, -2683018, -30926419, -14696000, -

2118 -7203346, -8994389, -30021019, 7394435}, -

2119 }, -

2120 { -

2121 {23838809, 1822728, -15738443, 15242727, 8318092, -3733104, -

2122 -21672180, -3492205, -4821741, 14799921}, -

2123 {13345610, 9759151, 3371034, -16137791, 16353039, 8577942, 31129804, -

2124 13496856, -9056018, 7402518}, -

2125 {2286874, -4435931, -20042458, -2008336, -13696227, 5038122, -

2126 11006906, -15760352, 8205061, 1607563}, -

2127 }, -

2128 { -

2129 {14414086, -8002132, 3331830, -3208217, 22249151, -5594188, -

2130 18364661, -2906958, 30019587, -9029278}, -

2131 {-27688051, 1585953, -10775053, 931069, -29120221, -11002319, -

2132 -14410829, 12029093, 9944378, 8024}, -

2133 {4368715, -3709630, 29874200, -15022983, -20230386, -11410704, -

2134 -16114594, -999085, -8142388, 5640030}, -

2135 }, -

2136 { -

2137 {10299610, 13746483, 11661824, 16234854, 7630238, 5998374, 9809887, -

2138 -16694564, 15219798, -14327783}, -

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3221 {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -

3222 -33102500, 9160280, 8473550, -3256838}, -

3223 {24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -

3224 -7689309, -16335821, -24568481, 11788948}, -

3225 }, -

3226 { -

3227 {-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -

3228 -20037437, 10410733, -24568470, -1458691}, -

3229 {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, -

3230 11871841, -12505194, -18513325, 8464118}, -

3231 {-23400612, 8348507, -14585951, -861714, -3950205, -6373419, -

3232 14325289, 8628612, 33313881, -8370517}, -

3233 }, -

3234 { -

3235 {-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -

3236 -24805667, -10236854, -8940735, -5818269}, -

3237 {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, -

3238 15989197, -12838188, 28358192, -4253904}, -

3239 {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -

3240 -16637684, 4072016, -5351664, 5596589}, -

3241 }, -

3242 { -

3243 {-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, -

3244 29266239, 2557221, 1768301, 15373193}, -

3245 {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -

3246 -4504991, -24660491, 3442910}, -

3247 {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, -

3248 22597931, 7176455, -18585478, 13365930}, -

3249 }, -

3250 { -

3251 {-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -

3252 -8570186, -9689599, -3031667}, -

3253 {25008904, -10771599, -4305031, -9638010, 16265036, 15721635, -

3254 683793, -11823784, 15723479, -15163481}, -

3255 {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, -

3256 11879682, 5400171, 519526, -1235876}, -

3257 }, -

3258 { -

3259 {22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -

3260 -20353881, 7315967, 16648397, 7605640}, -

3261 {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, -

3262 23994942, -5281555, -9468848, 4763278}, -

3263 {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, -

3264 31088447, -7764523, -11356529, 728112}, -

3265 }, -

3266 { -

3267 {26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -

3268 -4273545, -12555558, -29365436, -5498272}, -

3269 {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, -

3270 12327945, 10750447, 10014012}, -

3271 {-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -

3272 -27481051, -666732, 3424691, 7540221}, -

3273 }, -

3274 { -

3275 {30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -

3276 -16317219, -9244265, 15258046}, -

3277 {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, -

3278 2711395, 1062915, -5136345}, -

3279 {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -

3280 -6066489, 12194497, 32960380, 1459310}, -

3281 }, -

3282 }, -

3283 { -

3284 { -

3285 {19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -

3286 -6101885, 18638003, -11174937}, -

3287 {31395534, 15098109, 26581030, 8030562, -16527914, -5007134, -

3288 9012486, -7584354, -6643087, -5442636}, -

3289 {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, -

3290 9677543, -32294889, -6456008}, -

3291 }, -

3292 { -

3293 {-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -

3294 -7839692, -7852844, -8138429}, -

3295 {-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -

3296 -27333451, 10754588, -9431476, 5203576}, -

3297 {31834314, 14135496, -770007, 5159118, 20917671, -16768096, -

3298 -7467973, -7337524, 31809243, 7347066}, -

3299 }, -

3300 { -

3301 {-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, -

3302 19797970, -12211255, 15192876, -2087490}, -

3303 {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, -

3304 10609330, 12694420, 33473243, -13382104}, -

3305 {33184999, 11180355, 15832085, -11385430, -1633671, 225884, -

3306 15089336, -11023903, -6135662, 14480053}, -

3307 }, -

3308 { -

3309 {31308717, -5619998, 31030840, -1897099, 15674547, -6582883, -

3310 5496208, 13685227, 27595050, 8737275}, -

3311 {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -

3312 -31008351, -12610604, 26498114, 66511}, -

3313 {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, -

3314 30540766, -4286747, -13327787, -7515095}, -

3315 }, -

3316 { -

3317 {-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, -

3318 8205540, 13585437, -17127465, 15115439}, -

3319 {23711543, -672915, 31206561, -8362711, 6164647, -9709987, -

3320 -33535882, -1426096, 8236921, 16492939}, -

3321 {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, -

3322 19574902, 10071562, 6708380, -6222424}, -

3323 }, -

3324 { -

3325 {2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, -

3326 9328700, 29955601, -11678310}, -

3327 {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -

3328 -25892142, -12635595, -9917575, 6216608}, -

3329 {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, -

3330 24822830, -6146567, -26767480, 7525079}, -

3331 }, -

3332 { -

3333 {-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -

3334 -910336, -2782495, -19386633, 11994101}, -

3335 {21691500, -13624626, -641331, -14367021, 3285881, -3483596, -

3336 -25064666, 9718258, -7477437, 13381418}, -

3337 {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, -

3338 23111648, -6375247, 28535282, 15779576}, -

3339 }, -

3340 { -

3341 {30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -

3342 -14068454, 12021730, 9955285, -16303356}, -

3343 {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -

3344 -18426029, 9924399, 20194861, 13380996}, -

3345 {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -

3346 -1984914, 15707771, 26342023, 10146099}, -

3347 }, -

3348 }, -

3349 { -

3350 { -

3351 {-26016874, -219943, 21339191, -41388, 19745256, -2878700, -

3352 -29637280, 2227040, 21612326, -545728}, -

3353 {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, -

3354 25764461, 12243797, -20856566, 11649658}, -

3355 {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, -

3356 6114064, 33514190, 2333242}, -

3357 }, -

3358 { -

3359 {-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -

3360 -6679750, -12670638, 24350578, -13450001}, -

3361 {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -

3362 -31536088, -10406836, 8317860, 12352766}, -

3363 {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -

3364 -23552096, -2287550, 20712163, 6719373}, -

3365 }, -

3366 { -

3367 {26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -

3368 -3763210, 26224235, -3297458}, -

3369 {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, -

3370 21728352, 9493610, 18620611, -16428628}, -

3371 {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -

3372 -5269471, -9725556, -30701573, -16479657}, -

3373 }, -

3374 { -

3375 {-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, -

3376 12248509, -5240639, 13735342, 1934062}, -

3377 {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -

3378 -15136294, -3765346, -21277997, 5473616}, -

3379 {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -

3380 -7125085, 12469656, 29111212, -5451014}, -

3381 }, -

3382 { -

3383 {24244947, -15050407, -26262976, 2791540, -14997599, 16666678, -

3384 24367466, 6388839, -10295587, 452383}, -

3385 {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -

3386 -24236251, -5915248, 15766062, 8407814}, -

3387 {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -

3388 -8917023, -4388953, -8067909, 2276718}, -

3389 }, -

3390 { -

3391 {30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -

3392 -23827587, 5096219, 22740376, -7303417}, -

3393 {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, -

3394 24051124, 13742383, -15637599, 13295222}, -

3395 {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -

3396 -17720195, -4612972, -4451357, -14669444}, -

3397 }, -

3398 { -

3399 {-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -

3400 -2469266, -4141880, 7770569, 9620597}, -

3401 {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -

3402 -1694323, -33502340, -14767970}, -

3403 {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, -

3404 1220118, 30494170, -11440799}, -

3405 }, -

3406 { -

3407 {-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -

3408 -26739026, 926050, -1684339, -13333647}, -

3409 {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, -

3410 9021034, 9078865, 3353509, 4033511}, -

3411 {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, -

3412 23161163, 8839127, 27485041, 7356032}, -

3413 }, -

3414 }, -

3415 { -

3416 { -

3417 {9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, -

3418 2625015, 28431036, -16771834}, -

3419 {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -

3420 -22545972, 14150565, 15970762, 4099461}, -

3421 {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, -

3422 13617293, -9937143, 11465739, 8317062}, -

3423 }, -

3424 { -

3425 {-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, -

3426 14898637, 3848455, 20969334, -5157516}, -

3427 {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -

3428 -21610826, -3649888, 11177095, 14989547}, -

3429 {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, -

3430 13515641, 2581286, -28487508, 9930240}, -

3431 }, -

3432 { -

3433 {-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, -

3434 18345767, -13403753, 16291481, -5314038}, -

3435 {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, -

3436 6957617, 4368891, 9788741}, -

3437 {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -

3438 -21722536, -8613148, 16250552, -11111103}, -

3439 }, -

3440 { -

3441 {-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, -

3442 10604807, -30190403, 4782747}, -

3443 {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -

3444 -9981571, 4383045, 22546403, 437323}, -

3445 {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, -

3446 27343084, 2786261, -30633590, -14097016}, -

3447 }, -

3448 { -

3449 {-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -

3450 -19690631, 2355319, -19284671, -6114373}, -

3451 {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, -

3452 18952177, 15496498, -29380133, 11754228}, -

3453 {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, -

3454 7141596, 11724556, 22761615, -10134141}, -

3455 }, -

3456 { -

3457 {16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -

3458 -28741185, -12227393, 32851222, 11717399}, -

3459 {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, -

3460 31474879, 3483633, -1193175, -4030831}, -

3461 {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, -

3462 33142652, 6546660, -19985279, -3948376}, -

3463 }, -

3464 { -

3465 {-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -

3466 -8537131, -12833048, -30772034, -15486313}, -

3467 {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -

3468 -31135347, -16049879, 10928917, 3011958}, -

3469 {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -

3470 -30831056, -12805180, 18008031, 10258577}, -

3471 }, -

3472 { -

3473 {-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -

3474 -1853465, 1367120, 25127874, 6671743}, -

3475 {29701166, -14373934, -10878120, 9279288, -17568, 13127210, -

3476 21382910, 11042292, 25838796, 4642684}, -

3477 {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, -

3478 30468147, -13900640, 18423289, 4177476}, -

3479 }, -

3480 }, -

3481 }; -

3482 -

3483 static uint8_t negative(signed char b) { -

3484 uint32_t x = b; -

3485 x >>= 31; /* 1: yes; 0: no */ -

3486

return x;

never executed: return x;

3487 } -

3488 -

3489 static void table_select(ge_precomp *t, int pos, signed char b) { -

3490 ge_precomp minust; -

3491 uint8_t bnegative = negative(b); -

3492 uint8_t babs = b - ((uint8_t)((-bnegative) & b) << 1); -

3493 -

3494 ge_precomp_0(t); -

3495 cmov(t, &k25519Precomp[pos][0], equal(babs, 1)); -

3496 cmov(t, &k25519Precomp[pos][1], equal(babs, 2)); -

3497 cmov(t, &k25519Precomp[pos][2], equal(babs, 3)); -

3498 cmov(t, &k25519Precomp[pos][3], equal(babs, 4)); -

3499 cmov(t, &k25519Precomp[pos][4], equal(babs, 5)); -

3500 cmov(t, &k25519Precomp[pos][5], equal(babs, 6)); -

3501 cmov(t, &k25519Precomp[pos][6], equal(babs, 7)); -

3502 cmov(t, &k25519Precomp[pos][7], equal(babs, 8)); -

3503 fe_copy(minust.yplusx, t->yminusx); -

3504 fe_copy(minust.yminusx, t->yplusx); -

3505 fe_neg(minust.xy2d, t->xy2d); -

3506 cmov(t, &minust, bnegative); -

3507

}

never executed: end of block

3508 -

3509 /* h = a * B -

3510 * where a = a[0]+256*a[1]+...+256^31 a[31] -

3511 * B is the Ed25519 base point (x,4/5) with x positive. -

3512 * -

3513 * Preconditions: -

3514 * a[31] <= 127 */ -

3515 void x25519_ge_scalarmult_base(ge_p3 *h, const uint8_t *a) { -

3516 signed char e[64]; -

3517 signed char carry; -

3518 ge_p1p1 r; -

3519 ge_p2 s; -

3520 ge_precomp t; -

3521 int i; -

3522 -

3523

for (i = 0; i < 32; ++i) {

i < 32	Description
TRUE	never evaluated
FALSE	never evaluated

3524 e[2 * i + 0] = (a[i] >> 0) & 15; -

3525 e[2 * i + 1] = (a[i] >> 4) & 15; -

3526

}

never executed: end of block

3527 /* each e[i] is between 0 and 15 */ -

3528 /* e[63] is between 0 and 7 */ -

3529 -

3530 carry = 0; -

3531

for (i = 0; i < 63; ++i) {

i < 63	Description
TRUE	never evaluated
FALSE	never evaluated

3532 e[i] += carry; -

3533 carry = e[i] + 8; -

3534 carry >>= 4; -

3535 e[i] -= carry << 4; -

3536

}

never executed: end of block

3537 e[63] += carry; -

3538 /* each e[i] is between -8 and 8 */ -

3539 -

3540 ge_p3_0(h); -

3541

for (i = 1; i < 64; i += 2) {

i < 64	Description
TRUE	never evaluated
FALSE	never evaluated

3542 table_select(&t, i / 2, e[i]); -

3543 ge_madd(&r, h, &t); -

3544 x25519_ge_p1p1_to_p3(h, &r); -

3545

}

never executed: end of block

3546 -

3547 ge_p3_dbl(&r, h); -

3548 x25519_ge_p1p1_to_p2(&s, &r); -

3549 ge_p2_dbl(&r, &s); -

3550 x25519_ge_p1p1_to_p2(&s, &r); -

3551 ge_p2_dbl(&r, &s); -

3552 x25519_ge_p1p1_to_p2(&s, &r); -

3553 ge_p2_dbl(&r, &s); -

3554 x25519_ge_p1p1_to_p3(h, &r); -

3555 -

3556

for (i = 0; i < 64; i += 2) {

i < 64	Description
TRUE	never evaluated
FALSE	never evaluated

3557 table_select(&t, i / 2, e[i]); -

3558 ge_madd(&r, h, &t); -

3559 x25519_ge_p1p1_to_p3(h, &r); -

3560

}

never executed: end of block

3561

}

never executed: end of block

3562 -

3563 #endif -

3564 -

3565 static void cmov_cached(ge_cached *t, ge_cached *u, uint8_t b) { -

3566 fe_cmov(t->YplusX, u->YplusX, b); -

3567 fe_cmov(t->YminusX, u->YminusX, b); -

3568 fe_cmov(t->Z, u->Z, b); -

3569 fe_cmov(t->T2d, u->T2d, b); -

3570

}

never executed: end of block

3571 -

3572 /* r = scalar * A. -

3573 * where a = a[0]+256*a[1]+...+256^31 a[31]. */ -

3574 void x25519_ge_scalarmult(ge_p2 *r, const uint8_t *scalar, const ge_p3 *A) { -

3575 ge_p2 Ai_p2[8]; -

3576 ge_cached Ai[16]; -

3577 ge_p1p1 t; -

3578 -

3579 ge_cached_0(&Ai[0]); -

3580 x25519_ge_p3_to_cached(&Ai[1], A); -

3581 ge_p3_to_p2(&Ai_p2[1], A); -

3582 -

3583 unsigned i; -

3584

for (i = 2; i < 16; i += 2) {

i < 16	Description
TRUE	never evaluated
FALSE	never evaluated

3585 ge_p2_dbl(&t, &Ai_p2[i / 2]); -

3586 ge_p1p1_to_cached(&Ai[i], &t); -

3587

if (i < 8) {

i < 8	Description
TRUE	never evaluated
FALSE	never evaluated

3588 x25519_ge_p1p1_to_p2(&Ai_p2[i], &t); -

3589

}

never executed: end of block

3590 x25519_ge_add(&t, A, &Ai[i]); -

3591 ge_p1p1_to_cached(&Ai[i + 1], &t); -

3592

if (i < 7) {

i < 7	Description
TRUE	never evaluated
FALSE	never evaluated

3593 x25519_ge_p1p1_to_p2(&Ai_p2[i + 1], &t); -

3594

}

never executed: end of block

3595

}

never executed: end of block

3596 -

3597 ge_p2_0(r); -

3598 ge_p3 u; -

3599 -

3600

for (i = 0; i < 256; i += 4) {

i < 256	Description
TRUE	never evaluated
FALSE	never evaluated

3601 ge_p2_dbl(&t, r); -

3602 x25519_ge_p1p1_to_p2(r, &t); -

3603 ge_p2_dbl(&t, r); -

3604 x25519_ge_p1p1_to_p2(r, &t); -

3605 ge_p2_dbl(&t, r); -

3606 x25519_ge_p1p1_to_p2(r, &t); -

3607 ge_p2_dbl(&t, r); -

3608 x25519_ge_p1p1_to_p3(&u, &t); -

3609 -

3610 uint8_t index = scalar[31 - i/8]; -

3611 index >>= 4 - (i & 4); -

3612 index &= 0xf; -

3613 -

3614 unsigned j; -

3615 ge_cached selected; -

3616 ge_cached_0(&selected); -

3617

for (j = 0; j < 16; j++) {

j < 16	Description
TRUE	never evaluated
FALSE	never evaluated

3618 cmov_cached(&selected, &Ai[j], equal(j, index)); -

3619

}

never executed: end of block

3620 -

3621 x25519_ge_add(&t, &u, &selected); -

3622 x25519_ge_p1p1_to_p2(r, &t); -

3623

}

never executed: end of block

3624

}

never executed: end of block

3625 -

3626 #ifdef ED25519 -

3627 static void slide(signed char *r, const uint8_t *a) { -

3628 int i; -

3629 int b; -

3630 int k; -

3631 -

3632 for (i = 0; i < 256; ++i) { -

3633 r[i] = 1 & (a[i >> 3] >> (i & 7)); -

3634 } -

3635 -

3636 for (i = 0; i < 256; ++i) { -

3637 if (r[i]) { -

3638 for (b = 1; b <= 6 && i + b < 256; ++b) { -

3639 if (r[i + b]) { -

3640 if (r[i] + (r[i + b] << b) <= 15) { -

3641 r[i] += r[i + b] << b; -

3642 r[i + b] = 0; -

3643 } else if (r[i] - (r[i + b] << b) >= -15) { -

3644 r[i] -= r[i + b] << b; -

3645 for (k = i + b; k < 256; ++k) { -

3646 if (!r[k]) { -

3647 r[k] = 1; -

3648 break; -

3649 } -

3650 r[k] = 0; -

3651 } -

3652 } else { -

3653 break; -

3654 } -

3655 } -

3656 } -

3657 } -

3658 } -

3659 } -

3660 -

3661 static const ge_precomp Bi[8] = { -

3662 { -

3663 {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -

3664 -11754271, -6079156, 2047605}, -

3665 {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, -

3666 5043384, 19500929, -15469378}, -

3667 {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, -

3668 11864899, -24514362, -4438546}, -

3669 }, -

3670 { -

3671 {15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -

3672 -14772189, 28944400, -1550024}, -

3673 {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -

3674 -11775962, 7689662, 11199574}, -

3675 {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, -

3676 10017326, -17749093, -9920357}, -

3677 }, -

3678 { -

3679 {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, -

3680 14515107, -15438304, 10819380}, -

3681 {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, -

3682 12483688, -12668491, 5581306}, -

3683 {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, -

3684 13850243, -23678021, -15815942}, -

3685 }, -

3686 { -

3687 {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, -

3688 5230134, -23952439, -15175766}, -

3689 {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, -

3690 16520125, 30598449, 7715701}, -

3691 {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, -

3692 1370708, 29794553, -1409300}, -

3693 }, -

3694 { -

3695 {-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -

3696 -1361450, -13062696, 13821877}, -

3697 {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -

3698 -7212327, 18853322, -14220951}, -

3699 {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -

3700 -10431137, 2207753, -3209784}, -

3701 }, -

3702 { -

3703 {-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -

3704 -663000, -31111463, -16132436}, -

3705 {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, -

3706 15725684, 171356, 6466918}, -

3707 {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -

3708 -14088058, -30714912, 16193877}, -

3709 }, -

3710 { -

3711 {-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, -

3712 4729455, -18074513, 9256800}, -

3713 {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, -

3714 9761698, -19827198, 630305}, -

3715 {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -

3716 -15960994, -2449256, -14291300}, -

3717 }, -

3718 { -

3719 {-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, -

3720 15033784, 25105118, -7894876}, -

3721 {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, -

3722 1573892, -2625887, 2198790, -15804619}, -

3723 {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -

3724 -16236442, -32461234, -12290683}, -

3725 }, -

3726 }; -

3727 -

3728 /* r = a * A + b * B -

3729 * where a = a[0]+256*a[1]+...+256^31 a[31]. -

3730 * and b = b[0]+256*b[1]+...+256^31 b[31]. -

3731 * B is the Ed25519 base point (x,4/5) with x positive. */ -

3732 static void -

3733 ge_double_scalarmult_vartime(ge_p2 *r, const uint8_t *a, -

3734 const ge_p3 *A, const uint8_t *b) { -

3735 signed char aslide[256]; -

3736 signed char bslide[256]; -

3737 ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ -

3738 ge_p1p1 t; -

3739 ge_p3 u; -

3740 ge_p3 A2; -

3741 int i; -

3742 -

3743 slide(aslide, a); -

3744 slide(bslide, b); -

3745 -

3746 x25519_ge_p3_to_cached(&Ai[0], A); -

3747 ge_p3_dbl(&t, A); -

3748 x25519_ge_p1p1_to_p3(&A2, &t); -

3749 x25519_ge_add(&t, &A2, &Ai[0]); -

3750 x25519_ge_p1p1_to_p3(&u, &t); -

3751 x25519_ge_p3_to_cached(&Ai[1], &u); -

3752 x25519_ge_add(&t, &A2, &Ai[1]); -

3753 x25519_ge_p1p1_to_p3(&u, &t); -

3754 x25519_ge_p3_to_cached(&Ai[2], &u); -

3755 x25519_ge_add(&t, &A2, &Ai[2]); -

3756 x25519_ge_p1p1_to_p3(&u, &t); -

3757 x25519_ge_p3_to_cached(&Ai[3], &u); -

3758 x25519_ge_add(&t, &A2, &Ai[3]); -

3759 x25519_ge_p1p1_to_p3(&u, &t); -

3760 x25519_ge_p3_to_cached(&Ai[4], &u); -

3761 x25519_ge_add(&t, &A2, &Ai[4]); -

3762 x25519_ge_p1p1_to_p3(&u, &t); -

3763 x25519_ge_p3_to_cached(&Ai[5], &u); -

3764 x25519_ge_add(&t, &A2, &Ai[5]); -

3765 x25519_ge_p1p1_to_p3(&u, &t); -

3766 x25519_ge_p3_to_cached(&Ai[6], &u); -

3767 x25519_ge_add(&t, &A2, &Ai[6]); -

3768 x25519_ge_p1p1_to_p3(&u, &t); -

3769 x25519_ge_p3_to_cached(&Ai[7], &u); -

3770 -

3771 ge_p2_0(r); -

3772 -

3773 for (i = 255; i >= 0; --i) { -

3774 if (aslide[i] || bslide[i]) { -

3775 break; -

3776 } -

3777 } -

3778 -

3779 for (; i >= 0; --i) { -

3780 ge_p2_dbl(&t, r); -

3781 -

3782 if (aslide[i] > 0) { -

3783 x25519_ge_p1p1_to_p3(&u, &t); -

3784 x25519_ge_add(&t, &u, &Ai[aslide[i] / 2]); -

3785 } else if (aslide[i] < 0) { -

3786 x25519_ge_p1p1_to_p3(&u, &t); -

3787 x25519_ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); -

3788 } -

3789 -

3790 if (bslide[i] > 0) { -

3791 x25519_ge_p1p1_to_p3(&u, &t); -

3792 ge_madd(&t, &u, &Bi[bslide[i] / 2]); -

3793 } else if (bslide[i] < 0) { -

3794 x25519_ge_p1p1_to_p3(&u, &t); -

3795 ge_msub(&t, &u, &Bi[(-bslide[i]) / 2]); -

3796 } -

3797 -

3798 x25519_ge_p1p1_to_p2(r, &t); -

3799 } -

3800 } -

3801 #endif -

3802 -

3803 /* The set of scalars is \Z/l -

3804 * where l = 2^252 + 27742317777372353535851937790883648493. */ -

3805 -

3806 /* Input: -

3807 * s[0]+256*s[1]+...+256^63*s[63] = s -

3808 * -

3809 * Output: -

3810 * s[0]+256*s[1]+...+256^31*s[31] = s mod l -

3811 * where l = 2^252 + 27742317777372353535851937790883648493. -

3812 * Overwrites s in place. */ -

3813 void -

3814 x25519_sc_reduce(uint8_t *s) { -

3815 int64_t s0 = 2097151 & load_3(s); -

3816 int64_t s1 = 2097151 & (load_4(s + 2) >> 5); -

3817 int64_t s2 = 2097151 & (load_3(s + 5) >> 2); -

3818 int64_t s3 = 2097151 & (load_4(s + 7) >> 7); -

3819 int64_t s4 = 2097151 & (load_4(s + 10) >> 4); -

3820 int64_t s5 = 2097151 & (load_3(s + 13) >> 1); -

3821 int64_t s6 = 2097151 & (load_4(s + 15) >> 6); -

3822 int64_t s7 = 2097151 & (load_3(s + 18) >> 3); -

3823 int64_t s8 = 2097151 & load_3(s + 21); -

3824 int64_t s9 = 2097151 & (load_4(s + 23) >> 5); -

3825 int64_t s10 = 2097151 & (load_3(s + 26) >> 2); -

3826 int64_t s11 = 2097151 & (load_4(s + 28) >> 7); -

3827 int64_t s12 = 2097151 & (load_4(s + 31) >> 4); -

3828 int64_t s13 = 2097151 & (load_3(s + 34) >> 1); -

3829 int64_t s14 = 2097151 & (load_4(s + 36) >> 6); -

3830 int64_t s15 = 2097151 & (load_3(s + 39) >> 3); -

3831 int64_t s16 = 2097151 & load_3(s + 42); -

3832 int64_t s17 = 2097151 & (load_4(s + 44) >> 5); -

3833 int64_t s18 = 2097151 & (load_3(s + 47) >> 2); -

3834 int64_t s19 = 2097151 & (load_4(s + 49) >> 7); -

3835 int64_t s20 = 2097151 & (load_4(s + 52) >> 4); -

3836 int64_t s21 = 2097151 & (load_3(s + 55) >> 1); -

3837 int64_t s22 = 2097151 & (load_4(s + 57) >> 6); -

3838 int64_t s23 = (load_4(s + 60) >> 3); -

3839 int64_t carry0; -

3840 int64_t carry1; -

3841 int64_t carry2; -

3842 int64_t carry3; -

3843 int64_t carry4; -

3844 int64_t carry5; -

3845 int64_t carry6; -

3846 int64_t carry7; -

3847 int64_t carry8; -

3848 int64_t carry9; -

3849 int64_t carry10; -

3850 int64_t carry11; -

3851 int64_t carry12; -

3852 int64_t carry13; -

3853 int64_t carry14; -

3854 int64_t carry15; -

3855 int64_t carry16; -

3856 -

3857 s11 += s23 * 666643; -

3858 s12 += s23 * 470296; -

3859 s13 += s23 * 654183; -

3860 s14 -= s23 * 997805; -

3861 s15 += s23 * 136657; -

3862 s16 -= s23 * 683901; -

3863 s23 = 0; -

3864 -

3865 s10 += s22 * 666643; -

3866 s11 += s22 * 470296; -

3867 s12 += s22 * 654183; -

3868 s13 -= s22 * 997805; -

3869 s14 += s22 * 136657; -

3870 s15 -= s22 * 683901; -

3871 s22 = 0; -

3872 -

3873 s9 += s21 * 666643; -

3874 s10 += s21 * 470296; -

3875 s11 += s21 * 654183; -

3876 s12 -= s21 * 997805; -

3877 s13 += s21 * 136657; -

3878 s14 -= s21 * 683901; -

3879 s21 = 0; -

3880 -

3881 s8 += s20 * 666643; -

3882 s9 += s20 * 470296; -

3883 s10 += s20 * 654183; -

3884 s11 -= s20 * 997805; -

3885 s12 += s20 * 136657; -

3886 s13 -= s20 * 683901; -

3887 s20 = 0; -

3888 -

3889 s7 += s19 * 666643; -

3890 s8 += s19 * 470296; -

3891 s9 += s19 * 654183; -

3892 s10 -= s19 * 997805; -

3893 s11 += s19 * 136657; -

3894 s12 -= s19 * 683901; -

3895 s19 = 0; -

3896 -

3897 s6 += s18 * 666643; -

3898 s7 += s18 * 470296; -

3899 s8 += s18 * 654183; -

3900 s9 -= s18 * 997805; -

3901 s10 += s18 * 136657; -

3902 s11 -= s18 * 683901; -

3903 s18 = 0; -

3904 -

3905 carry6 = (s6 + (1 << 20)) >> 21; -

3906 s7 += carry6; -

3907 s6 -= carry6 << 21; -

3908 carry8 = (s8 + (1 << 20)) >> 21; -

3909 s9 += carry8; -

3910 s8 -= carry8 << 21; -

3911 carry10 = (s10 + (1 << 20)) >> 21; -

3912 s11 += carry10; -

3913 s10 -= carry10 << 21; -

3914 carry12 = (s12 + (1 << 20)) >> 21; -

3915 s13 += carry12; -

3916 s12 -= carry12 << 21; -

3917 carry14 = (s14 + (1 << 20)) >> 21; -

3918 s15 += carry14; -

3919 s14 -= carry14 << 21; -

3920 carry16 = (s16 + (1 << 20)) >> 21; -

3921 s17 += carry16; -

3922 s16 -= carry16 << 21; -

3923 -

3924 carry7 = (s7 + (1 << 20)) >> 21; -

3925 s8 += carry7; -

3926 s7 -= carry7 << 21; -

3927 carry9 = (s9 + (1 << 20)) >> 21; -

3928 s10 += carry9; -

3929 s9 -= carry9 << 21; -

3930 carry11 = (s11 + (1 << 20)) >> 21; -

3931 s12 += carry11; -

3932 s11 -= carry11 << 21; -

3933 carry13 = (s13 + (1 << 20)) >> 21; -

3934 s14 += carry13; -

3935 s13 -= carry13 << 21; -

3936 carry15 = (s15 + (1 << 20)) >> 21; -

3937 s16 += carry15; -

3938 s15 -= carry15 << 21; -

3939 -

3940 s5 += s17 * 666643; -

3941 s6 += s17 * 470296; -

3942 s7 += s17 * 654183; -

3943 s8 -= s17 * 997805; -

3944 s9 += s17 * 136657; -

3945 s10 -= s17 * 683901; -

3946 s17 = 0; -

3947 -

3948 s4 += s16 * 666643; -

3949 s5 += s16 * 470296; -

3950 s6 += s16 * 654183; -

3951 s7 -= s16 * 997805; -

3952 s8 += s16 * 136657; -

3953 s9 -= s16 * 683901; -

3954 s16 = 0; -

3955 -

3956 s3 += s15 * 666643; -

3957 s4 += s15 * 470296; -

3958 s5 += s15 * 654183; -

3959 s6 -= s15 * 997805; -

3960 s7 += s15 * 136657; -

3961 s8 -= s15 * 683901; -

3962 s15 = 0; -

3963 -

3964 s2 += s14 * 666643; -

3965 s3 += s14 * 470296; -

3966 s4 += s14 * 654183; -

3967 s5 -= s14 * 997805; -

3968 s6 += s14 * 136657; -

3969 s7 -= s14 * 683901; -

3970 s14 = 0; -

3971 -

3972 s1 += s13 * 666643; -

3973 s2 += s13 * 470296; -

3974 s3 += s13 * 654183; -

3975 s4 -= s13 * 997805; -

3976 s5 += s13 * 136657; -

3977 s6 -= s13 * 683901; -

3978 s13 = 0; -

3979 -

3980 s0 += s12 * 666643; -

3981 s1 += s12 * 470296; -

3982 s2 += s12 * 654183; -

3983 s3 -= s12 * 997805; -

3984 s4 += s12 * 136657; -

3985 s5 -= s12 * 683901; -

3986 s12 = 0; -

3987 -

3988 carry0 = (s0 + (1 << 20)) >> 21; -

3989 s1 += carry0; -

3990 s0 -= carry0 << 21; -

3991 carry2 = (s2 + (1 << 20)) >> 21; -

3992 s3 += carry2; -

3993 s2 -= carry2 << 21; -

3994 carry4 = (s4 + (1 << 20)) >> 21; -

3995 s5 += carry4; -

3996 s4 -= carry4 << 21; -

3997 carry6 = (s6 + (1 << 20)) >> 21; -

3998 s7 += carry6; -

3999 s6 -= carry6 << 21; -

4000 carry8 = (s8 + (1 << 20)) >> 21; -

4001 s9 += carry8; -

4002 s8 -= carry8 << 21; -

4003 carry10 = (s10 + (1 << 20)) >> 21; -

4004 s11 += carry10; -

4005 s10 -= carry10 << 21; -

4006 -

4007 carry1 = (s1 + (1 << 20)) >> 21; -

4008 s2 += carry1; -

4009 s1 -= carry1 << 21; -

4010 carry3 = (s3 + (1 << 20)) >> 21; -

4011 s4 += carry3; -

4012 s3 -= carry3 << 21; -

4013 carry5 = (s5 + (1 << 20)) >> 21; -

4014 s6 += carry5; -

4015 s5 -= carry5 << 21; -

4016 carry7 = (s7 + (1 << 20)) >> 21; -

4017 s8 += carry7; -

4018 s7 -= carry7 << 21; -

4019 carry9 = (s9 + (1 << 20)) >> 21; -

4020 s10 += carry9; -

4021 s9 -= carry9 << 21; -

4022 carry11 = (s11 + (1 << 20)) >> 21; -

4023 s12 += carry11; -

4024 s11 -= carry11 << 21; -

4025 -

4026 s0 += s12 * 666643; -

4027 s1 += s12 * 470296; -

4028 s2 += s12 * 654183; -

4029 s3 -= s12 * 997805; -

4030 s4 += s12 * 136657; -

4031 s5 -= s12 * 683901; -

4032 s12 = 0; -

4033 -

4034 carry0 = s0 >> 21; -

4035 s1 += carry0; -

4036 s0 -= carry0 << 21; -

4037 carry1 = s1 >> 21; -

4038 s2 += carry1; -

4039 s1 -= carry1 << 21; -

4040 carry2 = s2 >> 21; -

4041 s3 += carry2; -

4042 s2 -= carry2 << 21; -

4043 carry3 = s3 >> 21; -

4044 s4 += carry3; -

4045 s3 -= carry3 << 21; -

4046 carry4 = s4 >> 21; -

4047 s5 += carry4; -

4048 s4 -= carry4 << 21; -

4049 carry5 = s5 >> 21; -

4050 s6 += carry5; -

4051 s5 -= carry5 << 21; -

4052 carry6 = s6 >> 21; -

4053 s7 += carry6; -

4054 s6 -= carry6 << 21; -

4055 carry7 = s7 >> 21; -

4056 s8 += carry7; -

4057 s7 -= carry7 << 21; -

4058 carry8 = s8 >> 21; -

4059 s9 += carry8; -

4060 s8 -= carry8 << 21; -

4061 carry9 = s9 >> 21; -

4062 s10 += carry9; -

4063 s9 -= carry9 << 21; -

4064 carry10 = s10 >> 21; -

4065 s11 += carry10; -

4066 s10 -= carry10 << 21; -

4067 carry11 = s11 >> 21; -

4068 s12 += carry11; -

4069 s11 -= carry11 << 21; -

4070 -

4071 s0 += s12 * 666643; -

4072 s1 += s12 * 470296; -

4073 s2 += s12 * 654183; -

4074 s3 -= s12 * 997805; -

4075 s4 += s12 * 136657; -

4076 s5 -= s12 * 683901; -

4077 s12 = 0; -

4078 -

4079 carry0 = s0 >> 21; -

4080 s1 += carry0; -

4081 s0 -= carry0 << 21; -

4082 carry1 = s1 >> 21; -

4083 s2 += carry1; -

4084 s1 -= carry1 << 21; -

4085 carry2 = s2 >> 21; -

4086 s3 += carry2; -

4087 s2 -= carry2 << 21; -

4088 carry3 = s3 >> 21; -

4089 s4 += carry3; -

4090 s3 -= carry3 << 21; -

4091 carry4 = s4 >> 21; -

4092 s5 += carry4; -

4093 s4 -= carry4 << 21; -

4094 carry5 = s5 >> 21; -

4095 s6 += carry5; -

4096 s5 -= carry5 << 21; -

4097 carry6 = s6 >> 21; -

4098 s7 += carry6; -

4099 s6 -= carry6 << 21; -

4100 carry7 = s7 >> 21; -

4101 s8 += carry7; -

4102 s7 -= carry7 << 21; -

4103 carry8 = s8 >> 21; -

4104 s9 += carry8; -

4105 s8 -= carry8 << 21; -

4106 carry9 = s9 >> 21; -

4107 s10 += carry9; -

4108 s9 -= carry9 << 21; -

4109 carry10 = s10 >> 21; -

4110 s11 += carry10; -

4111 s10 -= carry10 << 21; -

4112 -

4113 s[0] = s0 >> 0; -

4114 s[1] = s0 >> 8; -

4115 s[2] = (s0 >> 16) | (s1 << 5); -

4116 s[3] = s1 >> 3; -

4117 s[4] = s1 >> 11; -

4118 s[5] = (s1 >> 19) | (s2 << 2); -

4119 s[6] = s2 >> 6; -

4120 s[7] = (s2 >> 14) | (s3 << 7); -

4121 s[8] = s3 >> 1; -

4122 s[9] = s3 >> 9; -

4123 s[10] = (s3 >> 17) | (s4 << 4); -

4124 s[11] = s4 >> 4; -

4125 s[12] = s4 >> 12; -

4126 s[13] = (s4 >> 20) | (s5 << 1); -

4127 s[14] = s5 >> 7; -

4128 s[15] = (s5 >> 15) | (s6 << 6); -

4129 s[16] = s6 >> 2; -

4130 s[17] = s6 >> 10; -

4131 s[18] = (s6 >> 18) | (s7 << 3); -

4132 s[19] = s7 >> 5; -

4133 s[20] = s7 >> 13; -

4134 s[21] = s8 >> 0; -

4135 s[22] = s8 >> 8; -

4136 s[23] = (s8 >> 16) | (s9 << 5); -

4137 s[24] = s9 >> 3; -

4138 s[25] = s9 >> 11; -

4139 s[26] = (s9 >> 19) | (s10 << 2); -

4140 s[27] = s10 >> 6; -

4141 s[28] = (s10 >> 14) | (s11 << 7); -

4142 s[29] = s11 >> 1; -

4143 s[30] = s11 >> 9; -

4144 s[31] = s11 >> 17; -

4145

}

never executed: end of block

4146 -

4147 #ifdef ED25519 -

4148 /* Input: -

4149 * a[0]+256*a[1]+...+256^31*a[31] = a -

4150 * b[0]+256*b[1]+...+256^31*b[31] = b -

4151 * c[0]+256*c[1]+...+256^31*c[31] = c -

4152 * -

4153 * Output: -

4154 * s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l -

4155 * where l = 2^252 + 27742317777372353535851937790883648493. */ -

4156 static void -

4157 sc_muladd(uint8_t *s, const uint8_t *a, const uint8_t *b, -

4158 const uint8_t *c) -

4159 { -

4160 int64_t a0 = 2097151 & load_3(a); -

4161 int64_t a1 = 2097151 & (load_4(a + 2) >> 5); -

4162 int64_t a2 = 2097151 & (load_3(a + 5) >> 2); -

4163 int64_t a3 = 2097151 & (load_4(a + 7) >> 7); -

4164 int64_t a4 = 2097151 & (load_4(a + 10) >> 4); -

4165 int64_t a5 = 2097151 & (load_3(a + 13) >> 1); -

4166 int64_t a6 = 2097151 & (load_4(a + 15) >> 6); -

4167 int64_t a7 = 2097151 & (load_3(a + 18) >> 3); -

4168 int64_t a8 = 2097151 & load_3(a + 21); -

4169 int64_t a9 = 2097151 & (load_4(a + 23) >> 5); -

4170 int64_t a10 = 2097151 & (load_3(a + 26) >> 2); -

4171 int64_t a11 = (load_4(a + 28) >> 7); -

4172 int64_t b0 = 2097151 & load_3(b); -

4173 int64_t b1 = 2097151 & (load_4(b + 2) >> 5); -

4174 int64_t b2 = 2097151 & (load_3(b + 5) >> 2); -

4175 int64_t b3 = 2097151 & (load_4(b + 7) >> 7); -

4176 int64_t b4 = 2097151 & (load_4(b + 10) >> 4); -

4177 int64_t b5 = 2097151 & (load_3(b + 13) >> 1); -

4178 int64_t b6 = 2097151 & (load_4(b + 15) >> 6); -

4179 int64_t b7 = 2097151 & (load_3(b + 18) >> 3); -

4180 int64_t b8 = 2097151 & load_3(b + 21); -

4181 int64_t b9 = 2097151 & (load_4(b + 23) >> 5); -

4182 int64_t b10 = 2097151 & (load_3(b + 26) >> 2); -

4183 int64_t b11 = (load_4(b + 28) >> 7); -

4184 int64_t c0 = 2097151 & load_3(c); -

4185 int64_t c1 = 2097151 & (load_4(c + 2) >> 5); -

4186 int64_t c2 = 2097151 & (load_3(c + 5) >> 2); -

4187 int64_t c3 = 2097151 & (load_4(c + 7) >> 7); -

4188 int64_t c4 = 2097151 & (load_4(c + 10) >> 4); -

4189 int64_t c5 = 2097151 & (load_3(c + 13) >> 1); -

4190 int64_t c6 = 2097151 & (load_4(c + 15) >> 6); -

4191 int64_t c7 = 2097151 & (load_3(c + 18) >> 3); -

4192 int64_t c8 = 2097151 & load_3(c + 21); -

4193 int64_t c9 = 2097151 & (load_4(c + 23) >> 5); -

4194 int64_t c10 = 2097151 & (load_3(c + 26) >> 2); -

4195 int64_t c11 = (load_4(c + 28) >> 7); -

4196 int64_t s0; -

4197 int64_t s1; -

4198 int64_t s2; -

4199 int64_t s3; -

4200 int64_t s4; -

4201 int64_t s5; -

4202 int64_t s6; -

4203 int64_t s7; -

4204 int64_t s8; -

4205 int64_t s9; -

4206 int64_t s10; -

4207 int64_t s11; -

4208 int64_t s12; -

4209 int64_t s13; -

4210 int64_t s14; -

4211 int64_t s15; -

4212 int64_t s16; -

4213 int64_t s17; -

4214 int64_t s18; -

4215 int64_t s19; -

4216 int64_t s20; -

4217 int64_t s21; -

4218 int64_t s22; -

4219 int64_t s23; -

4220 int64_t carry0; -

4221 int64_t carry1; -

4222 int64_t carry2; -

4223 int64_t carry3; -

4224 int64_t carry4; -

4225 int64_t carry5; -

4226 int64_t carry6; -

4227 int64_t carry7; -

4228 int64_t carry8; -

4229 int64_t carry9; -

4230 int64_t carry10; -

4231 int64_t carry11; -

4232 int64_t carry12; -

4233 int64_t carry13; -

4234 int64_t carry14; -

4235 int64_t carry15; -

4236 int64_t carry16; -

4237 int64_t carry17; -

4238 int64_t carry18; -

4239 int64_t carry19; -

4240 int64_t carry20; -

4241 int64_t carry21; -

4242 int64_t carry22; -

4243 -

4244 s0 = c0 + a0 * b0; -

4245 s1 = c1 + a0 * b1 + a1 * b0; -

4246 s2 = c2 + a0 * b2 + a1 * b1 + a2 * b0; -

4247 s3 = c3 + a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; -

4248 s4 = c4 + a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; -

4249 s5 = c5 + a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; -

4250 s6 = c6 + a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; -

4251 s7 = c7 + a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + -

4252 a6 * b1 + a7 * b0; -

4253 s8 = c8 + a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + -

4254 a6 * b2 + a7 * b1 + a8 * b0; -

4255 s9 = c9 + a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + -

4256 a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; -

4257 s10 = c10 + a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + -

4258 a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; -

4259 s11 = c11 + a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + -

4260 a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; -

4261 s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + a7 * b5 + -

4262 a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; -

4263 s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + a8 * b5 + -

4264 a9 * b4 + a10 * b3 + a11 * b2; -

4265 s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + a9 * b5 + -

4266 a10 * b4 + a11 * b3; -

4267 s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + a10 * b5 + -

4268 a11 * b4; -

4269 s16 = a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; -

4270 s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; -

4271 s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; -

4272 s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; -

4273 s20 = a9 * b11 + a10 * b10 + a11 * b9; -

4274 s21 = a10 * b11 + a11 * b10; -

4275 s22 = a11 * b11; -

4276 s23 = 0; -

4277 -

4278 carry0 = (s0 + (1 << 20)) >> 21; -

4279 s1 += carry0; -

4280 s0 -= carry0 << 21; -

4281 carry2 = (s2 + (1 << 20)) >> 21; -

4282 s3 += carry2; -

4283 s2 -= carry2 << 21; -

4284 carry4 = (s4 + (1 << 20)) >> 21; -

4285 s5 += carry4; -

4286 s4 -= carry4 << 21; -

4287 carry6 = (s6 + (1 << 20)) >> 21; -

4288 s7 += carry6; -

4289 s6 -= carry6 << 21; -

4290 carry8 = (s8 + (1 << 20)) >> 21; -

4291 s9 += carry8; -

4292 s8 -= carry8 << 21; -

4293 carry10 = (s10 + (1 << 20)) >> 21; -

4294 s11 += carry10; -

4295 s10 -= carry10 << 21; -

4296 carry12 = (s12 + (1 << 20)) >> 21; -

4297 s13 += carry12; -

4298 s12 -= carry12 << 21; -

4299 carry14 = (s14 + (1 << 20)) >> 21; -

4300 s15 += carry14; -

4301 s14 -= carry14 << 21; -

4302 carry16 = (s16 + (1 << 20)) >> 21; -

4303 s17 += carry16; -

4304 s16 -= carry16 << 21; -

4305 carry18 = (s18 + (1 << 20)) >> 21; -

4306 s19 += carry18; -

4307 s18 -= carry18 << 21; -

4308 carry20 = (s20 + (1 << 20)) >> 21; -

4309 s21 += carry20; -

4310 s20 -= carry20 << 21; -

4311 carry22 = (s22 + (1 << 20)) >> 21; -

4312 s23 += carry22; -

4313 s22 -= carry22 << 21; -

4314 -

4315 carry1 = (s1 + (1 << 20)) >> 21; -

4316 s2 += carry1; -

4317 s1 -= carry1 << 21; -

4318 carry3 = (s3 + (1 << 20)) >> 21; -

4319 s4 += carry3; -

4320 s3 -= carry3 << 21; -

4321 carry5 = (s5 + (1 << 20)) >> 21; -

4322 s6 += carry5; -

4323 s5 -= carry5 << 21; -

4324 carry7 = (s7 + (1 << 20)) >> 21; -

4325 s8 += carry7; -

4326 s7 -= carry7 << 21; -

4327 carry9 = (s9 + (1 << 20)) >> 21; -

4328 s10 += carry9; -

4329 s9 -= carry9 << 21; -

4330 carry11 = (s11 + (1 << 20)) >> 21; -

4331 s12 += carry11; -

4332 s11 -= carry11 << 21; -

4333 carry13 = (s13 + (1 << 20)) >> 21; -

4334 s14 += carry13; -

4335 s13 -= carry13 << 21; -

4336 carry15 = (s15 + (1 << 20)) >> 21; -

4337 s16 += carry15; -

4338 s15 -= carry15 << 21; -

4339 carry17 = (s17 + (1 << 20)) >> 21; -

4340 s18 += carry17; -

4341 s17 -= carry17 << 21; -

4342 carry19 = (s19 + (1 << 20)) >> 21; -

4343 s20 += carry19; -

4344 s19 -= carry19 << 21; -

4345 carry21 = (s21 + (1 << 20)) >> 21; -

4346 s22 += carry21; -

4347 s21 -= carry21 << 21; -

4348 -

4349 s11 += s23 * 666643; -

4350 s12 += s23 * 470296; -

4351 s13 += s23 * 654183; -

4352 s14 -= s23 * 997805; -

4353 s15 += s23 * 136657; -

4354 s16 -= s23 * 683901; -

4355 s23 = 0; -

4356 -

4357 s10 += s22 * 666643; -

4358 s11 += s22 * 470296; -

4359 s12 += s22 * 654183; -

4360 s13 -= s22 * 997805; -

4361 s14 += s22 * 136657; -

4362 s15 -= s22 * 683901; -

4363 s22 = 0; -

4364 -

4365 s9 += s21 * 666643; -

4366 s10 += s21 * 470296; -

4367 s11 += s21 * 654183; -

4368 s12 -= s21 * 997805; -

4369 s13 += s21 * 136657; -

4370 s14 -= s21 * 683901; -

4371 s21 = 0; -

4372 -

4373 s8 += s20 * 666643; -

4374 s9 += s20 * 470296; -

4375 s10 += s20 * 654183; -

4376 s11 -= s20 * 997805; -

4377 s12 += s20 * 136657; -

4378 s13 -= s20 * 683901; -

4379 s20 = 0; -

4380 -

4381 s7 += s19 * 666643; -

4382 s8 += s19 * 470296; -

4383 s9 += s19 * 654183; -

4384 s10 -= s19 * 997805; -

4385 s11 += s19 * 136657; -

4386 s12 -= s19 * 683901; -

4387 s19 = 0; -

4388 -

4389 s6 += s18 * 666643; -

4390 s7 += s18 * 470296; -

4391 s8 += s18 * 654183; -

4392 s9 -= s18 * 997805; -

4393 s10 += s18 * 136657; -

4394 s11 -= s18 * 683901; -

4395 s18 = 0; -

4396 -

4397 carry6 = (s6 + (1 << 20)) >> 21; -

4398 s7 += carry6; -

4399 s6 -= carry6 << 21; -

4400 carry8 = (s8 + (1 << 20)) >> 21; -

4401 s9 += carry8; -

4402 s8 -= carry8 << 21; -

4403 carry10 = (s10 + (1 << 20)) >> 21; -

4404 s11 += carry10; -

4405 s10 -= carry10 << 21; -

4406 carry12 = (s12 + (1 << 20)) >> 21; -

4407 s13 += carry12; -

4408 s12 -= carry12 << 21; -

4409 carry14 = (s14 + (1 << 20)) >> 21; -

4410 s15 += carry14; -

4411 s14 -= carry14 << 21; -

4412 carry16 = (s16 + (1 << 20)) >> 21; -

4413 s17 += carry16; -

4414 s16 -= carry16 << 21; -

4415 -

4416 carry7 = (s7 + (1 << 20)) >> 21; -

4417 s8 += carry7; -

4418 s7 -= carry7 << 21; -

4419 carry9 = (s9 + (1 << 20)) >> 21; -

4420 s10 += carry9; -

4421 s9 -= carry9 << 21; -

4422 carry11 = (s11 + (1 << 20)) >> 21; -

4423 s12 += carry11; -

4424 s11 -= carry11 << 21; -

4425 carry13 = (s13 + (1 << 20)) >> 21; -

4426 s14 += carry13; -

4427 s13 -= carry13 << 21; -

4428 carry15 = (s15 + (1 << 20)) >> 21; -

4429 s16 += carry15; -

4430 s15 -= carry15 << 21; -

4431 -

4432 s5 += s17 * 666643; -

4433 s6 += s17 * 470296; -

4434 s7 += s17 * 654183; -

4435 s8 -= s17 * 997805; -

4436 s9 += s17 * 136657; -

4437 s10 -= s17 * 683901; -

4438 s17 = 0; -

4439 -

4440 s4 += s16 * 666643; -

4441 s5 += s16 * 470296; -

4442 s6 += s16 * 654183; -

4443 s7 -= s16 * 997805; -

4444 s8 += s16 * 136657; -

4445 s9 -= s16 * 683901; -

4446 s16 = 0; -

4447 -

4448 s3 += s15 * 666643; -

4449 s4 += s15 * 470296; -

4450 s5 += s15 * 654183; -

4451 s6 -= s15 * 997805; -

4452 s7 += s15 * 136657; -

4453 s8 -= s15 * 683901; -

4454 s15 = 0; -

4455 -

4456 s2 += s14 * 666643; -

4457 s3 += s14 * 470296; -

4458 s4 += s14 * 654183; -

4459 s5 -= s14 * 997805; -

4460 s6 += s14 * 136657; -

4461 s7 -= s14 * 683901; -

4462 s14 = 0; -

4463 -

4464 s1 += s13 * 666643; -

4465 s2 += s13 * 470296; -

4466 s3 += s13 * 654183; -

4467 s4 -= s13 * 997805; -

4468 s5 += s13 * 136657; -

4469 s6 -= s13 * 683901; -

4470 s13 = 0; -

4471 -

4472 s0 += s12 * 666643; -

4473 s1 += s12 * 470296; -

4474 s2 += s12 * 654183; -

4475 s3 -= s12 * 997805; -

4476 s4 += s12 * 136657; -

4477 s5 -= s12 * 683901; -

4478 s12 = 0; -

4479 -

4480 carry0 = (s0 + (1 << 20)) >> 21; -

4481 s1 += carry0; -

4482 s0 -= carry0 << 21; -

4483 carry2 = (s2 + (1 << 20)) >> 21; -

4484 s3 += carry2; -

4485 s2 -= carry2 << 21; -

4486 carry4 = (s4 + (1 << 20)) >> 21; -

4487 s5 += carry4; -

4488 s4 -= carry4 << 21; -

4489 carry6 = (s6 + (1 << 20)) >> 21; -

4490 s7 += carry6; -

4491 s6 -= carry6 << 21; -

4492 carry8 = (s8 + (1 << 20)) >> 21; -

4493 s9 += carry8; -

4494 s8 -= carry8 << 21; -

4495 carry10 = (s10 + (1 << 20)) >> 21; -

4496 s11 += carry10; -

4497 s10 -= carry10 << 21; -

4498 -

4499 carry1 = (s1 + (1 << 20)) >> 21; -

4500 s2 += carry1; -

4501 s1 -= carry1 << 21; -

4502 carry3 = (s3 + (1 << 20)) >> 21; -

4503 s4 += carry3; -

4504 s3 -= carry3 << 21; -

4505 carry5 = (s5 + (1 << 20)) >> 21; -

4506 s6 += carry5; -

4507 s5 -= carry5 << 21; -

4508 carry7 = (s7 + (1 << 20)) >> 21; -

4509 s8 += carry7; -

4510 s7 -= carry7 << 21; -

4511 carry9 = (s9 + (1 << 20)) >> 21; -

4512 s10 += carry9; -

4513 s9 -= carry9 << 21; -

4514 carry11 = (s11 + (1 << 20)) >> 21; -

4515 s12 += carry11; -

4516 s11 -= carry11 << 21; -

4517 -

4518 s0 += s12 * 666643; -

4519 s1 += s12 * 470296; -

4520 s2 += s12 * 654183; -

4521 s3 -= s12 * 997805; -

4522 s4 += s12 * 136657; -

4523 s5 -= s12 * 683901; -

4524 s12 = 0; -

4525 -

4526 carry0 = s0 >> 21; -

4527 s1 += carry0; -

4528 s0 -= carry0 << 21; -

4529 carry1 = s1 >> 21; -

4530 s2 += carry1; -

4531 s1 -= carry1 << 21; -

4532 carry2 = s2 >> 21; -

4533 s3 += carry2; -

4534 s2 -= carry2 << 21; -

4535 carry3 = s3 >> 21; -

4536 s4 += carry3; -

4537 s3 -= carry3 << 21; -

4538 carry4 = s4 >> 21; -

4539 s5 += carry4; -

4540 s4 -= carry4 << 21; -

4541 carry5 = s5 >> 21; -

4542 s6 += carry5; -

4543 s5 -= carry5 << 21; -

4544 carry6 = s6 >> 21; -

4545 s7 += carry6; -

4546 s6 -= carry6 << 21; -

4547 carry7 = s7 >> 21; -

4548 s8 += carry7; -

4549 s7 -= carry7 << 21; -

4550 carry8 = s8 >> 21; -

4551 s9 += carry8; -

4552 s8 -= carry8 << 21; -

4553 carry9 = s9 >> 21; -

4554 s10 += carry9; -

4555 s9 -= carry9 << 21; -

4556 carry10 = s10 >> 21; -

4557 s11 += carry10; -

4558 s10 -= carry10 << 21; -

4559 carry11 = s11 >> 21; -

4560 s12 += carry11; -

4561 s11 -= carry11 << 21; -

4562 -

4563 s0 += s12 * 666643; -

4564 s1 += s12 * 470296; -

4565 s2 += s12 * 654183; -

4566 s3 -= s12 * 997805; -

4567 s4 += s12 * 136657; -

4568 s5 -= s12 * 683901; -

4569 s12 = 0; -

4570 -

4571 carry0 = s0 >> 21; -

4572 s1 += carry0; -

4573 s0 -= carry0 << 21; -

4574 carry1 = s1 >> 21; -

4575 s2 += carry1; -

4576 s1 -= carry1 << 21; -

4577 carry2 = s2 >> 21; -

4578 s3 += carry2; -

4579 s2 -= carry2 << 21; -

4580 carry3 = s3 >> 21; -

4581 s4 += carry3; -

4582 s3 -= carry3 << 21; -

4583 carry4 = s4 >> 21; -

4584 s5 += carry4; -

4585 s4 -= carry4 << 21; -

4586 carry5 = s5 >> 21; -

4587 s6 += carry5; -

4588 s5 -= carry5 << 21; -

4589 carry6 = s6 >> 21; -

4590 s7 += carry6; -

4591 s6 -= carry6 << 21; -

4592 carry7 = s7 >> 21; -

4593 s8 += carry7; -

4594 s7 -= carry7 << 21; -

4595 carry8 = s8 >> 21; -

4596 s9 += carry8; -

4597 s8 -= carry8 << 21; -

4598 carry9 = s9 >> 21; -

4599 s10 += carry9; -

4600 s9 -= carry9 << 21; -

4601 carry10 = s10 >> 21; -

4602 s11 += carry10; -

4603 s10 -= carry10 << 21; -

4604 -

4605 s[0] = s0 >> 0; -

4606 s[1] = s0 >> 8; -

4607 s[2] = (s0 >> 16) | (s1 << 5); -

4608 s[3] = s1 >> 3; -

4609 s[4] = s1 >> 11; -

4610 s[5] = (s1 >> 19) | (s2 << 2); -

4611 s[6] = s2 >> 6; -

4612 s[7] = (s2 >> 14) | (s3 << 7); -

4613 s[8] = s3 >> 1; -

4614 s[9] = s3 >> 9; -

4615 s[10] = (s3 >> 17) | (s4 << 4); -

4616 s[11] = s4 >> 4; -

4617 s[12] = s4 >> 12; -

4618 s[13] = (s4 >> 20) | (s5 << 1); -

4619 s[14] = s5 >> 7; -

4620 s[15] = (s5 >> 15) | (s6 << 6); -

4621 s[16] = s6 >> 2; -

4622 s[17] = s6 >> 10; -

4623 s[18] = (s6 >> 18) | (s7 << 3); -

4624 s[19] = s7 >> 5; -

4625 s[20] = s7 >> 13; -

4626 s[21] = s8 >> 0; -

4627 s[22] = s8 >> 8; -

4628 s[23] = (s8 >> 16) | (s9 << 5); -

4629 s[24] = s9 >> 3; -

4630 s[25] = s9 >> 11; -

4631 s[26] = (s9 >> 19) | (s10 << 2); -

4632 s[27] = s10 >> 6; -

4633 s[28] = (s10 >> 14) | (s11 << 7); -

4634 s[29] = s11 >> 1; -

4635 s[30] = s11 >> 9; -

4636 s[31] = s11 >> 17; -

4637 } -

4638 #endif -

4639 -

4640 #ifdef ED25519 -

4641 void ED25519_keypair(uint8_t out_public_key[32], uint8_t out_private_key[64]) { -

4642 uint8_t seed[32]; -

4643 arc4random_buf(seed, 32); -

4644 -

4645 uint8_t az[SHA512_DIGEST_LENGTH]; -

4646 SHA512(seed, 32, az); -

4647 -

4648 az[0] &= 248; -

4649 az[31] &= 63; -

4650 az[31] |= 64; -

4651 -

4652 ge_p3 A; -

4653 x25519_ge_scalarmult_base(&A, az); -

4654 ge_p3_tobytes(out_public_key, &A); -

4655 -

4656 memcpy(out_private_key, seed, 32); -

4657 memmove(out_private_key + 32, out_public_key, 32); -

4658 } -

4659 -

4660 int ED25519_sign(uint8_t *out_sig, const uint8_t *message, size_t message_len, -

4661 const uint8_t private_key[64]) { -

4662 uint8_t az[SHA512_DIGEST_LENGTH]; -

4663 SHA512(private_key, 32, az); -

4664 -

4665 az[0] &= 248; -

4666 az[31] &= 63; -

4667 az[31] |= 64; -

4668 -

4669 SHA512_CTX hash_ctx; -

4670 SHA512_Init(&hash_ctx); -

4671 SHA512_Update(&hash_ctx, az + 32, 32); -

4672 SHA512_Update(&hash_ctx, message, message_len); -

4673 uint8_t nonce[SHA512_DIGEST_LENGTH]; -

4674 SHA512_Final(nonce, &hash_ctx); -

4675 -

4676 x25519_sc_reduce(nonce); -

4677 ge_p3 R; -

4678 x25519_ge_scalarmult_base(&R, nonce); -

4679 ge_p3_tobytes(out_sig, &R); -

4680 -

4681 SHA512_Init(&hash_ctx); -

4682 SHA512_Update(&hash_ctx, out_sig, 32); -

4683 SHA512_Update(&hash_ctx, private_key + 32, 32); -

4684 SHA512_Update(&hash_ctx, message, message_len); -

4685 uint8_t hram[SHA512_DIGEST_LENGTH]; -

4686 SHA512_Final(hram, &hash_ctx); -

4687 -

4688 x25519_sc_reduce(hram); -

4689 sc_muladd(out_sig + 32, hram, az, nonce); -

4690 -

4691 return 1; -

4692 } -

4693 -

4694 int ED25519_verify(const uint8_t *message, size_t message_len, -

4695 const uint8_t signature[64], const uint8_t public_key[32]) { -

4696 ge_p3 A; -

4697 if ((signature[63] & 224) != 0 || -

4698 x25519_ge_frombytes_vartime(&A, public_key) != 0) { -

4699 return 0; -

4700 } -

4701 -

4702 fe_neg(A.X, A.X); -

4703 fe_neg(A.T, A.T); -

4704 -

4705 uint8_t pkcopy[32]; -

4706 memcpy(pkcopy, public_key, 32); -

4707 uint8_t rcopy[32]; -

4708 memcpy(rcopy, signature, 32); -

4709 uint8_t scopy[32]; -

4710 memcpy(scopy, signature + 32, 32); -

4711 -

4712 SHA512_CTX hash_ctx; -

4713 SHA512_Init(&hash_ctx); -

4714 SHA512_Update(&hash_ctx, signature, 32); -

4715 SHA512_Update(&hash_ctx, public_key, 32); -

4716 SHA512_Update(&hash_ctx, message, message_len); -

4717 uint8_t h[SHA512_DIGEST_LENGTH]; -

4718 SHA512_Final(h, &hash_ctx); -

4719 -

4720 x25519_sc_reduce(h); -

4721 -

4722 ge_p2 R; -

4723 ge_double_scalarmult_vartime(&R, h, &A, scopy); -

4724 -

4725 uint8_t rcheck[32]; -

4726 x25519_ge_tobytes(rcheck, &R); -

4727 -

4728 return timingsafe_memcmp(rcheck, rcopy, sizeof(rcheck)) == 0; -

4729 } -

4730 #endif -

4731 -

4732 /* Replace (f,g) with (g,f) if b == 1; -

4733 * replace (f,g) with (f,g) if b == 0. -

4734 * -

4735 * Preconditions: b in {0,1}. */ -

4736 static void fe_cswap(fe f, fe g, unsigned int b) { -

4737 b = 0-b; -

4738 unsigned i; -

4739

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

i < 10	Description
TRUE	evaluated 5237760 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 523776 times by 3 tests Evaluated by: ssltest tlstest x25519test

523776-5237760

4740 int32_t x = f[i] ^ g[i]; -

4741 x &= b; -

4742 f[i] ^= x; -

4743 g[i] ^= x; -

4744

}

executed 5237760 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

5237760

4745

}

executed 523776 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

523776

4746 -

4747 /* h = f * 121666 -

4748 * Can overlap h with f. -

4749 * -

4750 * Preconditions: -

4751 * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -

4752 * -

4753 * Postconditions: -

4754 * |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ -

4755 static void fe_mul121666(fe h, fe f) { -

4756 int32_t f0 = f[0]; -

4757 int32_t f1 = f[1]; -

4758 int32_t f2 = f[2]; -

4759 int32_t f3 = f[3]; -

4760 int32_t f4 = f[4]; -

4761 int32_t f5 = f[5]; -

4762 int32_t f6 = f[6]; -

4763 int32_t f7 = f[7]; -

4764 int32_t f8 = f[8]; -

4765 int32_t f9 = f[9]; -

4766 int64_t h0 = f0 * (int64_t) 121666; -

4767 int64_t h1 = f1 * (int64_t) 121666; -

4768 int64_t h2 = f2 * (int64_t) 121666; -

4769 int64_t h3 = f3 * (int64_t) 121666; -

4770 int64_t h4 = f4 * (int64_t) 121666; -

4771 int64_t h5 = f5 * (int64_t) 121666; -

4772 int64_t h6 = f6 * (int64_t) 121666; -

4773 int64_t h7 = f7 * (int64_t) 121666; -

4774 int64_t h8 = f8 * (int64_t) 121666; -

4775 int64_t h9 = f9 * (int64_t) 121666; -

4776 int64_t carry0; -

4777 int64_t carry1; -

4778 int64_t carry2; -

4779 int64_t carry3; -

4780 int64_t carry4; -

4781 int64_t carry5; -

4782 int64_t carry6; -

4783 int64_t carry7; -

4784 int64_t carry8; -

4785 int64_t carry9; -

4786 -

4787 carry9 = h9 + (1 << 24); h0 += (carry9 >> 25) * 19; h9 -= carry9 & kTop39Bits; -

4788 carry1 = h1 + (1 << 24); h2 += carry1 >> 25; h1 -= carry1 & kTop39Bits; -

4789 carry3 = h3 + (1 << 24); h4 += carry3 >> 25; h3 -= carry3 & kTop39Bits; -

4790 carry5 = h5 + (1 << 24); h6 += carry5 >> 25; h5 -= carry5 & kTop39Bits; -

4791 carry7 = h7 + (1 << 24); h8 += carry7 >> 25; h7 -= carry7 & kTop39Bits; -

4792 -

4793 carry0 = h0 + (1 << 25); h1 += carry0 >> 26; h0 -= carry0 & kTop38Bits; -

4794 carry2 = h2 + (1 << 25); h3 += carry2 >> 26; h2 -= carry2 & kTop38Bits; -

4795 carry4 = h4 + (1 << 25); h5 += carry4 >> 26; h4 -= carry4 & kTop38Bits; -

4796 carry6 = h6 + (1 << 25); h7 += carry6 >> 26; h6 -= carry6 & kTop38Bits; -

4797 carry8 = h8 + (1 << 25); h9 += carry8 >> 26; h8 -= carry8 & kTop38Bits; -

4798 -

4799 h[0] = h0; -

4800 h[1] = h1; -

4801 h[2] = h2; -

4802 h[3] = h3; -

4803 h[4] = h4; -

4804 h[5] = h5; -

4805 h[6] = h6; -

4806 h[7] = h7; -

4807 h[8] = h8; -

4808 h[9] = h9; -

4809

}

executed 260865 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

260865

4810 -

4811 void -

4812 x25519_scalar_mult_generic(uint8_t out[32], const uint8_t scalar[32], -

4813 const uint8_t point[32]) { -

4814 fe x1, x2, z2, x3, z3, tmp0, tmp1; -

4815 -

4816 uint8_t e[32]; -

4817 memcpy(e, scalar, 32); -

4818 e[0] &= 248; -

4819 e[31] &= 127; -

4820 e[31] |= 64; -

4821 fe_frombytes(x1, point); -

4822 fe_1(x2); -

4823 fe_0(z2); -

4824 fe_copy(x3, x1); -

4825 fe_1(z3); -

4826 -

4827 unsigned swap = 0; -

4828 int pos; -

4829

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

pos >= 0	Description
TRUE	evaluated 260865 times by 3 tests Evaluated by: ssltest tlstest x25519test
FALSE	evaluated 1023 times by 3 tests Evaluated by: ssltest tlstest x25519test

1023-260865

4830 unsigned b = 1 & (e[pos / 8] >> (pos & 7)); -

4831 swap ^= b; -

4832 fe_cswap(x2, x3, swap); -

4833 fe_cswap(z2, z3, swap); -

4834 swap = b; -

4835 fe_sub(tmp0, x3, z3); -

4836 fe_sub(tmp1, x2, z2); -

4837 fe_add(x2, x2, z2); -

4838 fe_add(z2, x3, z3); -

4839 fe_mul(z3, tmp0, x2); -

4840 fe_mul(z2, z2, tmp1); -

4841 fe_sq(tmp0, tmp1); -

4842 fe_sq(tmp1, x2); -

4843 fe_add(x3, z3, z2); -

4844 fe_sub(z2, z3, z2); -

4845 fe_mul(x2, tmp1, tmp0); -

4846 fe_sub(tmp1, tmp1, tmp0); -

4847 fe_sq(z2, z2); -

4848 fe_mul121666(z3, tmp1); -

4849 fe_sq(x3, x3); -

4850 fe_add(tmp0, tmp0, z3); -

4851 fe_mul(z3, x1, z2); -

4852 fe_mul(z2, tmp1, tmp0); -

4853

}

executed 260865 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

260865

4854 fe_cswap(x2, x3, swap); -

4855 fe_cswap(z2, z3, swap); -

4856 -

4857 fe_invert(z2, z2); -

4858 fe_mul(x2, x2, z2); -

4859 fe_tobytes(out, x2); -

4860

}

executed 1023 times by 3 tests: end of block

Executed by:

ssltest
tlstest
x25519test

1023

4861 -

4862 #ifdef unused -

4863 void -

4864 x25519_public_from_private_generic(uint8_t out_public_value[32], -

4865 const uint8_t private_key[32]) -

4866 { -

4867 uint8_t e[32]; -

4868 -

4869 memcpy(e, private_key, 32); -

4870 e[0] &= 248; -

4871 e[31] &= 127; -

4872 e[31] |= 64; -

4873 -

4874 ge_p3 A; -

4875 x25519_ge_scalarmult_base(&A, e); -

4876 -

4877 /* We only need the u-coordinate of the curve25519 point. The map is -

4878 * u=(y+1)/(1-y). Since y=Y/Z, this gives u=(Z+Y)/(Z-Y). */ -

4879 fe zplusy, zminusy, zminusy_inv; -

4880 fe_add(zplusy, A.Z, A.Y); -

4881 fe_sub(zminusy, A.Z, A.Y); -

4882 fe_invert(zminusy_inv, zminusy); -

4883 fe_mul(zplusy, zplusy, zminusy_inv); -

4884 fe_tobytes(out_public_value, zplusy); -

4885 } -

4886 #endif -

4887 -

4888 void -

4889 x25519_public_from_private(uint8_t out_public_value[32], -

4890 const uint8_t private_key[32]) -

4891 { -

4892 static const uint8_t kMongomeryBasePoint[32] = {9}; -

4893 -

4894 x25519_scalar_mult(out_public_value, private_key, kMongomeryBasePoint); -

4895

}

executed 10 times by 2 tests: end of block

Executed by:

ssltest
tlstest

4896 -

4897 void -

4898 X25519_keypair(uint8_t out_public_value[X25519_KEY_LENGTH], -

4899 uint8_t out_private_key[X25519_KEY_LENGTH]) -

4900 { -

4901 /* All X25519 implementations should decode scalars correctly (see -

4902 * https://tools.ietf.org/html/rfc7748#section-5). However, if an -

4903 * implementation doesn't then it might interoperate with random keys a -

4904 * fraction of the time because they'll, randomly, happen to be correctly -

4905 * formed. -

4906 * -

4907 * Thus we do the opposite of the masking here to make sure that our private -

4908 * keys are never correctly masked and so, hopefully, any incorrect -

4909 * implementations are deterministically broken. -

4910 * -

4911 * This does not affect security because, although we're throwing away -

4912 * entropy, a valid implementation of scalarmult should throw away the exact -

4913 * same bits anyway. */ -

4914 arc4random_buf(out_private_key, 32); -

4915 -

4916 out_private_key[0] |= 7; -

4917 out_private_key[31] &= 63; -

4918 out_private_key[31] |= 128; -

4919 -

4920 x25519_public_from_private(out_public_value, out_private_key); -

4921

}

executed 10 times by 2 tests: end of block

Executed by:

ssltest
tlstest

4922 -

4923 int -

4924 X25519(uint8_t out_shared_key[X25519_KEY_LENGTH], -

4925 const uint8_t private_key[X25519_KEY_LENGTH], -

4926 const uint8_t peer_public_value[X25519_KEY_LENGTH]) -

4927 { -

4928 static const uint8_t kZeros[32] = {0}; -

4929 -

4930 x25519_scalar_mult(out_shared_key, private_key, peer_public_value); -

4931 -

4932 /* The all-zero output results when the input is a point of small order. */ -

4933

return timingsafe_memcmp(kZeros, out_shared_key, 32) != 0;

executed 1013 times by 3 tests: return timingsafe_memcmp(kZeros, out_shared_key, 32) != 0;

Executed by:

ssltest
tlstest
x25519test

1013

4934 } -

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