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1 <?php 2 3 if (class_exists('ParagonIE_Sodium_Core_Curve25519', false)) { 4 return; 5 } 6 7 /** 8 * Class ParagonIE_Sodium_Core_Curve25519 9 * 10 * Implements Curve25519 core functions 11 * 12 * Based on the ref10 curve25519 code provided by libsodium 13 * 14 * @ref https://github.com/jedisct1/libsodium/blob/master/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c 15 */ 16 abstract class ParagonIE_Sodium_Core_Curve25519 extends ParagonIE_Sodium_Core_Curve25519_H 17 { 18 /** 19 * Get a field element of size 10 with a value of 0 20 * 21 * @internal You should not use this directly from another application 22 * 23 * @return ParagonIE_Sodium_Core_Curve25519_Fe 24 */ 25 public static function fe_0() 26 { 27 return new ParagonIE_Sodium_Core_Curve25519_Fe(); 28 } 29 30 /** 31 * Get a field element of size 10 with a value of 1 32 * 33 * @internal You should not use this directly from another application 34 * 35 * @return ParagonIE_Sodium_Core_Curve25519_Fe 36 */ 37 public static function fe_1() 38 { 39 $fe = new ParagonIE_Sodium_Core_Curve25519_Fe(); 40 $fe->e0 = 1; 41 return $fe; 42 } 43 44 /** 45 * Add two field elements. 46 * 47 * @internal You should not use this directly from another application 48 * 49 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 50 * @param ParagonIE_Sodium_Core_Curve25519_Fe $g 51 * @return ParagonIE_Sodium_Core_Curve25519_Fe 52 * @psalm-suppress MixedAssignment 53 * @psalm-suppress MixedOperand 54 */ 55 public static function fe_add( 56 ParagonIE_Sodium_Core_Curve25519_Fe $f, 57 ParagonIE_Sodium_Core_Curve25519_Fe $g 58 ) { 59 return new ParagonIE_Sodium_Core_Curve25519_Fe( 60 (int)($f->e0 + $g->e0), 61 (int)($f->e1 + $g->e1), 62 (int)($f->e2 + $g->e2), 63 (int)($f->e3 + $g->e3), 64 (int)($f->e4 + $g->e4), 65 (int)($f->e5 + $g->e5), 66 (int)($f->e6 + $g->e6), 67 (int)($f->e7 + $g->e7), 68 (int)($f->e8 + $g->e8), 69 (int)($f->e9 + $g->e9) 70 ); 71 } 72 73 /** 74 * Constant-time conditional move. 75 * 76 * @internal You should not use this directly from another application 77 * 78 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 79 * @param ParagonIE_Sodium_Core_Curve25519_Fe $g 80 * @param int $b 81 * @return ParagonIE_Sodium_Core_Curve25519_Fe 82 * @psalm-suppress MixedAssignment 83 */ 84 public static function fe_cmov( 85 ParagonIE_Sodium_Core_Curve25519_Fe $f, 86 ParagonIE_Sodium_Core_Curve25519_Fe $g, 87 $b = 0 88 ) { 89 $h = new ParagonIE_Sodium_Core_Curve25519_Fe(); 90 $b *= -1; 91 $x = (($f->e0 ^ $g->e0) & $b); $h->e0 = $f->e0 ^ $x; 92 $x = (($f->e1 ^ $g->e1) & $b); $h->e1 = $f->e1 ^ $x; 93 $x = (($f->e2 ^ $g->e2) & $b); $h->e2 = $f->e2 ^ $x; 94 $x = (($f->e3 ^ $g->e3) & $b); $h->e3 = $f->e3 ^ $x; 95 $x = (($f->e4 ^ $g->e4) & $b); $h->e4 = $f->e4 ^ $x; 96 $x = (($f->e5 ^ $g->e5) & $b); $h->e5 = $f->e5 ^ $x; 97 $x = (($f->e6 ^ $g->e6) & $b); $h->e6 = $f->e6 ^ $x; 98 $x = (($f->e7 ^ $g->e7) & $b); $h->e7 = $f->e7 ^ $x; 99 $x = (($f->e8 ^ $g->e8) & $b); $h->e8 = $f->e8 ^ $x; 100 $x = (($f->e9 ^ $g->e9) & $b); $h->e9 = $f->e9 ^ $x; 101 return $h; 102 } 103 104 /** 105 * Create a copy of a field element. 106 * 107 * @internal You should not use this directly from another application 108 * 109 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 110 * @return ParagonIE_Sodium_Core_Curve25519_Fe 111 */ 112 public static function fe_copy(ParagonIE_Sodium_Core_Curve25519_Fe $f) 113 { 114 return clone $f; 115 } 116 117 /** 118 * Give: 32-byte string. 119 * Receive: A field element object to use for internal calculations. 120 * 121 * @internal You should not use this directly from another application 122 * 123 * @param string $s 124 * @return ParagonIE_Sodium_Core_Curve25519_Fe 125 * @throws RangeException 126 * @throws TypeError 127 */ 128 public static function fe_frombytes($s) 129 { 130 if (self::strlen($s) !== 32) { 131 throw new RangeException('Expected a 32-byte string.'); 132 } 133 $h0 = self::load_4($s); 134 $h1 = self::load_3(self::substr($s, 4, 3)) << 6; 135 $h2 = self::load_3(self::substr($s, 7, 3)) << 5; 136 $h3 = self::load_3(self::substr($s, 10, 3)) << 3; 137 $h4 = self::load_3(self::substr($s, 13, 3)) << 2; 138 $h5 = self::load_4(self::substr($s, 16, 4)); 139 $h6 = self::load_3(self::substr($s, 20, 3)) << 7; 140 $h7 = self::load_3(self::substr($s, 23, 3)) << 5; 141 $h8 = self::load_3(self::substr($s, 26, 3)) << 4; 142 $h9 = (self::load_3(self::substr($s, 29, 3)) & 8388607) << 2; 143 144 $carry9 = ($h9 + (1 << 24)) >> 25; 145 $h0 += self::mul($carry9, 19, 5); 146 $h9 -= $carry9 << 25; 147 $carry1 = ($h1 + (1 << 24)) >> 25; 148 $h2 += $carry1; 149 $h1 -= $carry1 << 25; 150 $carry3 = ($h3 + (1 << 24)) >> 25; 151 $h4 += $carry3; 152 $h3 -= $carry3 << 25; 153 $carry5 = ($h5 + (1 << 24)) >> 25; 154 $h6 += $carry5; 155 $h5 -= $carry5 << 25; 156 $carry7 = ($h7 + (1 << 24)) >> 25; 157 $h8 += $carry7; 158 $h7 -= $carry7 << 25; 159 160 $carry0 = ($h0 + (1 << 25)) >> 26; 161 $h1 += $carry0; 162 $h0 -= $carry0 << 26; 163 $carry2 = ($h2 + (1 << 25)) >> 26; 164 $h3 += $carry2; 165 $h2 -= $carry2 << 26; 166 $carry4 = ($h4 + (1 << 25)) >> 26; 167 $h5 += $carry4; 168 $h4 -= $carry4 << 26; 169 $carry6 = ($h6 + (1 << 25)) >> 26; 170 $h7 += $carry6; 171 $h6 -= $carry6 << 26; 172 $carry8 = ($h8 + (1 << 25)) >> 26; 173 $h9 += $carry8; 174 $h8 -= $carry8 << 26; 175 176 return new ParagonIE_Sodium_Core_Curve25519_Fe( 177 (int) $h0, 178 (int) $h1, 179 (int) $h2, 180 (int) $h3, 181 (int) $h4, 182 (int) $h5, 183 (int) $h6, 184 (int) $h7, 185 (int) $h8, 186 (int) $h9 187 ); 188 } 189 190 /** 191 * Convert a field element to a byte string. 192 * 193 * @internal You should not use this directly from another application 194 * 195 * @param ParagonIE_Sodium_Core_Curve25519_Fe $h 196 * @return string 197 */ 198 public static function fe_tobytes(ParagonIE_Sodium_Core_Curve25519_Fe $h) 199 { 200 $h0 = (int) $h->e0; 201 $h1 = (int) $h->e1; 202 $h2 = (int) $h->e2; 203 $h3 = (int) $h->e3; 204 $h4 = (int) $h->e4; 205 $h5 = (int) $h->e5; 206 $h6 = (int) $h->e6; 207 $h7 = (int) $h->e7; 208 $h8 = (int) $h->e8; 209 $h9 = (int) $h->e9; 210 211 $q = (self::mul($h9, 19, 5) + (1 << 24)) >> 25; 212 $q = ($h0 + $q) >> 26; 213 $q = ($h1 + $q) >> 25; 214 $q = ($h2 + $q) >> 26; 215 $q = ($h3 + $q) >> 25; 216 $q = ($h4 + $q) >> 26; 217 $q = ($h5 + $q) >> 25; 218 $q = ($h6 + $q) >> 26; 219 $q = ($h7 + $q) >> 25; 220 $q = ($h8 + $q) >> 26; 221 $q = ($h9 + $q) >> 25; 222 223 $h0 += self::mul($q, 19, 5); 224 225 $carry0 = $h0 >> 26; 226 $h1 += $carry0; 227 $h0 -= $carry0 << 26; 228 $carry1 = $h1 >> 25; 229 $h2 += $carry1; 230 $h1 -= $carry1 << 25; 231 $carry2 = $h2 >> 26; 232 $h3 += $carry2; 233 $h2 -= $carry2 << 26; 234 $carry3 = $h3 >> 25; 235 $h4 += $carry3; 236 $h3 -= $carry3 << 25; 237 $carry4 = $h4 >> 26; 238 $h5 += $carry4; 239 $h4 -= $carry4 << 26; 240 $carry5 = $h5 >> 25; 241 $h6 += $carry5; 242 $h5 -= $carry5 << 25; 243 $carry6 = $h6 >> 26; 244 $h7 += $carry6; 245 $h6 -= $carry6 << 26; 246 $carry7 = $h7 >> 25; 247 $h8 += $carry7; 248 $h7 -= $carry7 << 25; 249 $carry8 = $h8 >> 26; 250 $h9 += $carry8; 251 $h8 -= $carry8 << 26; 252 $carry9 = $h9 >> 25; 253 $h9 -= $carry9 << 25; 254 255 /** 256 * @var array<int, int> 257 */ 258 $s = array( 259 (int) (($h0 >> 0) & 0xff), 260 (int) (($h0 >> 8) & 0xff), 261 (int) (($h0 >> 16) & 0xff), 262 (int) ((($h0 >> 24) | ($h1 << 2)) & 0xff), 263 (int) (($h1 >> 6) & 0xff), 264 (int) (($h1 >> 14) & 0xff), 265 (int) ((($h1 >> 22) | ($h2 << 3)) & 0xff), 266 (int) (($h2 >> 5) & 0xff), 267 (int) (($h2 >> 13) & 0xff), 268 (int) ((($h2 >> 21) | ($h3 << 5)) & 0xff), 269 (int) (($h3 >> 3) & 0xff), 270 (int) (($h3 >> 11) & 0xff), 271 (int) ((($h3 >> 19) | ($h4 << 6)) & 0xff), 272 (int) (($h4 >> 2) & 0xff), 273 (int) (($h4 >> 10) & 0xff), 274 (int) (($h4 >> 18) & 0xff), 275 (int) (($h5 >> 0) & 0xff), 276 (int) (($h5 >> 8) & 0xff), 277 (int) (($h5 >> 16) & 0xff), 278 (int) ((($h5 >> 24) | ($h6 << 1)) & 0xff), 279 (int) (($h6 >> 7) & 0xff), 280 (int) (($h6 >> 15) & 0xff), 281 (int) ((($h6 >> 23) | ($h7 << 3)) & 0xff), 282 (int) (($h7 >> 5) & 0xff), 283 (int) (($h7 >> 13) & 0xff), 284 (int) ((($h7 >> 21) | ($h8 << 4)) & 0xff), 285 (int) (($h8 >> 4) & 0xff), 286 (int) (($h8 >> 12) & 0xff), 287 (int) ((($h8 >> 20) | ($h9 << 6)) & 0xff), 288 (int) (($h9 >> 2) & 0xff), 289 (int) (($h9 >> 10) & 0xff), 290 (int) (($h9 >> 18) & 0xff) 291 ); 292 return self::intArrayToString($s); 293 } 294 295 /** 296 * Is a field element negative? (1 = yes, 0 = no. Used in calculations.) 297 * 298 * @internal You should not use this directly from another application 299 * 300 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 301 * @return int 302 * @throws SodiumException 303 * @throws TypeError 304 */ 305 public static function fe_isnegative(ParagonIE_Sodium_Core_Curve25519_Fe $f) 306 { 307 $str = self::fe_tobytes($f); 308 return (int) (self::chrToInt($str[0]) & 1); 309 } 310 311 /** 312 * Returns 0 if this field element results in all NUL bytes. 313 * 314 * @internal You should not use this directly from another application 315 * 316 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 317 * @return bool 318 * @throws SodiumException 319 * @throws TypeError 320 */ 321 public static function fe_isnonzero(ParagonIE_Sodium_Core_Curve25519_Fe $f) 322 { 323 static $zero; 324 if ($zero === null) { 325 $zero = str_repeat("\x00", 32); 326 } 327 /** @var string $zero */ 328 /** @var string $str */ 329 $str = self::fe_tobytes($f); 330 return !self::verify_32($str, (string) $zero); 331 } 332 333 /** 334 * Multiply two field elements 335 * 336 * h = f * g 337 * 338 * @internal You should not use this directly from another application 339 * 340 * @security Is multiplication a source of timing leaks? If so, can we do 341 * anything to prevent that from happening? 342 * 343 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 344 * @param ParagonIE_Sodium_Core_Curve25519_Fe $g 345 * @return ParagonIE_Sodium_Core_Curve25519_Fe 346 */ 347 public static function fe_mul( 348 ParagonIE_Sodium_Core_Curve25519_Fe $f, 349 ParagonIE_Sodium_Core_Curve25519_Fe $g 350 ) { 351 // Ensure limbs aren't oversized. 352 $f = self::fe_normalize($f); 353 $g = self::fe_normalize($g); 354 $f0 = $f->e0; 355 $f1 = $f->e1; 356 $f2 = $f->e2; 357 $f3 = $f->e3; 358 $f4 = $f->e4; 359 $f5 = $f->e5; 360 $f6 = $f->e6; 361 $f7 = $f->e7; 362 $f8 = $f->e8; 363 $f9 = $f->e9; 364 $g0 = $g->e0; 365 $g1 = $g->e1; 366 $g2 = $g->e2; 367 $g3 = $g->e3; 368 $g4 = $g->e4; 369 $g5 = $g->e5; 370 $g6 = $g->e6; 371 $g7 = $g->e7; 372 $g8 = $g->e8; 373 $g9 = $g->e9; 374 $g1_19 = self::mul($g1, 19, 5); 375 $g2_19 = self::mul($g2, 19, 5); 376 $g3_19 = self::mul($g3, 19, 5); 377 $g4_19 = self::mul($g4, 19, 5); 378 $g5_19 = self::mul($g5, 19, 5); 379 $g6_19 = self::mul($g6, 19, 5); 380 $g7_19 = self::mul($g7, 19, 5); 381 $g8_19 = self::mul($g8, 19, 5); 382 $g9_19 = self::mul($g9, 19, 5); 383 $f1_2 = $f1 << 1; 384 $f3_2 = $f3 << 1; 385 $f5_2 = $f5 << 1; 386 $f7_2 = $f7 << 1; 387 $f9_2 = $f9 << 1; 388 $f0g0 = self::mul($f0, $g0, 26); 389 $f0g1 = self::mul($f0, $g1, 25); 390 $f0g2 = self::mul($f0, $g2, 26); 391 $f0g3 = self::mul($f0, $g3, 25); 392 $f0g4 = self::mul($f0, $g4, 26); 393 $f0g5 = self::mul($f0, $g5, 25); 394 $f0g6 = self::mul($f0, $g6, 26); 395 $f0g7 = self::mul($f0, $g7, 25); 396 $f0g8 = self::mul($f0, $g8, 26); 397 $f0g9 = self::mul($f0, $g9, 26); 398 $f1g0 = self::mul($f1, $g0, 26); 399 $f1g1_2 = self::mul($f1_2, $g1, 25); 400 $f1g2 = self::mul($f1, $g2, 26); 401 $f1g3_2 = self::mul($f1_2, $g3, 25); 402 $f1g4 = self::mul($f1, $g4, 26); 403 $f1g5_2 = self::mul($f1_2, $g5, 25); 404 $f1g6 = self::mul($f1, $g6, 26); 405 $f1g7_2 = self::mul($f1_2, $g7, 25); 406 $f1g8 = self::mul($f1, $g8, 26); 407 $f1g9_38 = self::mul($g9_19, $f1_2, 26); 408 $f2g0 = self::mul($f2, $g0, 26); 409 $f2g1 = self::mul($f2, $g1, 25); 410 $f2g2 = self::mul($f2, $g2, 26); 411 $f2g3 = self::mul($f2, $g3, 25); 412 $f2g4 = self::mul($f2, $g4, 26); 413 $f2g5 = self::mul($f2, $g5, 25); 414 $f2g6 = self::mul($f2, $g6, 26); 415 $f2g7 = self::mul($f2, $g7, 25); 416 $f2g8_19 = self::mul($g8_19, $f2, 26); 417 $f2g9_19 = self::mul($g9_19, $f2, 26); 418 $f3g0 = self::mul($f3, $g0, 26); 419 $f3g1_2 = self::mul($f3_2, $g1, 25); 420 $f3g2 = self::mul($f3, $g2, 26); 421 $f3g3_2 = self::mul($f3_2, $g3, 25); 422 $f3g4 = self::mul($f3, $g4, 26); 423 $f3g5_2 = self::mul($f3_2, $g5, 25); 424 $f3g6 = self::mul($f3, $g6, 26); 425 $f3g7_38 = self::mul($g7_19, $f3_2, 26); 426 $f3g8_19 = self::mul($g8_19, $f3, 25); 427 $f3g9_38 = self::mul($g9_19, $f3_2, 26); 428 $f4g0 = self::mul($f4, $g0, 26); 429 $f4g1 = self::mul($f4, $g1, 25); 430 $f4g2 = self::mul($f4, $g2, 26); 431 $f4g3 = self::mul($f4, $g3, 25); 432 $f4g4 = self::mul($f4, $g4, 26); 433 $f4g5 = self::mul($f4, $g5, 25); 434 $f4g6_19 = self::mul($g6_19, $f4, 26); 435 $f4g7_19 = self::mul($g7_19, $f4, 26); 436 $f4g8_19 = self::mul($g8_19, $f4, 26); 437 $f4g9_19 = self::mul($g9_19, $f4, 26); 438 $f5g0 = self::mul($f5, $g0, 26); 439 $f5g1_2 = self::mul($f5_2, $g1, 25); 440 $f5g2 = self::mul($f5, $g2, 26); 441 $f5g3_2 = self::mul($f5_2, $g3, 25); 442 $f5g4 = self::mul($f5, $g4, 26); 443 $f5g5_38 = self::mul($g5_19, $f5_2, 26); 444 $f5g6_19 = self::mul($g6_19, $f5, 25); 445 $f5g7_38 = self::mul($g7_19, $f5_2, 26); 446 $f5g8_19 = self::mul($g8_19, $f5, 25); 447 $f5g9_38 = self::mul($g9_19, $f5_2, 26); 448 $f6g0 = self::mul($f6, $g0, 26); 449 $f6g1 = self::mul($f6, $g1, 25); 450 $f6g2 = self::mul($f6, $g2, 26); 451 $f6g3 = self::mul($f6, $g3, 25); 452 $f6g4_19 = self::mul($g4_19, $f6, 26); 453 $f6g5_19 = self::mul($g5_19, $f6, 26); 454 $f6g6_19 = self::mul($g6_19, $f6, 26); 455 $f6g7_19 = self::mul($g7_19, $f6, 26); 456 $f6g8_19 = self::mul($g8_19, $f6, 26); 457 $f6g9_19 = self::mul($g9_19, $f6, 26); 458 $f7g0 = self::mul($f7, $g0, 26); 459 $f7g1_2 = self::mul($f7_2, $g1, 25); 460 $f7g2 = self::mul($f7, $g2, 26); 461 $f7g3_38 = self::mul($g3_19, $f7_2, 26); 462 $f7g4_19 = self::mul($g4_19, $f7, 26); 463 $f7g5_38 = self::mul($g5_19, $f7_2, 26); 464 $f7g6_19 = self::mul($g6_19, $f7, 25); 465 $f7g7_38 = self::mul($g7_19, $f7_2, 26); 466 $f7g8_19 = self::mul($g8_19, $f7, 25); 467 $f7g9_38 = self::mul($g9_19,$f7_2, 26); 468 $f8g0 = self::mul($f8, $g0, 26); 469 $f8g1 = self::mul($f8, $g1, 25); 470 $f8g2_19 = self::mul($g2_19, $f8, 26); 471 $f8g3_19 = self::mul($g3_19, $f8, 26); 472 $f8g4_19 = self::mul($g4_19, $f8, 26); 473 $f8g5_19 = self::mul($g5_19, $f8, 26); 474 $f8g6_19 = self::mul($g6_19, $f8, 26); 475 $f8g7_19 = self::mul($g7_19, $f8, 26); 476 $f8g8_19 = self::mul($g8_19, $f8, 26); 477 $f8g9_19 = self::mul($g9_19, $f8, 26); 478 $f9g0 = self::mul($f9, $g0, 26); 479 $f9g1_38 = self::mul($g1_19, $f9_2, 26); 480 $f9g2_19 = self::mul($g2_19, $f9, 25); 481 $f9g3_38 = self::mul($g3_19, $f9_2, 26); 482 $f9g4_19 = self::mul($g4_19, $f9, 25); 483 $f9g5_38 = self::mul($g5_19, $f9_2, 26); 484 $f9g6_19 = self::mul($g6_19, $f9, 25); 485 $f9g7_38 = self::mul($g7_19, $f9_2, 26); 486 $f9g8_19 = self::mul($g8_19, $f9, 25); 487 $f9g9_38 = self::mul($g9_19, $f9_2, 26); 488 489 $h0 = $f0g0 + $f1g9_38 + $f2g8_19 + $f3g7_38 + $f4g6_19 + $f5g5_38 + $f6g4_19 + $f7g3_38 + $f8g2_19 + $f9g1_38; 490 $h1 = $f0g1 + $f1g0 + $f2g9_19 + $f3g8_19 + $f4g7_19 + $f5g6_19 + $f6g5_19 + $f7g4_19 + $f8g3_19 + $f9g2_19; 491 $h2 = $f0g2 + $f1g1_2 + $f2g0 + $f3g9_38 + $f4g8_19 + $f5g7_38 + $f6g6_19 + $f7g5_38 + $f8g4_19 + $f9g3_38; 492 $h3 = $f0g3 + $f1g2 + $f2g1 + $f3g0 + $f4g9_19 + $f5g8_19 + $f6g7_19 + $f7g6_19 + $f8g5_19 + $f9g4_19; 493 $h4 = $f0g4 + $f1g3_2 + $f2g2 + $f3g1_2 + $f4g0 + $f5g9_38 + $f6g8_19 + $f7g7_38 + $f8g6_19 + $f9g5_38; 494 $h5 = $f0g5 + $f1g4 + $f2g3 + $f3g2 + $f4g1 + $f5g0 + $f6g9_19 + $f7g8_19 + $f8g7_19 + $f9g6_19; 495 $h6 = $f0g6 + $f1g5_2 + $f2g4 + $f3g3_2 + $f4g2 + $f5g1_2 + $f6g0 + $f7g9_38 + $f8g8_19 + $f9g7_38; 496 $h7 = $f0g7 + $f1g6 + $f2g5 + $f3g4 + $f4g3 + $f5g2 + $f6g1 + $f7g0 + $f8g9_19 + $f9g8_19; 497 $h8 = $f0g8 + $f1g7_2 + $f2g6 + $f3g5_2 + $f4g4 + $f5g3_2 + $f6g2 + $f7g1_2 + $f8g0 + $f9g9_38; 498 $h9 = $f0g9 + $f1g8 + $f2g7 + $f3g6 + $f4g5 + $f5g4 + $f6g3 + $f7g2 + $f8g1 + $f9g0 ; 499 500 $carry0 = ($h0 + (1 << 25)) >> 26; 501 $h1 += $carry0; 502 $h0 -= $carry0 << 26; 503 $carry4 = ($h4 + (1 << 25)) >> 26; 504 $h5 += $carry4; 505 $h4 -= $carry4 << 26; 506 507 $carry1 = ($h1 + (1 << 24)) >> 25; 508 $h2 += $carry1; 509 $h1 -= $carry1 << 25; 510 $carry5 = ($h5 + (1 << 24)) >> 25; 511 $h6 += $carry5; 512 $h5 -= $carry5 << 25; 513 514 $carry2 = ($h2 + (1 << 25)) >> 26; 515 $h3 += $carry2; 516 $h2 -= $carry2 << 26; 517 $carry6 = ($h6 + (1 << 25)) >> 26; 518 $h7 += $carry6; 519 $h6 -= $carry6 << 26; 520 521 $carry3 = ($h3 + (1 << 24)) >> 25; 522 $h4 += $carry3; 523 $h3 -= $carry3 << 25; 524 $carry7 = ($h7 + (1 << 24)) >> 25; 525 $h8 += $carry7; 526 $h7 -= $carry7 << 25; 527 528 $carry4 = ($h4 + (1 << 25)) >> 26; 529 $h5 += $carry4; 530 $h4 -= $carry4 << 26; 531 $carry8 = ($h8 + (1 << 25)) >> 26; 532 $h9 += $carry8; 533 $h8 -= $carry8 << 26; 534 535 $carry9 = ($h9 + (1 << 24)) >> 25; 536 $h0 += self::mul($carry9, 19, 5); 537 $h9 -= $carry9 << 25; 538 539 $carry0 = ($h0 + (1 << 25)) >> 26; 540 $h1 += $carry0; 541 $h0 -= $carry0 << 26; 542 543 return self::fe_normalize( 544 new ParagonIE_Sodium_Core_Curve25519_Fe( 545 (int) $h0, 546 (int) $h1, 547 (int) $h2, 548 (int) $h3, 549 (int) $h4, 550 (int) $h5, 551 (int) $h6, 552 (int) $h7, 553 (int) $h8, 554 (int) $h9 555 ) 556 ); 557 } 558 559 /** 560 * Get the negative values for each piece of the field element. 561 * 562 * h = -f 563 * 564 * @internal You should not use this directly from another application 565 * 566 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 567 * @return ParagonIE_Sodium_Core_Curve25519_Fe 568 * @psalm-suppress MixedAssignment 569 */ 570 public static function fe_neg(ParagonIE_Sodium_Core_Curve25519_Fe $f) 571 { 572 return self::fe_normalize( 573 new ParagonIE_Sodium_Core_Curve25519_Fe( 574 -$f->e0, 575 -$f->e1, 576 -$f->e2, 577 -$f->e3, 578 -$f->e4, 579 -$f->e5, 580 -$f->e6, 581 -$f->e7, 582 -$f->e8, 583 -$f->e9 584 ) 585 ); 586 } 587 588 /** 589 * Square a field element 590 * 591 * h = f * f 592 * 593 * @internal You should not use this directly from another application 594 * 595 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 596 * @return ParagonIE_Sodium_Core_Curve25519_Fe 597 */ 598 public static function fe_sq(ParagonIE_Sodium_Core_Curve25519_Fe $f) 599 { 600 $f = self::fe_normalize($f); 601 $f0 = (int) $f->e0; 602 $f1 = (int) $f->e1; 603 $f2 = (int) $f->e2; 604 $f3 = (int) $f->e3; 605 $f4 = (int) $f->e4; 606 $f5 = (int) $f->e5; 607 $f6 = (int) $f->e6; 608 $f7 = (int) $f->e7; 609 $f8 = (int) $f->e8; 610 $f9 = (int) $f->e9; 611 612 $f0_2 = $f0 << 1; 613 $f1_2 = $f1 << 1; 614 $f2_2 = $f2 << 1; 615 $f3_2 = $f3 << 1; 616 $f4_2 = $f4 << 1; 617 $f5_2 = $f5 << 1; 618 $f6_2 = $f6 << 1; 619 $f7_2 = $f7 << 1; 620 $f5_38 = self::mul($f5, 38, 6); 621 $f6_19 = self::mul($f6, 19, 5); 622 $f7_38 = self::mul($f7, 38, 6); 623 $f8_19 = self::mul($f8, 19, 5); 624 $f9_38 = self::mul($f9, 38, 6); 625 $f0f0 = self::mul($f0, $f0, 26); 626 $f0f1_2 = self::mul($f0_2, $f1, 26); 627 $f0f2_2 = self::mul($f0_2, $f2, 26); 628 $f0f3_2 = self::mul($f0_2, $f3, 26); 629 $f0f4_2 = self::mul($f0_2, $f4, 26); 630 $f0f5_2 = self::mul($f0_2, $f5, 26); 631 $f0f6_2 = self::mul($f0_2, $f6, 26); 632 $f0f7_2 = self::mul($f0_2, $f7, 26); 633 $f0f8_2 = self::mul($f0_2, $f8, 26); 634 $f0f9_2 = self::mul($f0_2, $f9, 26); 635 $f1f1_2 = self::mul($f1_2, $f1, 26); 636 $f1f2_2 = self::mul($f1_2, $f2, 26); 637 $f1f3_4 = self::mul($f1_2, $f3_2, 26); 638 $f1f4_2 = self::mul($f1_2, $f4, 26); 639 $f1f5_4 = self::mul($f1_2, $f5_2, 26); 640 $f1f6_2 = self::mul($f1_2, $f6, 26); 641 $f1f7_4 = self::mul($f1_2, $f7_2, 26); 642 $f1f8_2 = self::mul($f1_2, $f8, 26); 643 $f1f9_76 = self::mul($f9_38, $f1_2, 27); 644 $f2f2 = self::mul($f2, $f2, 27); 645 $f2f3_2 = self::mul($f2_2, $f3, 27); 646 $f2f4_2 = self::mul($f2_2, $f4, 27); 647 $f2f5_2 = self::mul($f2_2, $f5, 27); 648 $f2f6_2 = self::mul($f2_2, $f6, 27); 649 $f2f7_2 = self::mul($f2_2, $f7, 27); 650 $f2f8_38 = self::mul($f8_19, $f2_2, 27); 651 $f2f9_38 = self::mul($f9_38, $f2, 26); 652 $f3f3_2 = self::mul($f3_2, $f3, 26); 653 $f3f4_2 = self::mul($f3_2, $f4, 26); 654 $f3f5_4 = self::mul($f3_2, $f5_2, 26); 655 $f3f6_2 = self::mul($f3_2, $f6, 26); 656 $f3f7_76 = self::mul($f7_38, $f3_2, 26); 657 $f3f8_38 = self::mul($f8_19, $f3_2, 26); 658 $f3f9_76 = self::mul($f9_38, $f3_2, 26); 659 $f4f4 = self::mul($f4, $f4, 26); 660 $f4f5_2 = self::mul($f4_2, $f5, 26); 661 $f4f6_38 = self::mul($f6_19, $f4_2, 27); 662 $f4f7_38 = self::mul($f7_38, $f4, 26); 663 $f4f8_38 = self::mul($f8_19, $f4_2, 27); 664 $f4f9_38 = self::mul($f9_38, $f4, 26); 665 $f5f5_38 = self::mul($f5_38, $f5, 26); 666 $f5f6_38 = self::mul($f6_19, $f5_2, 26); 667 $f5f7_76 = self::mul($f7_38, $f5_2, 26); 668 $f5f8_38 = self::mul($f8_19, $f5_2, 26); 669 $f5f9_76 = self::mul($f9_38, $f5_2, 26); 670 $f6f6_19 = self::mul($f6_19, $f6, 26); 671 $f6f7_38 = self::mul($f7_38, $f6, 26); 672 $f6f8_38 = self::mul($f8_19, $f6_2, 27); 673 $f6f9_38 = self::mul($f9_38, $f6, 26); 674 $f7f7_38 = self::mul($f7_38, $f7, 26); 675 $f7f8_38 = self::mul($f8_19, $f7_2, 26); 676 $f7f9_76 = self::mul($f9_38, $f7_2, 26); 677 $f8f8_19 = self::mul($f8_19, $f8, 26); 678 $f8f9_38 = self::mul($f9_38, $f8, 26); 679 $f9f9_38 = self::mul($f9_38, $f9, 26); 680 $h0 = $f0f0 + $f1f9_76 + $f2f8_38 + $f3f7_76 + $f4f6_38 + $f5f5_38; 681 $h1 = $f0f1_2 + $f2f9_38 + $f3f8_38 + $f4f7_38 + $f5f6_38; 682 $h2 = $f0f2_2 + $f1f1_2 + $f3f9_76 + $f4f8_38 + $f5f7_76 + $f6f6_19; 683 $h3 = $f0f3_2 + $f1f2_2 + $f4f9_38 + $f5f8_38 + $f6f7_38; 684 $h4 = $f0f4_2 + $f1f3_4 + $f2f2 + $f5f9_76 + $f6f8_38 + $f7f7_38; 685 $h5 = $f0f5_2 + $f1f4_2 + $f2f3_2 + $f6f9_38 + $f7f8_38; 686 $h6 = $f0f6_2 + $f1f5_4 + $f2f4_2 + $f3f3_2 + $f7f9_76 + $f8f8_19; 687 $h7 = $f0f7_2 + $f1f6_2 + $f2f5_2 + $f3f4_2 + $f8f9_38; 688 $h8 = $f0f8_2 + $f1f7_4 + $f2f6_2 + $f3f5_4 + $f4f4 + $f9f9_38; 689 $h9 = $f0f9_2 + $f1f8_2 + $f2f7_2 + $f3f6_2 + $f4f5_2; 690 691 $carry0 = ($h0 + (1 << 25)) >> 26; 692 $h1 += $carry0; 693 $h0 -= $carry0 << 26; 694 $carry4 = ($h4 + (1 << 25)) >> 26; 695 $h5 += $carry4; 696 $h4 -= $carry4 << 26; 697 698 $carry1 = ($h1 + (1 << 24)) >> 25; 699 $h2 += $carry1; 700 $h1 -= $carry1 << 25; 701 $carry5 = ($h5 + (1 << 24)) >> 25; 702 $h6 += $carry5; 703 $h5 -= $carry5 << 25; 704 705 $carry2 = ($h2 + (1 << 25)) >> 26; 706 $h3 += $carry2; 707 $h2 -= $carry2 << 26; 708 $carry6 = ($h6 + (1 << 25)) >> 26; 709 $h7 += $carry6; 710 $h6 -= $carry6 << 26; 711 712 $carry3 = ($h3 + (1 << 24)) >> 25; 713 $h4 += $carry3; 714 $h3 -= $carry3 << 25; 715 $carry7 = ($h7 + (1 << 24)) >> 25; 716 $h8 += $carry7; 717 $h7 -= $carry7 << 25; 718 719 $carry4 = ($h4 + (1 << 25)) >> 26; 720 $h5 += $carry4; 721 $h4 -= $carry4 << 26; 722 $carry8 = ($h8 + (1 << 25)) >> 26; 723 $h9 += $carry8; 724 $h8 -= $carry8 << 26; 725 726 $carry9 = ($h9 + (1 << 24)) >> 25; 727 $h0 += self::mul($carry9, 19, 5); 728 $h9 -= $carry9 << 25; 729 730 $carry0 = ($h0 + (1 << 25)) >> 26; 731 $h1 += $carry0; 732 $h0 -= $carry0 << 26; 733 734 return self::fe_normalize( 735 new ParagonIE_Sodium_Core_Curve25519_Fe( 736 (int) $h0, 737 (int) $h1, 738 (int) $h2, 739 (int) $h3, 740 (int) $h4, 741 (int) $h5, 742 (int) $h6, 743 (int) $h7, 744 (int) $h8, 745 (int) $h9 746 ) 747 ); 748 } 749 750 751 /** 752 * Square and double a field element 753 * 754 * h = 2 * f * f 755 * 756 * @internal You should not use this directly from another application 757 * 758 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 759 * @return ParagonIE_Sodium_Core_Curve25519_Fe 760 */ 761 public static function fe_sq2(ParagonIE_Sodium_Core_Curve25519_Fe $f) 762 { 763 $f = self::fe_normalize($f); 764 $f0 = (int) $f->e0; 765 $f1 = (int) $f->e1; 766 $f2 = (int) $f->e2; 767 $f3 = (int) $f->e3; 768 $f4 = (int) $f->e4; 769 $f5 = (int) $f->e5; 770 $f6 = (int) $f->e6; 771 $f7 = (int) $f->e7; 772 $f8 = (int) $f->e8; 773 $f9 = (int) $f->e9; 774 775 $f0_2 = $f0 << 1; 776 $f1_2 = $f1 << 1; 777 $f2_2 = $f2 << 1; 778 $f3_2 = $f3 << 1; 779 $f4_2 = $f4 << 1; 780 $f5_2 = $f5 << 1; 781 $f6_2 = $f6 << 1; 782 $f7_2 = $f7 << 1; 783 $f5_38 = self::mul($f5, 38, 6); /* 1.959375*2^30 */ 784 $f6_19 = self::mul($f6, 19, 5); /* 1.959375*2^30 */ 785 $f7_38 = self::mul($f7, 38, 6); /* 1.959375*2^30 */ 786 $f8_19 = self::mul($f8, 19, 5); /* 1.959375*2^30 */ 787 $f9_38 = self::mul($f9, 38, 6); /* 1.959375*2^30 */ 788 $f0f0 = self::mul($f0, $f0, 24); 789 $f0f1_2 = self::mul($f0_2, $f1, 24); 790 $f0f2_2 = self::mul($f0_2, $f2, 24); 791 $f0f3_2 = self::mul($f0_2, $f3, 24); 792 $f0f4_2 = self::mul($f0_2, $f4, 24); 793 $f0f5_2 = self::mul($f0_2, $f5, 24); 794 $f0f6_2 = self::mul($f0_2, $f6, 24); 795 $f0f7_2 = self::mul($f0_2, $f7, 24); 796 $f0f8_2 = self::mul($f0_2, $f8, 24); 797 $f0f9_2 = self::mul($f0_2, $f9, 24); 798 $f1f1_2 = self::mul($f1_2, $f1, 24); 799 $f1f2_2 = self::mul($f1_2, $f2, 24); 800 $f1f3_4 = self::mul($f1_2, $f3_2, 24); 801 $f1f4_2 = self::mul($f1_2, $f4, 24); 802 $f1f5_4 = self::mul($f1_2, $f5_2, 24); 803 $f1f6_2 = self::mul($f1_2, $f6, 24); 804 $f1f7_4 = self::mul($f1_2, $f7_2, 24); 805 $f1f8_2 = self::mul($f1_2, $f8, 24); 806 $f1f9_76 = self::mul($f9_38, $f1_2, 24); 807 $f2f2 = self::mul($f2, $f2, 24); 808 $f2f3_2 = self::mul($f2_2, $f3, 24); 809 $f2f4_2 = self::mul($f2_2, $f4, 24); 810 $f2f5_2 = self::mul($f2_2, $f5, 24); 811 $f2f6_2 = self::mul($f2_2, $f6, 24); 812 $f2f7_2 = self::mul($f2_2, $f7, 24); 813 $f2f8_38 = self::mul($f8_19, $f2_2, 25); 814 $f2f9_38 = self::mul($f9_38, $f2, 24); 815 $f3f3_2 = self::mul($f3_2, $f3, 24); 816 $f3f4_2 = self::mul($f3_2, $f4, 24); 817 $f3f5_4 = self::mul($f3_2, $f5_2, 24); 818 $f3f6_2 = self::mul($f3_2, $f6, 24); 819 $f3f7_76 = self::mul($f7_38, $f3_2, 24); 820 $f3f8_38 = self::mul($f8_19, $f3_2, 24); 821 $f3f9_76 = self::mul($f9_38, $f3_2, 24); 822 $f4f4 = self::mul($f4, $f4, 24); 823 $f4f5_2 = self::mul($f4_2, $f5, 24); 824 $f4f6_38 = self::mul($f6_19, $f4_2, 25); 825 $f4f7_38 = self::mul($f7_38, $f4, 24); 826 $f4f8_38 = self::mul($f8_19, $f4_2, 25); 827 $f4f9_38 = self::mul($f9_38, $f4, 24); 828 $f5f5_38 = self::mul($f5_38, $f5, 24); 829 $f5f6_38 = self::mul($f6_19, $f5_2, 24); 830 $f5f7_76 = self::mul($f7_38, $f5_2, 24); 831 $f5f8_38 = self::mul($f8_19, $f5_2, 24); 832 $f5f9_76 = self::mul($f9_38, $f5_2, 24); 833 $f6f6_19 = self::mul($f6_19, $f6, 24); 834 $f6f7_38 = self::mul($f7_38, $f6, 24); 835 $f6f8_38 = self::mul($f8_19, $f6_2, 25); 836 $f6f9_38 = self::mul($f9_38, $f6, 24); 837 $f7f7_38 = self::mul($f7_38, $f7, 24); 838 $f7f8_38 = self::mul($f8_19, $f7_2, 24); 839 $f7f9_76 = self::mul($f9_38, $f7_2, 24); 840 $f8f8_19 = self::mul($f8_19, $f8, 24); 841 $f8f9_38 = self::mul($f9_38, $f8, 24); 842 $f9f9_38 = self::mul($f9_38, $f9, 24); 843 844 $h0 = (int) ($f0f0 + $f1f9_76 + $f2f8_38 + $f3f7_76 + $f4f6_38 + $f5f5_38) << 1; 845 $h1 = (int) ($f0f1_2 + $f2f9_38 + $f3f8_38 + $f4f7_38 + $f5f6_38) << 1; 846 $h2 = (int) ($f0f2_2 + $f1f1_2 + $f3f9_76 + $f4f8_38 + $f5f7_76 + $f6f6_19) << 1; 847 $h3 = (int) ($f0f3_2 + $f1f2_2 + $f4f9_38 + $f5f8_38 + $f6f7_38) << 1; 848 $h4 = (int) ($f0f4_2 + $f1f3_4 + $f2f2 + $f5f9_76 + $f6f8_38 + $f7f7_38) << 1; 849 $h5 = (int) ($f0f5_2 + $f1f4_2 + $f2f3_2 + $f6f9_38 + $f7f8_38) << 1; 850 $h6 = (int) ($f0f6_2 + $f1f5_4 + $f2f4_2 + $f3f3_2 + $f7f9_76 + $f8f8_19) << 1; 851 $h7 = (int) ($f0f7_2 + $f1f6_2 + $f2f5_2 + $f3f4_2 + $f8f9_38) << 1; 852 $h8 = (int) ($f0f8_2 + $f1f7_4 + $f2f6_2 + $f3f5_4 + $f4f4 + $f9f9_38) << 1; 853 $h9 = (int) ($f0f9_2 + $f1f8_2 + $f2f7_2 + $f3f6_2 + $f4f5_2) << 1; 854 855 $carry0 = ($h0 + (1 << 25)) >> 26; 856 $h1 += $carry0; 857 $h0 -= $carry0 << 26; 858 $carry4 = ($h4 + (1 << 25)) >> 26; 859 $h5 += $carry4; 860 $h4 -= $carry4 << 26; 861 862 $carry1 = ($h1 + (1 << 24)) >> 25; 863 $h2 += $carry1; 864 $h1 -= $carry1 << 25; 865 $carry5 = ($h5 + (1 << 24)) >> 25; 866 $h6 += $carry5; 867 $h5 -= $carry5 << 25; 868 869 $carry2 = ($h2 + (1 << 25)) >> 26; 870 $h3 += $carry2; 871 $h2 -= $carry2 << 26; 872 $carry6 = ($h6 + (1 << 25)) >> 26; 873 $h7 += $carry6; 874 $h6 -= $carry6 << 26; 875 876 $carry3 = ($h3 + (1 << 24)) >> 25; 877 $h4 += $carry3; 878 $h3 -= $carry3 << 25; 879 $carry7 = ($h7 + (1 << 24)) >> 25; 880 $h8 += $carry7; 881 $h7 -= $carry7 << 25; 882 883 $carry4 = ($h4 + (1 << 25)) >> 26; 884 $h5 += $carry4; 885 $h4 -= $carry4 << 26; 886 $carry8 = ($h8 + (1 << 25)) >> 26; 887 $h9 += $carry8; 888 $h8 -= $carry8 << 26; 889 890 $carry9 = ($h9 + (1 << 24)) >> 25; 891 $h0 += self::mul($carry9, 19, 5); 892 $h9 -= $carry9 << 25; 893 894 $carry0 = ($h0 + (1 << 25)) >> 26; 895 $h1 += $carry0; 896 $h0 -= $carry0 << 26; 897 898 return self::fe_normalize( 899 new ParagonIE_Sodium_Core_Curve25519_Fe( 900 (int) $h0, 901 (int) $h1, 902 (int) $h2, 903 (int) $h3, 904 (int) $h4, 905 (int) $h5, 906 (int) $h6, 907 (int) $h7, 908 (int) $h8, 909 (int) $h9 910 ) 911 ); 912 } 913 914 /** 915 * @internal You should not use this directly from another application 916 * 917 * @param ParagonIE_Sodium_Core_Curve25519_Fe $Z 918 * @return ParagonIE_Sodium_Core_Curve25519_Fe 919 */ 920 public static function fe_invert(ParagonIE_Sodium_Core_Curve25519_Fe $Z) 921 { 922 $z = clone $Z; 923 $t0 = self::fe_sq($z); 924 $t1 = self::fe_sq($t0); 925 $t1 = self::fe_sq($t1); 926 $t1 = self::fe_mul($z, $t1); 927 $t0 = self::fe_mul($t0, $t1); 928 $t2 = self::fe_sq($t0); 929 $t1 = self::fe_mul($t1, $t2); 930 $t2 = self::fe_sq($t1); 931 for ($i = 1; $i < 5; ++$i) { 932 $t2 = self::fe_sq($t2); 933 } 934 $t1 = self::fe_mul($t2, $t1); 935 $t2 = self::fe_sq($t1); 936 for ($i = 1; $i < 10; ++$i) { 937 $t2 = self::fe_sq($t2); 938 } 939 $t2 = self::fe_mul($t2, $t1); 940 $t3 = self::fe_sq($t2); 941 for ($i = 1; $i < 20; ++$i) { 942 $t3 = self::fe_sq($t3); 943 } 944 $t2 = self::fe_mul($t3, $t2); 945 $t2 = self::fe_sq($t2); 946 for ($i = 1; $i < 10; ++$i) { 947 $t2 = self::fe_sq($t2); 948 } 949 $t1 = self::fe_mul($t2, $t1); 950 $t2 = self::fe_sq($t1); 951 for ($i = 1; $i < 50; ++$i) { 952 $t2 = self::fe_sq($t2); 953 } 954 $t2 = self::fe_mul($t2, $t1); 955 $t3 = self::fe_sq($t2); 956 for ($i = 1; $i < 100; ++$i) { 957 $t3 = self::fe_sq($t3); 958 } 959 $t2 = self::fe_mul($t3, $t2); 960 $t2 = self::fe_sq($t2); 961 for ($i = 1; $i < 50; ++$i) { 962 $t2 = self::fe_sq($t2); 963 } 964 $t1 = self::fe_mul($t2, $t1); 965 $t1 = self::fe_sq($t1); 966 for ($i = 1; $i < 5; ++$i) { 967 $t1 = self::fe_sq($t1); 968 } 969 return self::fe_mul($t1, $t0); 970 } 971 972 /** 973 * @internal You should not use this directly from another application 974 * 975 * @ref https://github.com/jedisct1/libsodium/blob/68564326e1e9dc57ef03746f85734232d20ca6fb/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c#L1054-L1106 976 * 977 * @param ParagonIE_Sodium_Core_Curve25519_Fe $z 978 * @return ParagonIE_Sodium_Core_Curve25519_Fe 979 */ 980 public static function fe_pow22523(ParagonIE_Sodium_Core_Curve25519_Fe $z) 981 { 982 $z = self::fe_normalize($z); 983 # fe_sq(t0, z); 984 # fe_sq(t1, t0); 985 # fe_sq(t1, t1); 986 # fe_mul(t1, z, t1); 987 # fe_mul(t0, t0, t1); 988 # fe_sq(t0, t0); 989 # fe_mul(t0, t1, t0); 990 # fe_sq(t1, t0); 991 $t0 = self::fe_sq($z); 992 $t1 = self::fe_sq($t0); 993 $t1 = self::fe_sq($t1); 994 $t1 = self::fe_mul($z, $t1); 995 $t0 = self::fe_mul($t0, $t1); 996 $t0 = self::fe_sq($t0); 997 $t0 = self::fe_mul($t1, $t0); 998 $t1 = self::fe_sq($t0); 999 1000 # for (i = 1; i < 5; ++i) { 1001 # fe_sq(t1, t1); 1002 # } 1003 for ($i = 1; $i < 5; ++$i) { 1004 $t1 = self::fe_sq($t1); 1005 } 1006 1007 # fe_mul(t0, t1, t0); 1008 # fe_sq(t1, t0); 1009 $t0 = self::fe_mul($t1, $t0); 1010 $t1 = self::fe_sq($t0); 1011 1012 # for (i = 1; i < 10; ++i) { 1013 # fe_sq(t1, t1); 1014 # } 1015 for ($i = 1; $i < 10; ++$i) { 1016 $t1 = self::fe_sq($t1); 1017 } 1018 1019 # fe_mul(t1, t1, t0); 1020 # fe_sq(t2, t1); 1021 $t1 = self::fe_mul($t1, $t0); 1022 $t2 = self::fe_sq($t1); 1023 1024 # for (i = 1; i < 20; ++i) { 1025 # fe_sq(t2, t2); 1026 # } 1027 for ($i = 1; $i < 20; ++$i) { 1028 $t2 = self::fe_sq($t2); 1029 } 1030 1031 # fe_mul(t1, t2, t1); 1032 # fe_sq(t1, t1); 1033 $t1 = self::fe_mul($t2, $t1); 1034 $t1 = self::fe_sq($t1); 1035 1036 # for (i = 1; i < 10; ++i) { 1037 # fe_sq(t1, t1); 1038 # } 1039 for ($i = 1; $i < 10; ++$i) { 1040 $t1 = self::fe_sq($t1); 1041 } 1042 1043 # fe_mul(t0, t1, t0); 1044 # fe_sq(t1, t0); 1045 $t0 = self::fe_mul($t1, $t0); 1046 $t1 = self::fe_sq($t0); 1047 1048 # for (i = 1; i < 50; ++i) { 1049 # fe_sq(t1, t1); 1050 # } 1051 for ($i = 1; $i < 50; ++$i) { 1052 $t1 = self::fe_sq($t1); 1053 } 1054 1055 # fe_mul(t1, t1, t0); 1056 # fe_sq(t2, t1); 1057 $t1 = self::fe_mul($t1, $t0); 1058 $t2 = self::fe_sq($t1); 1059 1060 # for (i = 1; i < 100; ++i) { 1061 # fe_sq(t2, t2); 1062 # } 1063 for ($i = 1; $i < 100; ++$i) { 1064 $t2 = self::fe_sq($t2); 1065 } 1066 1067 # fe_mul(t1, t2, t1); 1068 # fe_sq(t1, t1); 1069 $t1 = self::fe_mul($t2, $t1); 1070 $t1 = self::fe_sq($t1); 1071 1072 # for (i = 1; i < 50; ++i) { 1073 # fe_sq(t1, t1); 1074 # } 1075 for ($i = 1; $i < 50; ++$i) { 1076 $t1 = self::fe_sq($t1); 1077 } 1078 1079 # fe_mul(t0, t1, t0); 1080 # fe_sq(t0, t0); 1081 # fe_sq(t0, t0); 1082 # fe_mul(out, t0, z); 1083 $t0 = self::fe_mul($t1, $t0); 1084 $t0 = self::fe_sq($t0); 1085 $t0 = self::fe_sq($t0); 1086 return self::fe_mul($t0, $z); 1087 } 1088 1089 /** 1090 * Subtract two field elements. 1091 * 1092 * h = f - g 1093 * 1094 * Preconditions: 1095 * |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. 1096 * |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. 1097 * 1098 * Postconditions: 1099 * |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. 1100 * 1101 * @internal You should not use this directly from another application 1102 * 1103 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 1104 * @param ParagonIE_Sodium_Core_Curve25519_Fe $g 1105 * @return ParagonIE_Sodium_Core_Curve25519_Fe 1106 * @psalm-suppress MixedOperand 1107 */ 1108 public static function fe_sub(ParagonIE_Sodium_Core_Curve25519_Fe $f, ParagonIE_Sodium_Core_Curve25519_Fe $g) 1109 { 1110 return self::fe_normalize( 1111 new ParagonIE_Sodium_Core_Curve25519_Fe( 1112 (int) ($f->e0 - $g->e0), 1113 (int) ($f->e1 - $g->e1), 1114 (int) ($f->e2 - $g->e2), 1115 (int) ($f->e3 - $g->e3), 1116 (int) ($f->e4 - $g->e4), 1117 (int) ($f->e5 - $g->e5), 1118 (int) ($f->e6 - $g->e6), 1119 (int) ($f->e7 - $g->e7), 1120 (int) ($f->e8 - $g->e8), 1121 (int) ($f->e9 - $g->e9) 1122 ) 1123 ); 1124 } 1125 1126 /** 1127 * Add two group elements. 1128 * 1129 * r = p + q 1130 * 1131 * @internal You should not use this directly from another application 1132 * 1133 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p 1134 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q 1135 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 1136 */ 1137 public static function ge_add( 1138 ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p, 1139 ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q 1140 ) { 1141 $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); 1142 $r->X = self::fe_add($p->Y, $p->X); 1143 $r->Y = self::fe_sub($p->Y, $p->X); 1144 $r->Z = self::fe_mul($r->X, $q->YplusX); 1145 $r->Y = self::fe_mul($r->Y, $q->YminusX); 1146 $r->T = self::fe_mul($q->T2d, $p->T); 1147 $r->X = self::fe_mul($p->Z, $q->Z); 1148 $t0 = self::fe_add($r->X, $r->X); 1149 $r->X = self::fe_sub($r->Z, $r->Y); 1150 $r->Y = self::fe_add($r->Z, $r->Y); 1151 $r->Z = self::fe_add($t0, $r->T); 1152 $r->T = self::fe_sub($t0, $r->T); 1153 return $r; 1154 } 1155 1156 /** 1157 * @internal You should not use this directly from another application 1158 * 1159 * @ref https://github.com/jedisct1/libsodium/blob/157c4a80c13b117608aeae12178b2d38825f9f8f/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c#L1185-L1215 1160 * @param string $a 1161 * @return array<int, mixed> 1162 * @throws SodiumException 1163 * @throws TypeError 1164 */ 1165 public static function slide($a) 1166 { 1167 if (self::strlen($a) < 256) { 1168 if (self::strlen($a) < 16) { 1169 $a = str_pad($a, 256, '0', STR_PAD_RIGHT); 1170 } 1171 } 1172 /** @var array<int, int> $r */ 1173 $r = array(); 1174 1175 /** @var int $i */ 1176 for ($i = 0; $i < 256; ++$i) { 1177 $r[$i] = (int) ( 1178 1 & ( 1179 self::chrToInt($a[(int) ($i >> 3)]) 1180 >> 1181 ($i & 7) 1182 ) 1183 ); 1184 } 1185 1186 for ($i = 0;$i < 256;++$i) { 1187 if ($r[$i]) { 1188 for ($b = 1;$b <= 6 && $i + $b < 256;++$b) { 1189 if ($r[$i + $b]) { 1190 if ($r[$i] + ($r[$i + $b] << $b) <= 15) { 1191 $r[$i] += $r[$i + $b] << $b; 1192 $r[$i + $b] = 0; 1193 } elseif ($r[$i] - ($r[$i + $b] << $b) >= -15) { 1194 $r[$i] -= $r[$i + $b] << $b; 1195 for ($k = $i + $b; $k < 256; ++$k) { 1196 if (!$r[$k]) { 1197 $r[$k] = 1; 1198 break; 1199 } 1200 $r[$k] = 0; 1201 } 1202 } else { 1203 break; 1204 } 1205 } 1206 } 1207 } 1208 } 1209 return $r; 1210 } 1211 1212 /** 1213 * @internal You should not use this directly from another application 1214 * 1215 * @param string $s 1216 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 1217 * @throws SodiumException 1218 * @throws TypeError 1219 */ 1220 public static function ge_frombytes_negate_vartime($s) 1221 { 1222 static $d = null; 1223 if (!$d) { 1224 $d = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$d); 1225 } 1226 1227 # fe_frombytes(h->Y,s); 1228 # fe_1(h->Z); 1229 $h = new ParagonIE_Sodium_Core_Curve25519_Ge_P3( 1230 self::fe_0(), 1231 self::fe_frombytes($s), 1232 self::fe_1() 1233 ); 1234 1235 # fe_sq(u,h->Y); 1236 # fe_mul(v,u,d); 1237 # fe_sub(u,u,h->Z); /* u = y^2-1 */ 1238 # fe_add(v,v,h->Z); /* v = dy^2+1 */ 1239 $u = self::fe_sq($h->Y); 1240 /** @var ParagonIE_Sodium_Core_Curve25519_Fe $d */ 1241 $v = self::fe_mul($u, $d); 1242 $u = self::fe_sub($u, $h->Z); /* u = y^2 - 1 */ 1243 $v = self::fe_add($v, $h->Z); /* v = dy^2 + 1 */ 1244 1245 # fe_sq(v3,v); 1246 # fe_mul(v3,v3,v); /* v3 = v^3 */ 1247 # fe_sq(h->X,v3); 1248 # fe_mul(h->X,h->X,v); 1249 # fe_mul(h->X,h->X,u); /* x = uv^7 */ 1250 $v3 = self::fe_sq($v); 1251 $v3 = self::fe_mul($v3, $v); /* v3 = v^3 */ 1252 $h->X = self::fe_sq($v3); 1253 $h->X = self::fe_mul($h->X, $v); 1254 $h->X = self::fe_mul($h->X, $u); /* x = uv^7 */ 1255 1256 # fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */ 1257 # fe_mul(h->X,h->X,v3); 1258 # fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */ 1259 $h->X = self::fe_pow22523($h->X); /* x = (uv^7)^((q-5)/8) */ 1260 $h->X = self::fe_mul($h->X, $v3); 1261 $h->X = self::fe_mul($h->X, $u); /* x = uv^3(uv^7)^((q-5)/8) */ 1262 1263 # fe_sq(vxx,h->X); 1264 # fe_mul(vxx,vxx,v); 1265 # fe_sub(check,vxx,u); /* vx^2-u */ 1266 $vxx = self::fe_sq($h->X); 1267 $vxx = self::fe_mul($vxx, $v); 1268 $check = self::fe_sub($vxx, $u); /* vx^2 - u */ 1269 1270 # if (fe_isnonzero(check)) { 1271 # fe_add(check,vxx,u); /* vx^2+u */ 1272 # if (fe_isnonzero(check)) { 1273 # return -1; 1274 # } 1275 # fe_mul(h->X,h->X,sqrtm1); 1276 # } 1277 if (self::fe_isnonzero($check)) { 1278 $check = self::fe_add($vxx, $u); /* vx^2 + u */ 1279 if (self::fe_isnonzero($check)) { 1280 throw new RangeException('Internal check failed.'); 1281 } 1282 $h->X = self::fe_mul( 1283 $h->X, 1284 ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$sqrtm1) 1285 ); 1286 } 1287 1288 # if (fe_isnegative(h->X) == (s[31] >> 7)) { 1289 # fe_neg(h->X,h->X); 1290 # } 1291 $i = self::chrToInt($s[31]); 1292 if (self::fe_isnegative($h->X) === ($i >> 7)) { 1293 $h->X = self::fe_neg($h->X); 1294 } 1295 1296 # fe_mul(h->T,h->X,h->Y); 1297 $h->T = self::fe_mul($h->X, $h->Y); 1298 return $h; 1299 } 1300 1301 /** 1302 * @internal You should not use this directly from another application 1303 * 1304 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R 1305 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p 1306 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q 1307 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 1308 */ 1309 public static function ge_madd( 1310 ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R, 1311 ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p, 1312 ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q 1313 ) { 1314 $r = clone $R; 1315 $r->X = self::fe_add($p->Y, $p->X); 1316 $r->Y = self::fe_sub($p->Y, $p->X); 1317 $r->Z = self::fe_mul($r->X, $q->yplusx); 1318 $r->Y = self::fe_mul($r->Y, $q->yminusx); 1319 $r->T = self::fe_mul($q->xy2d, $p->T); 1320 $t0 = self::fe_add(clone $p->Z, clone $p->Z); 1321 $r->X = self::fe_sub($r->Z, $r->Y); 1322 $r->Y = self::fe_add($r->Z, $r->Y); 1323 $r->Z = self::fe_add($t0, $r->T); 1324 $r->T = self::fe_sub($t0, $r->T); 1325 1326 return $r; 1327 } 1328 1329 /** 1330 * @internal You should not use this directly from another application 1331 * 1332 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R 1333 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p 1334 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q 1335 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 1336 */ 1337 public static function ge_msub( 1338 ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $R, 1339 ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p, 1340 ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $q 1341 ) { 1342 $r = clone $R; 1343 1344 $r->X = self::fe_add($p->Y, $p->X); 1345 $r->Y = self::fe_sub($p->Y, $p->X); 1346 $r->Z = self::fe_mul($r->X, $q->yminusx); 1347 $r->Y = self::fe_mul($r->Y, $q->yplusx); 1348 $r->T = self::fe_mul($q->xy2d, $p->T); 1349 $t0 = self::fe_add($p->Z, $p->Z); 1350 $r->X = self::fe_sub($r->Z, $r->Y); 1351 $r->Y = self::fe_add($r->Z, $r->Y); 1352 $r->Z = self::fe_sub($t0, $r->T); 1353 $r->T = self::fe_add($t0, $r->T); 1354 1355 return $r; 1356 } 1357 1358 /** 1359 * @internal You should not use this directly from another application 1360 * 1361 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p 1362 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P2 1363 */ 1364 public static function ge_p1p1_to_p2(ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p) 1365 { 1366 $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P2(); 1367 $r->X = self::fe_mul($p->X, $p->T); 1368 $r->Y = self::fe_mul($p->Y, $p->Z); 1369 $r->Z = self::fe_mul($p->Z, $p->T); 1370 return $r; 1371 } 1372 1373 /** 1374 * @internal You should not use this directly from another application 1375 * 1376 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p 1377 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 1378 */ 1379 public static function ge_p1p1_to_p3(ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 $p) 1380 { 1381 $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P3(); 1382 $r->X = self::fe_mul($p->X, $p->T); 1383 $r->Y = self::fe_mul($p->Y, $p->Z); 1384 $r->Z = self::fe_mul($p->Z, $p->T); 1385 $r->T = self::fe_mul($p->X, $p->Y); 1386 return $r; 1387 } 1388 1389 /** 1390 * @internal You should not use this directly from another application 1391 * 1392 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P2 1393 */ 1394 public static function ge_p2_0() 1395 { 1396 return new ParagonIE_Sodium_Core_Curve25519_Ge_P2( 1397 self::fe_0(), 1398 self::fe_1(), 1399 self::fe_1() 1400 ); 1401 } 1402 1403 /** 1404 * @internal You should not use this directly from another application 1405 * 1406 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P2 $p 1407 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 1408 */ 1409 public static function ge_p2_dbl(ParagonIE_Sodium_Core_Curve25519_Ge_P2 $p) 1410 { 1411 $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); 1412 1413 $r->X = self::fe_sq($p->X); 1414 $r->Z = self::fe_sq($p->Y); 1415 $r->T = self::fe_sq2($p->Z); 1416 $r->Y = self::fe_add($p->X, $p->Y); 1417 $t0 = self::fe_sq($r->Y); 1418 $r->Y = self::fe_add($r->Z, $r->X); 1419 $r->Z = self::fe_sub($r->Z, $r->X); 1420 $r->X = self::fe_sub($t0, $r->Y); 1421 $r->T = self::fe_sub($r->T, $r->Z); 1422 1423 return $r; 1424 } 1425 1426 /** 1427 * @internal You should not use this directly from another application 1428 * 1429 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 1430 */ 1431 public static function ge_p3_0() 1432 { 1433 return new ParagonIE_Sodium_Core_Curve25519_Ge_P3( 1434 self::fe_0(), 1435 self::fe_1(), 1436 self::fe_1(), 1437 self::fe_0() 1438 ); 1439 } 1440 1441 /** 1442 * @internal You should not use this directly from another application 1443 * 1444 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p 1445 * @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached 1446 */ 1447 public static function ge_p3_to_cached(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p) 1448 { 1449 static $d2 = null; 1450 if ($d2 === null) { 1451 $d2 = ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$d2); 1452 } 1453 /** @var ParagonIE_Sodium_Core_Curve25519_Fe $d2 */ 1454 $r = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(); 1455 $r->YplusX = self::fe_add($p->Y, $p->X); 1456 $r->YminusX = self::fe_sub($p->Y, $p->X); 1457 $r->Z = self::fe_copy($p->Z); 1458 $r->T2d = self::fe_mul($p->T, $d2); 1459 return $r; 1460 } 1461 1462 /** 1463 * @internal You should not use this directly from another application 1464 * 1465 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p 1466 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P2 1467 */ 1468 public static function ge_p3_to_p2(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p) 1469 { 1470 return new ParagonIE_Sodium_Core_Curve25519_Ge_P2( 1471 self::fe_copy($p->X), 1472 self::fe_copy($p->Y), 1473 self::fe_copy($p->Z) 1474 ); 1475 } 1476 1477 /** 1478 * @internal You should not use this directly from another application 1479 * 1480 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $h 1481 * @return string 1482 * @throws SodiumException 1483 * @throws TypeError 1484 */ 1485 public static function ge_p3_tobytes(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $h) 1486 { 1487 $recip = self::fe_invert($h->Z); 1488 $x = self::fe_mul($h->X, $recip); 1489 $y = self::fe_mul($h->Y, $recip); 1490 $s = self::fe_tobytes($y); 1491 $s[31] = self::intToChr( 1492 self::chrToInt($s[31]) ^ (self::fe_isnegative($x) << 7) 1493 ); 1494 return $s; 1495 } 1496 1497 /** 1498 * @internal You should not use this directly from another application 1499 * 1500 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p 1501 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 1502 */ 1503 public static function ge_p3_dbl(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p) 1504 { 1505 $q = self::ge_p3_to_p2($p); 1506 return self::ge_p2_dbl($q); 1507 } 1508 1509 /** 1510 * @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp 1511 */ 1512 public static function ge_precomp_0() 1513 { 1514 return new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( 1515 self::fe_1(), 1516 self::fe_1(), 1517 self::fe_0() 1518 ); 1519 } 1520 1521 /** 1522 * @internal You should not use this directly from another application 1523 * 1524 * @param int $b 1525 * @param int $c 1526 * @return int 1527 */ 1528 public static function equal($b, $c) 1529 { 1530 return (int) ((($b ^ $c) - 1) >> 31) & 1; 1531 } 1532 1533 /** 1534 * @internal You should not use this directly from another application 1535 * 1536 * @param int|string $char 1537 * @return int (1 = yes, 0 = no) 1538 * @throws SodiumException 1539 * @throws TypeError 1540 */ 1541 public static function negative($char) 1542 { 1543 if (is_int($char)) { 1544 return ($char >> 63) & 1; 1545 } 1546 $x = self::chrToInt(self::substr($char, 0, 1)); 1547 return (int) ($x >> 63); 1548 } 1549 1550 /** 1551 * Conditional move 1552 * 1553 * @internal You should not use this directly from another application 1554 * 1555 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $t 1556 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $u 1557 * @param int $b 1558 * @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp 1559 */ 1560 public static function cmov( 1561 ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $t, 1562 ParagonIE_Sodium_Core_Curve25519_Ge_Precomp $u, 1563 $b 1564 ) { 1565 if (!is_int($b)) { 1566 throw new InvalidArgumentException('Expected an integer.'); 1567 } 1568 return new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( 1569 self::fe_cmov($t->yplusx, $u->yplusx, $b), 1570 self::fe_cmov($t->yminusx, $u->yminusx, $b), 1571 self::fe_cmov($t->xy2d, $u->xy2d, $b) 1572 ); 1573 } 1574 1575 /** 1576 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $t 1577 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $u 1578 * @param int $b 1579 * @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached 1580 */ 1581 public static function ge_cmov_cached( 1582 ParagonIE_Sodium_Core_Curve25519_Ge_Cached $t, 1583 ParagonIE_Sodium_Core_Curve25519_Ge_Cached $u, 1584 $b 1585 ) { 1586 $b &= 1; 1587 $ret = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached(); 1588 $ret->YplusX = self::fe_cmov($t->YplusX, $u->YplusX, $b); 1589 $ret->YminusX = self::fe_cmov($t->YminusX, $u->YminusX, $b); 1590 $ret->Z = self::fe_cmov($t->Z, $u->Z, $b); 1591 $ret->T2d = self::fe_cmov($t->T2d, $u->T2d, $b); 1592 return $ret; 1593 } 1594 1595 /** 1596 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached[] $cached 1597 * @param int $b 1598 * @return ParagonIE_Sodium_Core_Curve25519_Ge_Cached 1599 * @throws SodiumException 1600 */ 1601 public static function ge_cmov8_cached(array $cached, $b) 1602 { 1603 // const unsigned char bnegative = negative(b); 1604 // const unsigned char babs = b - (((-bnegative) & b) * ((signed char) 1 << 1)); 1605 $bnegative = self::negative($b); 1606 $babs = $b - (((-$bnegative) & $b) << 1); 1607 1608 // ge25519_cached_0(t); 1609 $t = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached( 1610 self::fe_1(), 1611 self::fe_1(), 1612 self::fe_1(), 1613 self::fe_0() 1614 ); 1615 1616 // ge25519_cmov_cached(t, &cached[0], equal(babs, 1)); 1617 // ge25519_cmov_cached(t, &cached[1], equal(babs, 2)); 1618 // ge25519_cmov_cached(t, &cached[2], equal(babs, 3)); 1619 // ge25519_cmov_cached(t, &cached[3], equal(babs, 4)); 1620 // ge25519_cmov_cached(t, &cached[4], equal(babs, 5)); 1621 // ge25519_cmov_cached(t, &cached[5], equal(babs, 6)); 1622 // ge25519_cmov_cached(t, &cached[6], equal(babs, 7)); 1623 // ge25519_cmov_cached(t, &cached[7], equal(babs, 8)); 1624 for ($x = 0; $x < 8; ++$x) { 1625 $t = self::ge_cmov_cached($t, $cached[$x], self::equal($babs, $x + 1)); 1626 } 1627 1628 // fe25519_copy(minust.YplusX, t->YminusX); 1629 // fe25519_copy(minust.YminusX, t->YplusX); 1630 // fe25519_copy(minust.Z, t->Z); 1631 // fe25519_neg(minust.T2d, t->T2d); 1632 $minust = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached( 1633 self::fe_copy($t->YminusX), 1634 self::fe_copy($t->YplusX), 1635 self::fe_copy($t->Z), 1636 self::fe_neg($t->T2d) 1637 ); 1638 return self::ge_cmov_cached($t, $minust, $bnegative); 1639 } 1640 1641 /** 1642 * @internal You should not use this directly from another application 1643 * 1644 * @param int $pos 1645 * @param int $b 1646 * @return ParagonIE_Sodium_Core_Curve25519_Ge_Precomp 1647 * @throws SodiumException 1648 * @throws TypeError 1649 * @psalm-suppress MixedArgument 1650 * @psalm-suppress MixedArrayAccess 1651 * @psalm-suppress MixedArrayOffset 1652 */ 1653 public static function ge_select($pos = 0, $b = 0) 1654 { 1655 static $base = null; 1656 if ($base === null) { 1657 $base = array(); 1658 /** @var int $i */ 1659 foreach (self::$base as $i => $bas) { 1660 for ($j = 0; $j < 8; ++$j) { 1661 $base[$i][$j] = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( 1662 ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][0]), 1663 ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][1]), 1664 ParagonIE_Sodium_Core_Curve25519_Fe::fromArray($bas[$j][2]) 1665 ); 1666 } 1667 } 1668 } 1669 /** @var array<int, array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp>> $base */ 1670 if (!is_int($pos)) { 1671 throw new InvalidArgumentException('Position must be an integer'); 1672 } 1673 if ($pos < 0 || $pos > 31) { 1674 throw new RangeException('Position is out of range [0, 31]'); 1675 } 1676 1677 $bnegative = self::negative($b); 1678 $babs = $b - (((-$bnegative) & $b) << 1); 1679 1680 $t = self::ge_precomp_0(); 1681 for ($i = 0; $i < 8; ++$i) { 1682 $t = self::cmov( 1683 $t, 1684 $base[$pos][$i], 1685 self::equal($babs, $i + 1) 1686 ); 1687 } 1688 $minusT = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( 1689 self::fe_copy($t->yminusx), 1690 self::fe_copy($t->yplusx), 1691 self::fe_neg($t->xy2d) 1692 ); 1693 return self::cmov($t, $minusT, $bnegative); 1694 } 1695 1696 /** 1697 * Subtract two group elements. 1698 * 1699 * r = p - q 1700 * 1701 * @internal You should not use this directly from another application 1702 * 1703 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p 1704 * @param ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q 1705 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P1p1 1706 */ 1707 public static function ge_sub( 1708 ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p, 1709 ParagonIE_Sodium_Core_Curve25519_Ge_Cached $q 1710 ) { 1711 $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); 1712 1713 $r->X = self::fe_add($p->Y, $p->X); 1714 $r->Y = self::fe_sub($p->Y, $p->X); 1715 $r->Z = self::fe_mul($r->X, $q->YminusX); 1716 $r->Y = self::fe_mul($r->Y, $q->YplusX); 1717 $r->T = self::fe_mul($q->T2d, $p->T); 1718 $r->X = self::fe_mul($p->Z, $q->Z); 1719 $t0 = self::fe_add($r->X, $r->X); 1720 $r->X = self::fe_sub($r->Z, $r->Y); 1721 $r->Y = self::fe_add($r->Z, $r->Y); 1722 $r->Z = self::fe_sub($t0, $r->T); 1723 $r->T = self::fe_add($t0, $r->T); 1724 1725 return $r; 1726 } 1727 1728 /** 1729 * Convert a group element to a byte string. 1730 * 1731 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P2 $h 1732 * @return string 1733 * @throws SodiumException 1734 * @throws TypeError 1735 */ 1736 public static function ge_tobytes(ParagonIE_Sodium_Core_Curve25519_Ge_P2 $h) 1737 { 1738 $recip = self::fe_invert($h->Z); 1739 $x = self::fe_mul($h->X, $recip); 1740 $y = self::fe_mul($h->Y, $recip); 1741 $s = self::fe_tobytes($y); 1742 $s[31] = self::intToChr( 1743 self::chrToInt($s[31]) ^ (self::fe_isnegative($x) << 7) 1744 ); 1745 return $s; 1746 } 1747 1748 /** 1749 * @internal You should not use this directly from another application 1750 * 1751 * @param string $a 1752 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A 1753 * @param string $b 1754 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P2 1755 * @throws SodiumException 1756 * @throws TypeError 1757 * @psalm-suppress MixedArgument 1758 * @psalm-suppress MixedArrayAccess 1759 */ 1760 public static function ge_double_scalarmult_vartime( 1761 $a, 1762 ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A, 1763 $b 1764 ) { 1765 /** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Cached> $Ai */ 1766 $Ai = array(); 1767 1768 /** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Precomp> $Bi */ 1769 static $Bi = array(); 1770 if (!$Bi) { 1771 for ($i = 0; $i < 8; ++$i) { 1772 $Bi[$i] = new ParagonIE_Sodium_Core_Curve25519_Ge_Precomp( 1773 ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][0]), 1774 ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][1]), 1775 ParagonIE_Sodium_Core_Curve25519_Fe::fromArray(self::$base2[$i][2]) 1776 ); 1777 } 1778 } 1779 for ($i = 0; $i < 8; ++$i) { 1780 $Ai[$i] = new ParagonIE_Sodium_Core_Curve25519_Ge_Cached( 1781 self::fe_0(), 1782 self::fe_0(), 1783 self::fe_0(), 1784 self::fe_0() 1785 ); 1786 } 1787 1788 # slide(aslide,a); 1789 # slide(bslide,b); 1790 /** @var array<int, int> $aslide */ 1791 $aslide = self::slide($a); 1792 /** @var array<int, int> $bslide */ 1793 $bslide = self::slide($b); 1794 1795 # ge_p3_to_cached(&Ai[0],A); 1796 # ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t); 1797 $Ai[0] = self::ge_p3_to_cached($A); 1798 $t = self::ge_p3_dbl($A); 1799 $A2 = self::ge_p1p1_to_p3($t); 1800 1801 # ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u); 1802 # ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u); 1803 # ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u); 1804 # ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u); 1805 # ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u); 1806 # ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u); 1807 # ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u); 1808 for ($i = 0; $i < 7; ++$i) { 1809 $t = self::ge_add($A2, $Ai[$i]); 1810 $u = self::ge_p1p1_to_p3($t); 1811 $Ai[$i + 1] = self::ge_p3_to_cached($u); 1812 } 1813 1814 # ge_p2_0(r); 1815 $r = self::ge_p2_0(); 1816 1817 # for (i = 255;i >= 0;--i) { 1818 # if (aslide[i] || bslide[i]) break; 1819 # } 1820 $i = 255; 1821 for (; $i >= 0; --$i) { 1822 if ($aslide[$i] || $bslide[$i]) { 1823 break; 1824 } 1825 } 1826 1827 # for (;i >= 0;--i) { 1828 for (; $i >= 0; --$i) { 1829 # ge_p2_dbl(&t,r); 1830 $t = self::ge_p2_dbl($r); 1831 1832 # if (aslide[i] > 0) { 1833 if ($aslide[$i] > 0) { 1834 # ge_p1p1_to_p3(&u,&t); 1835 # ge_add(&t,&u,&Ai[aslide[i]/2]); 1836 $u = self::ge_p1p1_to_p3($t); 1837 $t = self::ge_add( 1838 $u, 1839 $Ai[(int) floor($aslide[$i] / 2)] 1840 ); 1841 # } else if (aslide[i] < 0) { 1842 } elseif ($aslide[$i] < 0) { 1843 # ge_p1p1_to_p3(&u,&t); 1844 # ge_sub(&t,&u,&Ai[(-aslide[i])/2]); 1845 $u = self::ge_p1p1_to_p3($t); 1846 $t = self::ge_sub( 1847 $u, 1848 $Ai[(int) floor(-$aslide[$i] / 2)] 1849 ); 1850 } 1851 1852 # if (bslide[i] > 0) { 1853 if ($bslide[$i] > 0) { 1854 /** @var int $index */ 1855 $index = (int) floor($bslide[$i] / 2); 1856 # ge_p1p1_to_p3(&u,&t); 1857 # ge_madd(&t,&u,&Bi[bslide[i]/2]); 1858 $u = self::ge_p1p1_to_p3($t); 1859 $t = self::ge_madd($t, $u, $Bi[$index]); 1860 # } else if (bslide[i] < 0) { 1861 } elseif ($bslide[$i] < 0) { 1862 /** @var int $index */ 1863 $index = (int) floor(-$bslide[$i] / 2); 1864 # ge_p1p1_to_p3(&u,&t); 1865 # ge_msub(&t,&u,&Bi[(-bslide[i])/2]); 1866 $u = self::ge_p1p1_to_p3($t); 1867 $t = self::ge_msub($t, $u, $Bi[$index]); 1868 } 1869 # ge_p1p1_to_p2(r,&t); 1870 $r = self::ge_p1p1_to_p2($t); 1871 } 1872 return $r; 1873 } 1874 1875 /** 1876 * @internal You should not use this directly from another application 1877 * 1878 * @param string $a 1879 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $p 1880 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 1881 * @throws SodiumException 1882 * @throws TypeError 1883 * @psalm-suppress MixedAssignment 1884 * @psalm-suppress MixedOperand 1885 */ 1886 public static function ge_scalarmult($a, $p) 1887 { 1888 $e = array_fill(0, 64, 0); 1889 1890 /** @var ParagonIE_Sodium_Core_Curve25519_Ge_Cached[] $pi */ 1891 $pi = array(); 1892 1893 // ge25519_p3_to_cached(&pi[1 - 1], p); /* p */ 1894 $pi[0] = self::ge_p3_to_cached($p); 1895 1896 // ge25519_p3_dbl(&t2, p); 1897 // ge25519_p1p1_to_p3(&p2, &t2); 1898 // ge25519_p3_to_cached(&pi[2 - 1], &p2); /* 2p = 2*p */ 1899 $t2 = self::ge_p3_dbl($p); 1900 $p2 = self::ge_p1p1_to_p3($t2); 1901 $pi[1] = self::ge_p3_to_cached($p2); 1902 1903 // ge25519_add_cached(&t3, p, &pi[2 - 1]); 1904 // ge25519_p1p1_to_p3(&p3, &t3); 1905 // ge25519_p3_to_cached(&pi[3 - 1], &p3); /* 3p = 2p+p */ 1906 $t3 = self::ge_add($p, $pi[1]); 1907 $p3 = self::ge_p1p1_to_p3($t3); 1908 $pi[2] = self::ge_p3_to_cached($p3); 1909 1910 // ge25519_p3_dbl(&t4, &p2); 1911 // ge25519_p1p1_to_p3(&p4, &t4); 1912 // ge25519_p3_to_cached(&pi[4 - 1], &p4); /* 4p = 2*2p */ 1913 $t4 = self::ge_p3_dbl($p2); 1914 $p4 = self::ge_p1p1_to_p3($t4); 1915 $pi[3] = self::ge_p3_to_cached($p4); 1916 1917 // ge25519_add_cached(&t5, p, &pi[4 - 1]); 1918 // ge25519_p1p1_to_p3(&p5, &t5); 1919 // ge25519_p3_to_cached(&pi[5 - 1], &p5); /* 5p = 4p+p */ 1920 $t5 = self::ge_add($p, $pi[3]); 1921 $p5 = self::ge_p1p1_to_p3($t5); 1922 $pi[4] = self::ge_p3_to_cached($p5); 1923 1924 // ge25519_p3_dbl(&t6, &p3); 1925 // ge25519_p1p1_to_p3(&p6, &t6); 1926 // ge25519_p3_to_cached(&pi[6 - 1], &p6); /* 6p = 2*3p */ 1927 $t6 = self::ge_p3_dbl($p3); 1928 $p6 = self::ge_p1p1_to_p3($t6); 1929 $pi[5] = self::ge_p3_to_cached($p6); 1930 1931 // ge25519_add_cached(&t7, p, &pi[6 - 1]); 1932 // ge25519_p1p1_to_p3(&p7, &t7); 1933 // ge25519_p3_to_cached(&pi[7 - 1], &p7); /* 7p = 6p+p */ 1934 $t7 = self::ge_add($p, $pi[5]); 1935 $p7 = self::ge_p1p1_to_p3($t7); 1936 $pi[6] = self::ge_p3_to_cached($p7); 1937 1938 // ge25519_p3_dbl(&t8, &p4); 1939 // ge25519_p1p1_to_p3(&p8, &t8); 1940 // ge25519_p3_to_cached(&pi[8 - 1], &p8); /* 8p = 2*4p */ 1941 $t8 = self::ge_p3_dbl($p4); 1942 $p8 = self::ge_p1p1_to_p3($t8); 1943 $pi[7] = self::ge_p3_to_cached($p8); 1944 1945 1946 // for (i = 0; i < 32; ++i) { 1947 // e[2 * i + 0] = (a[i] >> 0) & 15; 1948 // e[2 * i + 1] = (a[i] >> 4) & 15; 1949 // } 1950 for ($i = 0; $i < 32; ++$i) { 1951 $e[($i << 1) ] = self::chrToInt($a[$i]) & 15; 1952 $e[($i << 1) + 1] = (self::chrToInt($a[$i]) >> 4) & 15; 1953 } 1954 // /* each e[i] is between 0 and 15 */ 1955 // /* e[63] is between 0 and 7 */ 1956 1957 // carry = 0; 1958 // for (i = 0; i < 63; ++i) { 1959 // e[i] += carry; 1960 // carry = e[i] + 8; 1961 // carry >>= 4; 1962 // e[i] -= carry * ((signed char) 1 << 4); 1963 // } 1964 $carry = 0; 1965 for ($i = 0; $i < 63; ++$i) { 1966 $e[$i] += $carry; 1967 $carry = $e[$i] + 8; 1968 $carry >>= 4; 1969 $e[$i] -= $carry << 4; 1970 } 1971 // e[63] += carry; 1972 // /* each e[i] is between -8 and 8 */ 1973 $e[63] += $carry; 1974 1975 // ge25519_p3_0(h); 1976 $h = self::ge_p3_0(); 1977 1978 // for (i = 63; i != 0; i--) { 1979 for ($i = 63; $i != 0; --$i) { 1980 // ge25519_cmov8_cached(&t, pi, e[i]); 1981 $t = self::ge_cmov8_cached($pi, $e[$i]); 1982 // ge25519_add_cached(&r, h, &t); 1983 $r = self::ge_add($h, $t); 1984 1985 // ge25519_p1p1_to_p2(&s, &r); 1986 // ge25519_p2_dbl(&r, &s); 1987 // ge25519_p1p1_to_p2(&s, &r); 1988 // ge25519_p2_dbl(&r, &s); 1989 // ge25519_p1p1_to_p2(&s, &r); 1990 // ge25519_p2_dbl(&r, &s); 1991 // ge25519_p1p1_to_p2(&s, &r); 1992 // ge25519_p2_dbl(&r, &s); 1993 $s = self::ge_p1p1_to_p2($r); 1994 $r = self::ge_p2_dbl($s); 1995 $s = self::ge_p1p1_to_p2($r); 1996 $r = self::ge_p2_dbl($s); 1997 $s = self::ge_p1p1_to_p2($r); 1998 $r = self::ge_p2_dbl($s); 1999 $s = self::ge_p1p1_to_p2($r); 2000 $r = self::ge_p2_dbl($s); 2001 2002 // ge25519_p1p1_to_p3(h, &r); /* *16 */ 2003 $h = self::ge_p1p1_to_p3($r); /* *16 */ 2004 } 2005 2006 // ge25519_cmov8_cached(&t, pi, e[i]); 2007 // ge25519_add_cached(&r, h, &t); 2008 // ge25519_p1p1_to_p3(h, &r); 2009 $t = self::ge_cmov8_cached($pi, $e[0]); 2010 $r = self::ge_add($h, $t); 2011 return self::ge_p1p1_to_p3($r); 2012 } 2013 2014 /** 2015 * @internal You should not use this directly from another application 2016 * 2017 * @param string $a 2018 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 2019 * @throws SodiumException 2020 * @throws TypeError 2021 * @psalm-suppress MixedAssignment 2022 * @psalm-suppress MixedOperand 2023 */ 2024 public static function ge_scalarmult_base($a) 2025 { 2026 /** @var array<int, int> $e */ 2027 $e = array(); 2028 $r = new ParagonIE_Sodium_Core_Curve25519_Ge_P1p1(); 2029 2030 for ($i = 0; $i < 32; ++$i) { 2031 $dbl = (int) $i << 1; 2032 $e[$dbl] = (int) self::chrToInt($a[$i]) & 15; 2033 $e[$dbl + 1] = (int) (self::chrToInt($a[$i]) >> 4) & 15; 2034 } 2035 2036 $carry = 0; 2037 for ($i = 0; $i < 63; ++$i) { 2038 $e[$i] += $carry; 2039 $carry = $e[$i] + 8; 2040 $carry >>= 4; 2041 $e[$i] -= $carry << 4; 2042 } 2043 $e[63] += (int) $carry; 2044 2045 $h = self::ge_p3_0(); 2046 2047 for ($i = 1; $i < 64; $i += 2) { 2048 $t = self::ge_select((int) floor($i / 2), (int) $e[$i]); 2049 $r = self::ge_madd($r, $h, $t); 2050 $h = self::ge_p1p1_to_p3($r); 2051 } 2052 2053 $r = self::ge_p3_dbl($h); 2054 2055 $s = self::ge_p1p1_to_p2($r); 2056 $r = self::ge_p2_dbl($s); 2057 $s = self::ge_p1p1_to_p2($r); 2058 $r = self::ge_p2_dbl($s); 2059 $s = self::ge_p1p1_to_p2($r); 2060 $r = self::ge_p2_dbl($s); 2061 2062 $h = self::ge_p1p1_to_p3($r); 2063 2064 for ($i = 0; $i < 64; $i += 2) { 2065 $t = self::ge_select($i >> 1, (int) $e[$i]); 2066 $r = self::ge_madd($r, $h, $t); 2067 $h = self::ge_p1p1_to_p3($r); 2068 } 2069 return $h; 2070 } 2071 2072 /** 2073 * Calculates (ab + c) mod l 2074 * where l = 2^252 + 27742317777372353535851937790883648493 2075 * 2076 * @internal You should not use this directly from another application 2077 * 2078 * @param string $a 2079 * @param string $b 2080 * @param string $c 2081 * @return string 2082 * @throws TypeError 2083 */ 2084 public static function sc_muladd($a, $b, $c) 2085 { 2086 $a0 = 2097151 & self::load_3(self::substr($a, 0, 3)); 2087 $a1 = 2097151 & (self::load_4(self::substr($a, 2, 4)) >> 5); 2088 $a2 = 2097151 & (self::load_3(self::substr($a, 5, 3)) >> 2); 2089 $a3 = 2097151 & (self::load_4(self::substr($a, 7, 4)) >> 7); 2090 $a4 = 2097151 & (self::load_4(self::substr($a, 10, 4)) >> 4); 2091 $a5 = 2097151 & (self::load_3(self::substr($a, 13, 3)) >> 1); 2092 $a6 = 2097151 & (self::load_4(self::substr($a, 15, 4)) >> 6); 2093 $a7 = 2097151 & (self::load_3(self::substr($a, 18, 3)) >> 3); 2094 $a8 = 2097151 & self::load_3(self::substr($a, 21, 3)); 2095 $a9 = 2097151 & (self::load_4(self::substr($a, 23, 4)) >> 5); 2096 $a10 = 2097151 & (self::load_3(self::substr($a, 26, 3)) >> 2); 2097 $a11 = (self::load_4(self::substr($a, 28, 4)) >> 7); 2098 2099 $b0 = 2097151 & self::load_3(self::substr($b, 0, 3)); 2100 $b1 = 2097151 & (self::load_4(self::substr($b, 2, 4)) >> 5); 2101 $b2 = 2097151 & (self::load_3(self::substr($b, 5, 3)) >> 2); 2102 $b3 = 2097151 & (self::load_4(self::substr($b, 7, 4)) >> 7); 2103 $b4 = 2097151 & (self::load_4(self::substr($b, 10, 4)) >> 4); 2104 $b5 = 2097151 & (self::load_3(self::substr($b, 13, 3)) >> 1); 2105 $b6 = 2097151 & (self::load_4(self::substr($b, 15, 4)) >> 6); 2106 $b7 = 2097151 & (self::load_3(self::substr($b, 18, 3)) >> 3); 2107 $b8 = 2097151 & self::load_3(self::substr($b, 21, 3)); 2108 $b9 = 2097151 & (self::load_4(self::substr($b, 23, 4)) >> 5); 2109 $b10 = 2097151 & (self::load_3(self::substr($b, 26, 3)) >> 2); 2110 $b11 = (self::load_4(self::substr($b, 28, 4)) >> 7); 2111 2112 $c0 = 2097151 & self::load_3(self::substr($c, 0, 3)); 2113 $c1 = 2097151 & (self::load_4(self::substr($c, 2, 4)) >> 5); 2114 $c2 = 2097151 & (self::load_3(self::substr($c, 5, 3)) >> 2); 2115 $c3 = 2097151 & (self::load_4(self::substr($c, 7, 4)) >> 7); 2116 $c4 = 2097151 & (self::load_4(self::substr($c, 10, 4)) >> 4); 2117 $c5 = 2097151 & (self::load_3(self::substr($c, 13, 3)) >> 1); 2118 $c6 = 2097151 & (self::load_4(self::substr($c, 15, 4)) >> 6); 2119 $c7 = 2097151 & (self::load_3(self::substr($c, 18, 3)) >> 3); 2120 $c8 = 2097151 & self::load_3(self::substr($c, 21, 3)); 2121 $c9 = 2097151 & (self::load_4(self::substr($c, 23, 4)) >> 5); 2122 $c10 = 2097151 & (self::load_3(self::substr($c, 26, 3)) >> 2); 2123 $c11 = (self::load_4(self::substr($c, 28, 4)) >> 7); 2124 2125 /* Can't really avoid the pyramid here: */ 2126 $s0 = $c0 + self::mul($a0, $b0, 24); 2127 $s1 = $c1 + self::mul($a0, $b1, 24) + self::mul($a1, $b0, 24); 2128 $s2 = $c2 + self::mul($a0, $b2, 24) + self::mul($a1, $b1, 24) + self::mul($a2, $b0, 24); 2129 $s3 = $c3 + self::mul($a0, $b3, 24) + self::mul($a1, $b2, 24) + self::mul($a2, $b1, 24) + self::mul($a3, $b0, 24); 2130 $s4 = $c4 + self::mul($a0, $b4, 24) + self::mul($a1, $b3, 24) + self::mul($a2, $b2, 24) + self::mul($a3, $b1, 24) + 2131 self::mul($a4, $b0, 24); 2132 $s5 = $c5 + self::mul($a0, $b5, 24) + self::mul($a1, $b4, 24) + self::mul($a2, $b3, 24) + self::mul($a3, $b2, 24) + 2133 self::mul($a4, $b1, 24) + self::mul($a5, $b0, 24); 2134 $s6 = $c6 + self::mul($a0, $b6, 24) + self::mul($a1, $b5, 24) + self::mul($a2, $b4, 24) + self::mul($a3, $b3, 24) + 2135 self::mul($a4, $b2, 24) + self::mul($a5, $b1, 24) + self::mul($a6, $b0, 24); 2136 $s7 = $c7 + self::mul($a0, $b7, 24) + self::mul($a1, $b6, 24) + self::mul($a2, $b5, 24) + self::mul($a3, $b4, 24) + 2137 self::mul($a4, $b3, 24) + self::mul($a5, $b2, 24) + self::mul($a6, $b1, 24) + self::mul($a7, $b0, 24); 2138 $s8 = $c8 + self::mul($a0, $b8, 24) + self::mul($a1, $b7, 24) + self::mul($a2, $b6, 24) + self::mul($a3, $b5, 24) + 2139 self::mul($a4, $b4, 24) + self::mul($a5, $b3, 24) + self::mul($a6, $b2, 24) + self::mul($a7, $b1, 24) + 2140 self::mul($a8, $b0, 24); 2141 $s9 = $c9 + self::mul($a0, $b9, 24) + self::mul($a1, $b8, 24) + self::mul($a2, $b7, 24) + self::mul($a3, $b6, 24) + 2142 self::mul($a4, $b5, 24) + self::mul($a5, $b4, 24) + self::mul($a6, $b3, 24) + self::mul($a7, $b2, 24) + 2143 self::mul($a8, $b1, 24) + self::mul($a9, $b0, 24); 2144 $s10 = $c10 + self::mul($a0, $b10, 24) + self::mul($a1, $b9, 24) + self::mul($a2, $b8, 24) + self::mul($a3, $b7, 24) + 2145 self::mul($a4, $b6, 24) + self::mul($a5, $b5, 24) + self::mul($a6, $b4, 24) + self::mul($a7, $b3, 24) + 2146 self::mul($a8, $b2, 24) + self::mul($a9, $b1, 24) + self::mul($a10, $b0, 24); 2147 $s11 = $c11 + self::mul($a0, $b11, 24) + self::mul($a1, $b10, 24) + self::mul($a2, $b9, 24) + self::mul($a3, $b8, 24) + 2148 self::mul($a4, $b7, 24) + self::mul($a5, $b6, 24) + self::mul($a6, $b5, 24) + self::mul($a7, $b4, 24) + 2149 self::mul($a8, $b3, 24) + self::mul($a9, $b2, 24) + self::mul($a10, $b1, 24) + self::mul($a11, $b0, 24); 2150 $s12 = self::mul($a1, $b11, 24) + self::mul($a2, $b10, 24) + self::mul($a3, $b9, 24) + self::mul($a4, $b8, 24) + 2151 self::mul($a5, $b7, 24) + self::mul($a6, $b6, 24) + self::mul($a7, $b5, 24) + self::mul($a8, $b4, 24) + 2152 self::mul($a9, $b3, 24) + self::mul($a10, $b2, 24) + self::mul($a11, $b1, 24); 2153 $s13 = self::mul($a2, $b11, 24) + self::mul($a3, $b10, 24) + self::mul($a4, $b9, 24) + self::mul($a5, $b8, 24) + 2154 self::mul($a6, $b7, 24) + self::mul($a7, $b6, 24) + self::mul($a8, $b5, 24) + self::mul($a9, $b4, 24) + 2155 self::mul($a10, $b3, 24) + self::mul($a11, $b2, 24); 2156 $s14 = self::mul($a3, $b11, 24) + self::mul($a4, $b10, 24) + self::mul($a5, $b9, 24) + self::mul($a6, $b8, 24) + 2157 self::mul($a7, $b7, 24) + self::mul($a8, $b6, 24) + self::mul($a9, $b5, 24) + self::mul($a10, $b4, 24) + 2158 self::mul($a11, $b3, 24); 2159 $s15 = self::mul($a4, $b11, 24) + self::mul($a5, $b10, 24) + self::mul($a6, $b9, 24) + self::mul($a7, $b8, 24) + 2160 self::mul($a8, $b7, 24) + self::mul($a9, $b6, 24) + self::mul($a10, $b5, 24) + self::mul($a11, $b4, 24); 2161 $s16 = self::mul($a5, $b11, 24) + self::mul($a6, $b10, 24) + self::mul($a7, $b9, 24) + self::mul($a8, $b8, 24) + 2162 self::mul($a9, $b7, 24) + self::mul($a10, $b6, 24) + self::mul($a11, $b5, 24); 2163 $s17 = self::mul($a6, $b11, 24) + self::mul($a7, $b10, 24) + self::mul($a8, $b9, 24) + self::mul($a9, $b8, 24) + 2164 self::mul($a10, $b7, 24) + self::mul($a11, $b6, 24); 2165 $s18 = self::mul($a7, $b11, 24) + self::mul($a8, $b10, 24) + self::mul($a9, $b9, 24) + self::mul($a10, $b8, 24) + 2166 self::mul($a11, $b7, 24); 2167 $s19 = self::mul($a8, $b11, 24) + self::mul($a9, $b10, 24) + self::mul($a10, $b9, 24) + self::mul($a11, $b8, 24); 2168 $s20 = self::mul($a9, $b11, 24) + self::mul($a10, $b10, 24) + self::mul($a11, $b9, 24); 2169 $s21 = self::mul($a10, $b11, 24) + self::mul($a11, $b10, 24); 2170 $s22 = self::mul($a11, $b11, 24); 2171 $s23 = 0; 2172 2173 $carry0 = ($s0 + (1 << 20)) >> 21; 2174 $s1 += $carry0; 2175 $s0 -= $carry0 << 21; 2176 $carry2 = ($s2 + (1 << 20)) >> 21; 2177 $s3 += $carry2; 2178 $s2 -= $carry2 << 21; 2179 $carry4 = ($s4 + (1 << 20)) >> 21; 2180 $s5 += $carry4; 2181 $s4 -= $carry4 << 21; 2182 $carry6 = ($s6 + (1 << 20)) >> 21; 2183 $s7 += $carry6; 2184 $s6 -= $carry6 << 21; 2185 $carry8 = ($s8 + (1 << 20)) >> 21; 2186 $s9 += $carry8; 2187 $s8 -= $carry8 << 21; 2188 $carry10 = ($s10 + (1 << 20)) >> 21; 2189 $s11 += $carry10; 2190 $s10 -= $carry10 << 21; 2191 $carry12 = ($s12 + (1 << 20)) >> 21; 2192 $s13 += $carry12; 2193 $s12 -= $carry12 << 21; 2194 $carry14 = ($s14 + (1 << 20)) >> 21; 2195 $s15 += $carry14; 2196 $s14 -= $carry14 << 21; 2197 $carry16 = ($s16 + (1 << 20)) >> 21; 2198 $s17 += $carry16; 2199 $s16 -= $carry16 << 21; 2200 $carry18 = ($s18 + (1 << 20)) >> 21; 2201 $s19 += $carry18; 2202 $s18 -= $carry18 << 21; 2203 $carry20 = ($s20 + (1 << 20)) >> 21; 2204 $s21 += $carry20; 2205 $s20 -= $carry20 << 21; 2206 $carry22 = ($s22 + (1 << 20)) >> 21; 2207 $s23 += $carry22; 2208 $s22 -= $carry22 << 21; 2209 2210 $carry1 = ($s1 + (1 << 20)) >> 21; 2211 $s2 += $carry1; 2212 $s1 -= $carry1 << 21; 2213 $carry3 = ($s3 + (1 << 20)) >> 21; 2214 $s4 += $carry3; 2215 $s3 -= $carry3 << 21; 2216 $carry5 = ($s5 + (1 << 20)) >> 21; 2217 $s6 += $carry5; 2218 $s5 -= $carry5 << 21; 2219 $carry7 = ($s7 + (1 << 20)) >> 21; 2220 $s8 += $carry7; 2221 $s7 -= $carry7 << 21; 2222 $carry9 = ($s9 + (1 << 20)) >> 21; 2223 $s10 += $carry9; 2224 $s9 -= $carry9 << 21; 2225 $carry11 = ($s11 + (1 << 20)) >> 21; 2226 $s12 += $carry11; 2227 $s11 -= $carry11 << 21; 2228 $carry13 = ($s13 + (1 << 20)) >> 21; 2229 $s14 += $carry13; 2230 $s13 -= $carry13 << 21; 2231 $carry15 = ($s15 + (1 << 20)) >> 21; 2232 $s16 += $carry15; 2233 $s15 -= $carry15 << 21; 2234 $carry17 = ($s17 + (1 << 20)) >> 21; 2235 $s18 += $carry17; 2236 $s17 -= $carry17 << 21; 2237 $carry19 = ($s19 + (1 << 20)) >> 21; 2238 $s20 += $carry19; 2239 $s19 -= $carry19 << 21; 2240 $carry21 = ($s21 + (1 << 20)) >> 21; 2241 $s22 += $carry21; 2242 $s21 -= $carry21 << 21; 2243 2244 $s11 += self::mul($s23, 666643, 20); 2245 $s12 += self::mul($s23, 470296, 19); 2246 $s13 += self::mul($s23, 654183, 20); 2247 $s14 -= self::mul($s23, 997805, 20); 2248 $s15 += self::mul($s23, 136657, 18); 2249 $s16 -= self::mul($s23, 683901, 20); 2250 2251 $s10 += self::mul($s22, 666643, 20); 2252 $s11 += self::mul($s22, 470296, 19); 2253 $s12 += self::mul($s22, 654183, 20); 2254 $s13 -= self::mul($s22, 997805, 20); 2255 $s14 += self::mul($s22, 136657, 18); 2256 $s15 -= self::mul($s22, 683901, 20); 2257 2258 $s9 += self::mul($s21, 666643, 20); 2259 $s10 += self::mul($s21, 470296, 19); 2260 $s11 += self::mul($s21, 654183, 20); 2261 $s12 -= self::mul($s21, 997805, 20); 2262 $s13 += self::mul($s21, 136657, 18); 2263 $s14 -= self::mul($s21, 683901, 20); 2264 2265 $s8 += self::mul($s20, 666643, 20); 2266 $s9 += self::mul($s20, 470296, 19); 2267 $s10 += self::mul($s20, 654183, 20); 2268 $s11 -= self::mul($s20, 997805, 20); 2269 $s12 += self::mul($s20, 136657, 18); 2270 $s13 -= self::mul($s20, 683901, 20); 2271 2272 $s7 += self::mul($s19, 666643, 20); 2273 $s8 += self::mul($s19, 470296, 19); 2274 $s9 += self::mul($s19, 654183, 20); 2275 $s10 -= self::mul($s19, 997805, 20); 2276 $s11 += self::mul($s19, 136657, 18); 2277 $s12 -= self::mul($s19, 683901, 20); 2278 2279 $s6 += self::mul($s18, 666643, 20); 2280 $s7 += self::mul($s18, 470296, 19); 2281 $s8 += self::mul($s18, 654183, 20); 2282 $s9 -= self::mul($s18, 997805, 20); 2283 $s10 += self::mul($s18, 136657, 18); 2284 $s11 -= self::mul($s18, 683901, 20); 2285 2286 $carry6 = ($s6 + (1 << 20)) >> 21; 2287 $s7 += $carry6; 2288 $s6 -= $carry6 << 21; 2289 $carry8 = ($s8 + (1 << 20)) >> 21; 2290 $s9 += $carry8; 2291 $s8 -= $carry8 << 21; 2292 $carry10 = ($s10 + (1 << 20)) >> 21; 2293 $s11 += $carry10; 2294 $s10 -= $carry10 << 21; 2295 $carry12 = ($s12 + (1 << 20)) >> 21; 2296 $s13 += $carry12; 2297 $s12 -= $carry12 << 21; 2298 $carry14 = ($s14 + (1 << 20)) >> 21; 2299 $s15 += $carry14; 2300 $s14 -= $carry14 << 21; 2301 $carry16 = ($s16 + (1 << 20)) >> 21; 2302 $s17 += $carry16; 2303 $s16 -= $carry16 << 21; 2304 2305 $carry7 = ($s7 + (1 << 20)) >> 21; 2306 $s8 += $carry7; 2307 $s7 -= $carry7 << 21; 2308 $carry9 = ($s9 + (1 << 20)) >> 21; 2309 $s10 += $carry9; 2310 $s9 -= $carry9 << 21; 2311 $carry11 = ($s11 + (1 << 20)) >> 21; 2312 $s12 += $carry11; 2313 $s11 -= $carry11 << 21; 2314 $carry13 = ($s13 + (1 << 20)) >> 21; 2315 $s14 += $carry13; 2316 $s13 -= $carry13 << 21; 2317 $carry15 = ($s15 + (1 << 20)) >> 21; 2318 $s16 += $carry15; 2319 $s15 -= $carry15 << 21; 2320 2321 $s5 += self::mul($s17, 666643, 20); 2322 $s6 += self::mul($s17, 470296, 19); 2323 $s7 += self::mul($s17, 654183, 20); 2324 $s8 -= self::mul($s17, 997805, 20); 2325 $s9 += self::mul($s17, 136657, 18); 2326 $s10 -= self::mul($s17, 683901, 20); 2327 2328 $s4 += self::mul($s16, 666643, 20); 2329 $s5 += self::mul($s16, 470296, 19); 2330 $s6 += self::mul($s16, 654183, 20); 2331 $s7 -= self::mul($s16, 997805, 20); 2332 $s8 += self::mul($s16, 136657, 18); 2333 $s9 -= self::mul($s16, 683901, 20); 2334 2335 $s3 += self::mul($s15, 666643, 20); 2336 $s4 += self::mul($s15, 470296, 19); 2337 $s5 += self::mul($s15, 654183, 20); 2338 $s6 -= self::mul($s15, 997805, 20); 2339 $s7 += self::mul($s15, 136657, 18); 2340 $s8 -= self::mul($s15, 683901, 20); 2341 2342 $s2 += self::mul($s14, 666643, 20); 2343 $s3 += self::mul($s14, 470296, 19); 2344 $s4 += self::mul($s14, 654183, 20); 2345 $s5 -= self::mul($s14, 997805, 20); 2346 $s6 += self::mul($s14, 136657, 18); 2347 $s7 -= self::mul($s14, 683901, 20); 2348 2349 $s1 += self::mul($s13, 666643, 20); 2350 $s2 += self::mul($s13, 470296, 19); 2351 $s3 += self::mul($s13, 654183, 20); 2352 $s4 -= self::mul($s13, 997805, 20); 2353 $s5 += self::mul($s13, 136657, 18); 2354 $s6 -= self::mul($s13, 683901, 20); 2355 2356 $s0 += self::mul($s12, 666643, 20); 2357 $s1 += self::mul($s12, 470296, 19); 2358 $s2 += self::mul($s12, 654183, 20); 2359 $s3 -= self::mul($s12, 997805, 20); 2360 $s4 += self::mul($s12, 136657, 18); 2361 $s5 -= self::mul($s12, 683901, 20); 2362 $s12 = 0; 2363 2364 $carry0 = ($s0 + (1 << 20)) >> 21; 2365 $s1 += $carry0; 2366 $s0 -= $carry0 << 21; 2367 $carry2 = ($s2 + (1 << 20)) >> 21; 2368 $s3 += $carry2; 2369 $s2 -= $carry2 << 21; 2370 $carry4 = ($s4 + (1 << 20)) >> 21; 2371 $s5 += $carry4; 2372 $s4 -= $carry4 << 21; 2373 $carry6 = ($s6 + (1 << 20)) >> 21; 2374 $s7 += $carry6; 2375 $s6 -= $carry6 << 21; 2376 $carry8 = ($s8 + (1 << 20)) >> 21; 2377 $s9 += $carry8; 2378 $s8 -= $carry8 << 21; 2379 $carry10 = ($s10 + (1 << 20)) >> 21; 2380 $s11 += $carry10; 2381 $s10 -= $carry10 << 21; 2382 2383 $carry1 = ($s1 + (1 << 20)) >> 21; 2384 $s2 += $carry1; 2385 $s1 -= $carry1 << 21; 2386 $carry3 = ($s3 + (1 << 20)) >> 21; 2387 $s4 += $carry3; 2388 $s3 -= $carry3 << 21; 2389 $carry5 = ($s5 + (1 << 20)) >> 21; 2390 $s6 += $carry5; 2391 $s5 -= $carry5 << 21; 2392 $carry7 = ($s7 + (1 << 20)) >> 21; 2393 $s8 += $carry7; 2394 $s7 -= $carry7 << 21; 2395 $carry9 = ($s9 + (1 << 20)) >> 21; 2396 $s10 += $carry9; 2397 $s9 -= $carry9 << 21; 2398 $carry11 = ($s11 + (1 << 20)) >> 21; 2399 $s12 += $carry11; 2400 $s11 -= $carry11 << 21; 2401 2402 $s0 += self::mul($s12, 666643, 20); 2403 $s1 += self::mul($s12, 470296, 19); 2404 $s2 += self::mul($s12, 654183, 20); 2405 $s3 -= self::mul($s12, 997805, 20); 2406 $s4 += self::mul($s12, 136657, 18); 2407 $s5 -= self::mul($s12, 683901, 20); 2408 $s12 = 0; 2409 2410 $carry0 = $s0 >> 21; 2411 $s1 += $carry0; 2412 $s0 -= $carry0 << 21; 2413 $carry1 = $s1 >> 21; 2414 $s2 += $carry1; 2415 $s1 -= $carry1 << 21; 2416 $carry2 = $s2 >> 21; 2417 $s3 += $carry2; 2418 $s2 -= $carry2 << 21; 2419 $carry3 = $s3 >> 21; 2420 $s4 += $carry3; 2421 $s3 -= $carry3 << 21; 2422 $carry4 = $s4 >> 21; 2423 $s5 += $carry4; 2424 $s4 -= $carry4 << 21; 2425 $carry5 = $s5 >> 21; 2426 $s6 += $carry5; 2427 $s5 -= $carry5 << 21; 2428 $carry6 = $s6 >> 21; 2429 $s7 += $carry6; 2430 $s6 -= $carry6 << 21; 2431 $carry7 = $s7 >> 21; 2432 $s8 += $carry7; 2433 $s7 -= $carry7 << 21; 2434 $carry8 = $s8 >> 21; 2435 $s9 += $carry8; 2436 $s8 -= $carry8 << 21; 2437 $carry9 = $s9 >> 21; 2438 $s10 += $carry9; 2439 $s9 -= $carry9 << 21; 2440 $carry10 = $s10 >> 21; 2441 $s11 += $carry10; 2442 $s10 -= $carry10 << 21; 2443 $carry11 = $s11 >> 21; 2444 $s12 += $carry11; 2445 $s11 -= $carry11 << 21; 2446 2447 $s0 += self::mul($s12, 666643, 20); 2448 $s1 += self::mul($s12, 470296, 19); 2449 $s2 += self::mul($s12, 654183, 20); 2450 $s3 -= self::mul($s12, 997805, 20); 2451 $s4 += self::mul($s12, 136657, 18); 2452 $s5 -= self::mul($s12, 683901, 20); 2453 2454 $carry0 = $s0 >> 21; 2455 $s1 += $carry0; 2456 $s0 -= $carry0 << 21; 2457 $carry1 = $s1 >> 21; 2458 $s2 += $carry1; 2459 $s1 -= $carry1 << 21; 2460 $carry2 = $s2 >> 21; 2461 $s3 += $carry2; 2462 $s2 -= $carry2 << 21; 2463 $carry3 = $s3 >> 21; 2464 $s4 += $carry3; 2465 $s3 -= $carry3 << 21; 2466 $carry4 = $s4 >> 21; 2467 $s5 += $carry4; 2468 $s4 -= $carry4 << 21; 2469 $carry5 = $s5 >> 21; 2470 $s6 += $carry5; 2471 $s5 -= $carry5 << 21; 2472 $carry6 = $s6 >> 21; 2473 $s7 += $carry6; 2474 $s6 -= $carry6 << 21; 2475 $carry7 = $s7 >> 21; 2476 $s8 += $carry7; 2477 $s7 -= $carry7 << 21; 2478 $carry8 = $s8 >> 21; 2479 $s9 += $carry8; 2480 $s8 -= $carry8 << 21; 2481 $carry9 = $s9 >> 21; 2482 $s10 += $carry9; 2483 $s9 -= $carry9 << 21; 2484 $carry10 = $s10 >> 21; 2485 $s11 += $carry10; 2486 $s10 -= $carry10 << 21; 2487 2488 /** 2489 * @var array<int, int> 2490 */ 2491 $arr = array( 2492 (int) (0xff & ($s0 >> 0)), 2493 (int) (0xff & ($s0 >> 8)), 2494 (int) (0xff & (($s0 >> 16) | $s1 << 5)), 2495 (int) (0xff & ($s1 >> 3)), 2496 (int) (0xff & ($s1 >> 11)), 2497 (int) (0xff & (($s1 >> 19) | $s2 << 2)), 2498 (int) (0xff & ($s2 >> 6)), 2499 (int) (0xff & (($s2 >> 14) | $s3 << 7)), 2500 (int) (0xff & ($s3 >> 1)), 2501 (int) (0xff & ($s3 >> 9)), 2502 (int) (0xff & (($s3 >> 17) | $s4 << 4)), 2503 (int) (0xff & ($s4 >> 4)), 2504 (int) (0xff & ($s4 >> 12)), 2505 (int) (0xff & (($s4 >> 20) | $s5 << 1)), 2506 (int) (0xff & ($s5 >> 7)), 2507 (int) (0xff & (($s5 >> 15) | $s6 << 6)), 2508 (int) (0xff & ($s6 >> 2)), 2509 (int) (0xff & ($s6 >> 10)), 2510 (int) (0xff & (($s6 >> 18) | $s7 << 3)), 2511 (int) (0xff & ($s7 >> 5)), 2512 (int) (0xff & ($s7 >> 13)), 2513 (int) (0xff & ($s8 >> 0)), 2514 (int) (0xff & ($s8 >> 8)), 2515 (int) (0xff & (($s8 >> 16) | $s9 << 5)), 2516 (int) (0xff & ($s9 >> 3)), 2517 (int) (0xff & ($s9 >> 11)), 2518 (int) (0xff & (($s9 >> 19) | $s10 << 2)), 2519 (int) (0xff & ($s10 >> 6)), 2520 (int) (0xff & (($s10 >> 14) | $s11 << 7)), 2521 (int) (0xff & ($s11 >> 1)), 2522 (int) (0xff & ($s11 >> 9)), 2523 0xff & ($s11 >> 17) 2524 ); 2525 return self::intArrayToString($arr); 2526 } 2527 2528 /** 2529 * @internal You should not use this directly from another application 2530 * 2531 * @param string $s 2532 * @return string 2533 * @throws TypeError 2534 */ 2535 public static function sc_reduce($s) 2536 { 2537 $s0 = 2097151 & self::load_3(self::substr($s, 0, 3)); 2538 $s1 = 2097151 & (self::load_4(self::substr($s, 2, 4)) >> 5); 2539 $s2 = 2097151 & (self::load_3(self::substr($s, 5, 3)) >> 2); 2540 $s3 = 2097151 & (self::load_4(self::substr($s, 7, 4)) >> 7); 2541 $s4 = 2097151 & (self::load_4(self::substr($s, 10, 4)) >> 4); 2542 $s5 = 2097151 & (self::load_3(self::substr($s, 13, 3)) >> 1); 2543 $s6 = 2097151 & (self::load_4(self::substr($s, 15, 4)) >> 6); 2544 $s7 = 2097151 & (self::load_3(self::substr($s, 18, 4)) >> 3); 2545 $s8 = 2097151 & self::load_3(self::substr($s, 21, 3)); 2546 $s9 = 2097151 & (self::load_4(self::substr($s, 23, 4)) >> 5); 2547 $s10 = 2097151 & (self::load_3(self::substr($s, 26, 3)) >> 2); 2548 $s11 = 2097151 & (self::load_4(self::substr($s, 28, 4)) >> 7); 2549 $s12 = 2097151 & (self::load_4(self::substr($s, 31, 4)) >> 4); 2550 $s13 = 2097151 & (self::load_3(self::substr($s, 34, 3)) >> 1); 2551 $s14 = 2097151 & (self::load_4(self::substr($s, 36, 4)) >> 6); 2552 $s15 = 2097151 & (self::load_3(self::substr($s, 39, 4)) >> 3); 2553 $s16 = 2097151 & self::load_3(self::substr($s, 42, 3)); 2554 $s17 = 2097151 & (self::load_4(self::substr($s, 44, 4)) >> 5); 2555 $s18 = 2097151 & (self::load_3(self::substr($s, 47, 3)) >> 2); 2556 $s19 = 2097151 & (self::load_4(self::substr($s, 49, 4)) >> 7); 2557 $s20 = 2097151 & (self::load_4(self::substr($s, 52, 4)) >> 4); 2558 $s21 = 2097151 & (self::load_3(self::substr($s, 55, 3)) >> 1); 2559 $s22 = 2097151 & (self::load_4(self::substr($s, 57, 4)) >> 6); 2560 $s23 = 0x1fffffff & (self::load_4(self::substr($s, 60, 4)) >> 3); 2561 2562 $s11 += self::mul($s23, 666643, 20); 2563 $s12 += self::mul($s23, 470296, 19); 2564 $s13 += self::mul($s23, 654183, 20); 2565 $s14 -= self::mul($s23, 997805, 20); 2566 $s15 += self::mul($s23, 136657, 18); 2567 $s16 -= self::mul($s23, 683901, 20); 2568 2569 $s10 += self::mul($s22, 666643, 20); 2570 $s11 += self::mul($s22, 470296, 19); 2571 $s12 += self::mul($s22, 654183, 20); 2572 $s13 -= self::mul($s22, 997805, 20); 2573 $s14 += self::mul($s22, 136657, 18); 2574 $s15 -= self::mul($s22, 683901, 20); 2575 2576 $s9 += self::mul($s21, 666643, 20); 2577 $s10 += self::mul($s21, 470296, 19); 2578 $s11 += self::mul($s21, 654183, 20); 2579 $s12 -= self::mul($s21, 997805, 20); 2580 $s13 += self::mul($s21, 136657, 18); 2581 $s14 -= self::mul($s21, 683901, 20); 2582 2583 $s8 += self::mul($s20, 666643, 20); 2584 $s9 += self::mul($s20, 470296, 19); 2585 $s10 += self::mul($s20, 654183, 20); 2586 $s11 -= self::mul($s20, 997805, 20); 2587 $s12 += self::mul($s20, 136657, 18); 2588 $s13 -= self::mul($s20, 683901, 20); 2589 2590 $s7 += self::mul($s19, 666643, 20); 2591 $s8 += self::mul($s19, 470296, 19); 2592 $s9 += self::mul($s19, 654183, 20); 2593 $s10 -= self::mul($s19, 997805, 20); 2594 $s11 += self::mul($s19, 136657, 18); 2595 $s12 -= self::mul($s19, 683901, 20); 2596 2597 $s6 += self::mul($s18, 666643, 20); 2598 $s7 += self::mul($s18, 470296, 19); 2599 $s8 += self::mul($s18, 654183, 20); 2600 $s9 -= self::mul($s18, 997805, 20); 2601 $s10 += self::mul($s18, 136657, 18); 2602 $s11 -= self::mul($s18, 683901, 20); 2603 2604 $carry6 = ($s6 + (1 << 20)) >> 21; 2605 $s7 += $carry6; 2606 $s6 -= $carry6 << 21; 2607 $carry8 = ($s8 + (1 << 20)) >> 21; 2608 $s9 += $carry8; 2609 $s8 -= $carry8 << 21; 2610 $carry10 = ($s10 + (1 << 20)) >> 21; 2611 $s11 += $carry10; 2612 $s10 -= $carry10 << 21; 2613 $carry12 = ($s12 + (1 << 20)) >> 21; 2614 $s13 += $carry12; 2615 $s12 -= $carry12 << 21; 2616 $carry14 = ($s14 + (1 << 20)) >> 21; 2617 $s15 += $carry14; 2618 $s14 -= $carry14 << 21; 2619 $carry16 = ($s16 + (1 << 20)) >> 21; 2620 $s17 += $carry16; 2621 $s16 -= $carry16 << 21; 2622 2623 $carry7 = ($s7 + (1 << 20)) >> 21; 2624 $s8 += $carry7; 2625 $s7 -= $carry7 << 21; 2626 $carry9 = ($s9 + (1 << 20)) >> 21; 2627 $s10 += $carry9; 2628 $s9 -= $carry9 << 21; 2629 $carry11 = ($s11 + (1 << 20)) >> 21; 2630 $s12 += $carry11; 2631 $s11 -= $carry11 << 21; 2632 $carry13 = ($s13 + (1 << 20)) >> 21; 2633 $s14 += $carry13; 2634 $s13 -= $carry13 << 21; 2635 $carry15 = ($s15 + (1 << 20)) >> 21; 2636 $s16 += $carry15; 2637 $s15 -= $carry15 << 21; 2638 2639 $s5 += self::mul($s17, 666643, 20); 2640 $s6 += self::mul($s17, 470296, 19); 2641 $s7 += self::mul($s17, 654183, 20); 2642 $s8 -= self::mul($s17, 997805, 20); 2643 $s9 += self::mul($s17, 136657, 18); 2644 $s10 -= self::mul($s17, 683901, 20); 2645 2646 $s4 += self::mul($s16, 666643, 20); 2647 $s5 += self::mul($s16, 470296, 19); 2648 $s6 += self::mul($s16, 654183, 20); 2649 $s7 -= self::mul($s16, 997805, 20); 2650 $s8 += self::mul($s16, 136657, 18); 2651 $s9 -= self::mul($s16, 683901, 20); 2652 2653 $s3 += self::mul($s15, 666643, 20); 2654 $s4 += self::mul($s15, 470296, 19); 2655 $s5 += self::mul($s15, 654183, 20); 2656 $s6 -= self::mul($s15, 997805, 20); 2657 $s7 += self::mul($s15, 136657, 18); 2658 $s8 -= self::mul($s15, 683901, 20); 2659 2660 $s2 += self::mul($s14, 666643, 20); 2661 $s3 += self::mul($s14, 470296, 19); 2662 $s4 += self::mul($s14, 654183, 20); 2663 $s5 -= self::mul($s14, 997805, 20); 2664 $s6 += self::mul($s14, 136657, 18); 2665 $s7 -= self::mul($s14, 683901, 20); 2666 2667 $s1 += self::mul($s13, 666643, 20); 2668 $s2 += self::mul($s13, 470296, 19); 2669 $s3 += self::mul($s13, 654183, 20); 2670 $s4 -= self::mul($s13, 997805, 20); 2671 $s5 += self::mul($s13, 136657, 18); 2672 $s6 -= self::mul($s13, 683901, 20); 2673 2674 $s0 += self::mul($s12, 666643, 20); 2675 $s1 += self::mul($s12, 470296, 19); 2676 $s2 += self::mul($s12, 654183, 20); 2677 $s3 -= self::mul($s12, 997805, 20); 2678 $s4 += self::mul($s12, 136657, 18); 2679 $s5 -= self::mul($s12, 683901, 20); 2680 $s12 = 0; 2681 2682 $carry0 = ($s0 + (1 << 20)) >> 21; 2683 $s1 += $carry0; 2684 $s0 -= $carry0 << 21; 2685 $carry2 = ($s2 + (1 << 20)) >> 21; 2686 $s3 += $carry2; 2687 $s2 -= $carry2 << 21; 2688 $carry4 = ($s4 + (1 << 20)) >> 21; 2689 $s5 += $carry4; 2690 $s4 -= $carry4 << 21; 2691 $carry6 = ($s6 + (1 << 20)) >> 21; 2692 $s7 += $carry6; 2693 $s6 -= $carry6 << 21; 2694 $carry8 = ($s8 + (1 << 20)) >> 21; 2695 $s9 += $carry8; 2696 $s8 -= $carry8 << 21; 2697 $carry10 = ($s10 + (1 << 20)) >> 21; 2698 $s11 += $carry10; 2699 $s10 -= $carry10 << 21; 2700 2701 $carry1 = ($s1 + (1 << 20)) >> 21; 2702 $s2 += $carry1; 2703 $s1 -= $carry1 << 21; 2704 $carry3 = ($s3 + (1 << 20)) >> 21; 2705 $s4 += $carry3; 2706 $s3 -= $carry3 << 21; 2707 $carry5 = ($s5 + (1 << 20)) >> 21; 2708 $s6 += $carry5; 2709 $s5 -= $carry5 << 21; 2710 $carry7 = ($s7 + (1 << 20)) >> 21; 2711 $s8 += $carry7; 2712 $s7 -= $carry7 << 21; 2713 $carry9 = ($s9 + (1 << 20)) >> 21; 2714 $s10 += $carry9; 2715 $s9 -= $carry9 << 21; 2716 $carry11 = ($s11 + (1 << 20)) >> 21; 2717 $s12 += $carry11; 2718 $s11 -= $carry11 << 21; 2719 2720 $s0 += self::mul($s12, 666643, 20); 2721 $s1 += self::mul($s12, 470296, 19); 2722 $s2 += self::mul($s12, 654183, 20); 2723 $s3 -= self::mul($s12, 997805, 20); 2724 $s4 += self::mul($s12, 136657, 18); 2725 $s5 -= self::mul($s12, 683901, 20); 2726 $s12 = 0; 2727 2728 $carry0 = $s0 >> 21; 2729 $s1 += $carry0; 2730 $s0 -= $carry0 << 21; 2731 $carry1 = $s1 >> 21; 2732 $s2 += $carry1; 2733 $s1 -= $carry1 << 21; 2734 $carry2 = $s2 >> 21; 2735 $s3 += $carry2; 2736 $s2 -= $carry2 << 21; 2737 $carry3 = $s3 >> 21; 2738 $s4 += $carry3; 2739 $s3 -= $carry3 << 21; 2740 $carry4 = $s4 >> 21; 2741 $s5 += $carry4; 2742 $s4 -= $carry4 << 21; 2743 $carry5 = $s5 >> 21; 2744 $s6 += $carry5; 2745 $s5 -= $carry5 << 21; 2746 $carry6 = $s6 >> 21; 2747 $s7 += $carry6; 2748 $s6 -= $carry6 << 21; 2749 $carry7 = $s7 >> 21; 2750 $s8 += $carry7; 2751 $s7 -= $carry7 << 21; 2752 $carry8 = $s8 >> 21; 2753 $s9 += $carry8; 2754 $s8 -= $carry8 << 21; 2755 $carry9 = $s9 >> 21; 2756 $s10 += $carry9; 2757 $s9 -= $carry9 << 21; 2758 $carry10 = $s10 >> 21; 2759 $s11 += $carry10; 2760 $s10 -= $carry10 << 21; 2761 $carry11 = $s11 >> 21; 2762 $s12 += $carry11; 2763 $s11 -= $carry11 << 21; 2764 2765 $s0 += self::mul($s12, 666643, 20); 2766 $s1 += self::mul($s12, 470296, 19); 2767 $s2 += self::mul($s12, 654183, 20); 2768 $s3 -= self::mul($s12, 997805, 20); 2769 $s4 += self::mul($s12, 136657, 18); 2770 $s5 -= self::mul($s12, 683901, 20); 2771 2772 $carry0 = $s0 >> 21; 2773 $s1 += $carry0; 2774 $s0 -= $carry0 << 21; 2775 $carry1 = $s1 >> 21; 2776 $s2 += $carry1; 2777 $s1 -= $carry1 << 21; 2778 $carry2 = $s2 >> 21; 2779 $s3 += $carry2; 2780 $s2 -= $carry2 << 21; 2781 $carry3 = $s3 >> 21; 2782 $s4 += $carry3; 2783 $s3 -= $carry3 << 21; 2784 $carry4 = $s4 >> 21; 2785 $s5 += $carry4; 2786 $s4 -= $carry4 << 21; 2787 $carry5 = $s5 >> 21; 2788 $s6 += $carry5; 2789 $s5 -= $carry5 << 21; 2790 $carry6 = $s6 >> 21; 2791 $s7 += $carry6; 2792 $s6 -= $carry6 << 21; 2793 $carry7 = $s7 >> 21; 2794 $s8 += $carry7; 2795 $s7 -= $carry7 << 21; 2796 $carry8 = $s8 >> 21; 2797 $s9 += $carry8; 2798 $s8 -= $carry8 << 21; 2799 $carry9 = $s9 >> 21; 2800 $s10 += $carry9; 2801 $s9 -= $carry9 << 21; 2802 $carry10 = $s10 >> 21; 2803 $s11 += $carry10; 2804 $s10 -= $carry10 << 21; 2805 2806 /** 2807 * @var array<int, int> 2808 */ 2809 $arr = array( 2810 (int) (0xff & ($s0 >> 0)), 2811 (int) (0xff & ($s0 >> 8)), 2812 (int) (0xff & (($s0 >> 16) | $s1 << 5)), 2813 (int) (0xff & ($s1 >> 3)), 2814 (int) (0xff & ($s1 >> 11)), 2815 (int) (0xff & (($s1 >> 19) | $s2 << 2)), 2816 (int) (0xff & ($s2 >> 6)), 2817 (int) (0xff & (($s2 >> 14) | $s3 << 7)), 2818 (int) (0xff & ($s3 >> 1)), 2819 (int) (0xff & ($s3 >> 9)), 2820 (int) (0xff & (($s3 >> 17) | $s4 << 4)), 2821 (int) (0xff & ($s4 >> 4)), 2822 (int) (0xff & ($s4 >> 12)), 2823 (int) (0xff & (($s4 >> 20) | $s5 << 1)), 2824 (int) (0xff & ($s5 >> 7)), 2825 (int) (0xff & (($s5 >> 15) | $s6 << 6)), 2826 (int) (0xff & ($s6 >> 2)), 2827 (int) (0xff & ($s6 >> 10)), 2828 (int) (0xff & (($s6 >> 18) | $s7 << 3)), 2829 (int) (0xff & ($s7 >> 5)), 2830 (int) (0xff & ($s7 >> 13)), 2831 (int) (0xff & ($s8 >> 0)), 2832 (int) (0xff & ($s8 >> 8)), 2833 (int) (0xff & (($s8 >> 16) | $s9 << 5)), 2834 (int) (0xff & ($s9 >> 3)), 2835 (int) (0xff & ($s9 >> 11)), 2836 (int) (0xff & (($s9 >> 19) | $s10 << 2)), 2837 (int) (0xff & ($s10 >> 6)), 2838 (int) (0xff & (($s10 >> 14) | $s11 << 7)), 2839 (int) (0xff & ($s11 >> 1)), 2840 (int) (0xff & ($s11 >> 9)), 2841 (int) (0xff & ($s11 >> 17)) 2842 ); 2843 return self::intArrayToString($arr); 2844 } 2845 2846 /** 2847 * multiply by the order of the main subgroup l = 2^252+27742317777372353535851937790883648493 2848 * 2849 * @param ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A 2850 * @return ParagonIE_Sodium_Core_Curve25519_Ge_P3 2851 */ 2852 public static function ge_mul_l(ParagonIE_Sodium_Core_Curve25519_Ge_P3 $A) 2853 { 2854 $aslide = array( 2855 13, 0, 0, 0, 0, -1, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 2856 0, 0, 0, -3, 0, 0, 0, 0, -13, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0, 2857 0, 0, 0, -13, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 2858 0, 0, 11, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -1, 2859 0, 0, 0, 0, 3, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 2860 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7, 0, 0, 0, 0, 5, 0, 0, 0, 0, 2861 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2862 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2863 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2864 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2865 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2866 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 2867 ); 2868 2869 /** @var array<int, ParagonIE_Sodium_Core_Curve25519_Ge_Cached> $Ai size 8 */ 2870 $Ai = array(); 2871 2872 # ge_p3_to_cached(&Ai[0], A); 2873 $Ai[0] = self::ge_p3_to_cached($A); 2874 # ge_p3_dbl(&t, A); 2875 $t = self::ge_p3_dbl($A); 2876 # ge_p1p1_to_p3(&A2, &t); 2877 $A2 = self::ge_p1p1_to_p3($t); 2878 2879 for ($i = 1; $i < 8; ++$i) { 2880 # ge_add(&t, &A2, &Ai[0]); 2881 $t = self::ge_add($A2, $Ai[$i - 1]); 2882 # ge_p1p1_to_p3(&u, &t); 2883 $u = self::ge_p1p1_to_p3($t); 2884 # ge_p3_to_cached(&Ai[i], &u); 2885 $Ai[$i] = self::ge_p3_to_cached($u); 2886 } 2887 2888 $r = self::ge_p3_0(); 2889 for ($i = 252; $i >= 0; --$i) { 2890 $t = self::ge_p3_dbl($r); 2891 if ($aslide[$i] > 0) { 2892 # ge_p1p1_to_p3(&u, &t); 2893 $u = self::ge_p1p1_to_p3($t); 2894 # ge_add(&t, &u, &Ai[aslide[i] / 2]); 2895 $t = self::ge_add($u, $Ai[(int)($aslide[$i] / 2)]); 2896 } elseif ($aslide[$i] < 0) { 2897 # ge_p1p1_to_p3(&u, &t); 2898 $u = self::ge_p1p1_to_p3($t); 2899 # ge_sub(&t, &u, &Ai[(-aslide[i]) / 2]); 2900 $t = self::ge_sub($u, $Ai[(int)(-$aslide[$i] / 2)]); 2901 } 2902 } 2903 2904 # ge_p1p1_to_p3(r, &t); 2905 return self::ge_p1p1_to_p3($t); 2906 } 2907 2908 /** 2909 * @param string $a 2910 * @param string $b 2911 * @return string 2912 */ 2913 public static function sc25519_mul($a, $b) 2914 { 2915 // int64_t a0 = 2097151 & load_3(a); 2916 // int64_t a1 = 2097151 & (load_4(a + 2) >> 5); 2917 // int64_t a2 = 2097151 & (load_3(a + 5) >> 2); 2918 // int64_t a3 = 2097151 & (load_4(a + 7) >> 7); 2919 // int64_t a4 = 2097151 & (load_4(a + 10) >> 4); 2920 // int64_t a5 = 2097151 & (load_3(a + 13) >> 1); 2921 // int64_t a6 = 2097151 & (load_4(a + 15) >> 6); 2922 // int64_t a7 = 2097151 & (load_3(a + 18) >> 3); 2923 // int64_t a8 = 2097151 & load_3(a + 21); 2924 // int64_t a9 = 2097151 & (load_4(a + 23) >> 5); 2925 // int64_t a10 = 2097151 & (load_3(a + 26) >> 2); 2926 // int64_t a11 = (load_4(a + 28) >> 7); 2927 $a0 = 2097151 & self::load_3(self::substr($a, 0, 3)); 2928 $a1 = 2097151 & (self::load_4(self::substr($a, 2, 4)) >> 5); 2929 $a2 = 2097151 & (self::load_3(self::substr($a, 5, 3)) >> 2); 2930 $a3 = 2097151 & (self::load_4(self::substr($a, 7, 4)) >> 7); 2931 $a4 = 2097151 & (self::load_4(self::substr($a, 10, 4)) >> 4); 2932 $a5 = 2097151 & (self::load_3(self::substr($a, 13, 3)) >> 1); 2933 $a6 = 2097151 & (self::load_4(self::substr($a, 15, 4)) >> 6); 2934 $a7 = 2097151 & (self::load_3(self::substr($a, 18, 3)) >> 3); 2935 $a8 = 2097151 & self::load_3(self::substr($a, 21, 3)); 2936 $a9 = 2097151 & (self::load_4(self::substr($a, 23, 4)) >> 5); 2937 $a10 = 2097151 & (self::load_3(self::substr($a, 26, 3)) >> 2); 2938 $a11 = (self::load_4(self::substr($a, 28, 4)) >> 7); 2939 2940 // int64_t b0 = 2097151 & load_3(b); 2941 // int64_t b1 = 2097151 & (load_4(b + 2) >> 5); 2942 // int64_t b2 = 2097151 & (load_3(b + 5) >> 2); 2943 // int64_t b3 = 2097151 & (load_4(b + 7) >> 7); 2944 // int64_t b4 = 2097151 & (load_4(b + 10) >> 4); 2945 // int64_t b5 = 2097151 & (load_3(b + 13) >> 1); 2946 // int64_t b6 = 2097151 & (load_4(b + 15) >> 6); 2947 // int64_t b7 = 2097151 & (load_3(b + 18) >> 3); 2948 // int64_t b8 = 2097151 & load_3(b + 21); 2949 // int64_t b9 = 2097151 & (load_4(b + 23) >> 5); 2950 // int64_t b10 = 2097151 & (load_3(b + 26) >> 2); 2951 // int64_t b11 = (load_4(b + 28) >> 7); 2952 $b0 = 2097151 & self::load_3(self::substr($b, 0, 3)); 2953 $b1 = 2097151 & (self::load_4(self::substr($b, 2, 4)) >> 5); 2954 $b2 = 2097151 & (self::load_3(self::substr($b, 5, 3)) >> 2); 2955 $b3 = 2097151 & (self::load_4(self::substr($b, 7, 4)) >> 7); 2956 $b4 = 2097151 & (self::load_4(self::substr($b, 10, 4)) >> 4); 2957 $b5 = 2097151 & (self::load_3(self::substr($b, 13, 3)) >> 1); 2958 $b6 = 2097151 & (self::load_4(self::substr($b, 15, 4)) >> 6); 2959 $b7 = 2097151 & (self::load_3(self::substr($b, 18, 3)) >> 3); 2960 $b8 = 2097151 & self::load_3(self::substr($b, 21, 3)); 2961 $b9 = 2097151 & (self::load_4(self::substr($b, 23, 4)) >> 5); 2962 $b10 = 2097151 & (self::load_3(self::substr($b, 26, 3)) >> 2); 2963 $b11 = (self::load_4(self::substr($b, 28, 4)) >> 7); 2964 2965 // s0 = a0 * b0; 2966 // s1 = a0 * b1 + a1 * b0; 2967 // s2 = a0 * b2 + a1 * b1 + a2 * b0; 2968 // s3 = a0 * b3 + a1 * b2 + a2 * b1 + a3 * b0; 2969 // s4 = a0 * b4 + a1 * b3 + a2 * b2 + a3 * b1 + a4 * b0; 2970 // s5 = a0 * b5 + a1 * b4 + a2 * b3 + a3 * b2 + a4 * b1 + a5 * b0; 2971 // s6 = a0 * b6 + a1 * b5 + a2 * b4 + a3 * b3 + a4 * b2 + a5 * b1 + a6 * b0; 2972 // s7 = a0 * b7 + a1 * b6 + a2 * b5 + a3 * b4 + a4 * b3 + a5 * b2 + 2973 // a6 * b1 + a7 * b0; 2974 // s8 = a0 * b8 + a1 * b7 + a2 * b6 + a3 * b5 + a4 * b4 + a5 * b3 + 2975 // a6 * b2 + a7 * b1 + a8 * b0; 2976 // s9 = a0 * b9 + a1 * b8 + a2 * b7 + a3 * b6 + a4 * b5 + a5 * b4 + 2977 // a6 * b3 + a7 * b2 + a8 * b1 + a9 * b0; 2978 // s10 = a0 * b10 + a1 * b9 + a2 * b8 + a3 * b7 + a4 * b6 + a5 * b5 + 2979 // a6 * b4 + a7 * b3 + a8 * b2 + a9 * b1 + a10 * b0; 2980 // s11 = a0 * b11 + a1 * b10 + a2 * b9 + a3 * b8 + a4 * b7 + a5 * b6 + 2981 // a6 * b5 + a7 * b4 + a8 * b3 + a9 * b2 + a10 * b1 + a11 * b0; 2982 // s12 = a1 * b11 + a2 * b10 + a3 * b9 + a4 * b8 + a5 * b7 + a6 * b6 + 2983 // a7 * b5 + a8 * b4 + a9 * b3 + a10 * b2 + a11 * b1; 2984 // s13 = a2 * b11 + a3 * b10 + a4 * b9 + a5 * b8 + a6 * b7 + a7 * b6 + 2985 // a8 * b5 + a9 * b4 + a10 * b3 + a11 * b2; 2986 // s14 = a3 * b11 + a4 * b10 + a5 * b9 + a6 * b8 + a7 * b7 + a8 * b6 + 2987 // a9 * b5 + a10 * b4 + a11 * b3; 2988 // s15 = a4 * b11 + a5 * b10 + a6 * b9 + a7 * b8 + a8 * b7 + a9 * b6 + 2989 // a10 * b5 + a11 * b4; 2990 // s16 = 2991 // a5 * b11 + a6 * b10 + a7 * b9 + a8 * b8 + a9 * b7 + a10 * b6 + a11 * b5; 2992 // s17 = a6 * b11 + a7 * b10 + a8 * b9 + a9 * b8 + a10 * b7 + a11 * b6; 2993 // s18 = a7 * b11 + a8 * b10 + a9 * b9 + a10 * b8 + a11 * b7; 2994 // s19 = a8 * b11 + a9 * b10 + a10 * b9 + a11 * b8; 2995 // s20 = a9 * b11 + a10 * b10 + a11 * b9; 2996 // s21 = a10 * b11 + a11 * b10; 2997 // s22 = a11 * b11; 2998 // s23 = 0; 2999 $s0 = self::mul($a0, $b0, 22); 3000 $s1 = self::mul($a0, $b1, 22) + self::mul($a1, $b0, 22); 3001 $s2 = self::mul($a0, $b2, 22) + self::mul($a1, $b1, 22) + self::mul($a2, $b0, 22); 3002 $s3 = self::mul($a0, $b3, 22) + self::mul($a1, $b2, 22) + self::mul($a2, $b1, 22) + self::mul($a3, $b0, 22); 3003 $s4 = self::mul($a0, $b4, 22) + self::mul($a1, $b3, 22) + self::mul($a2, $b2, 22) + self::mul($a3, $b1, 22) + 3004 self::mul($a4, $b0, 22); 3005 $s5 = self::mul($a0, $b5, 22) + self::mul($a1, $b4, 22) + self::mul($a2, $b3, 22) + self::mul($a3, $b2, 22) + 3006 self::mul($a4, $b1, 22) + self::mul($a5, $b0, 22); 3007 $s6 = self::mul($a0, $b6, 22) + self::mul($a1, $b5, 22) + self::mul($a2, $b4, 22) + self::mul($a3, $b3, 22) + 3008 self::mul($a4, $b2, 22) + self::mul($a5, $b1, 22) + self::mul($a6, $b0, 22); 3009 $s7 = self::mul($a0, $b7, 22) + self::mul($a1, $b6, 22) + self::mul($a2, $b5, 22) + self::mul($a3, $b4, 22) + 3010 self::mul($a4, $b3, 22) + self::mul($a5, $b2, 22) + self::mul($a6, $b1, 22) + self::mul($a7, $b0, 22); 3011 $s8 = self::mul($a0, $b8, 22) + self::mul($a1, $b7, 22) + self::mul($a2, $b6, 22) + self::mul($a3, $b5, 22) + 3012 self::mul($a4, $b4, 22) + self::mul($a5, $b3, 22) + self::mul($a6, $b2, 22) + self::mul($a7, $b1, 22) + 3013 self::mul($a8, $b0, 22); 3014 $s9 = self::mul($a0, $b9, 22) + self::mul($a1, $b8, 22) + self::mul($a2, $b7, 22) + self::mul($a3, $b6, 22) + 3015 self::mul($a4, $b5, 22) + self::mul($a5, $b4, 22) + self::mul($a6, $b3, 22) + self::mul($a7, $b2, 22) + 3016 self::mul($a8, $b1, 22) + self::mul($a9, $b0, 22); 3017 $s10 = self::mul($a0, $b10, 22) + self::mul($a1, $b9, 22) + self::mul($a2, $b8, 22) + self::mul($a3, $b7, 22) + 3018 self::mul($a4, $b6, 22) + self::mul($a5, $b5, 22) + self::mul($a6, $b4, 22) + self::mul($a7, $b3, 22) + 3019 self::mul($a8, $b2, 22) + self::mul($a9, $b1, 22) + self::mul($a10, $b0, 22); 3020 $s11 = self::mul($a0, $b11, 22) + self::mul($a1, $b10, 22) + self::mul($a2, $b9, 22) + self::mul($a3, $b8, 22) + 3021 self::mul($a4, $b7, 22) + self::mul($a5, $b6, 22) + self::mul($a6, $b5, 22) + self::mul($a7, $b4, 22) + 3022 self::mul($a8, $b3, 22) + self::mul($a9, $b2, 22) + self::mul($a10, $b1, 22) + self::mul($a11, $b0, 22); 3023 $s12 = self::mul($a1, $b11, 22) + self::mul($a2, $b10, 22) + self::mul($a3, $b9, 22) + self::mul($a4, $b8, 22) + 3024 self::mul($a5, $b7, 22) + self::mul($a6, $b6, 22) + self::mul($a7, $b5, 22) + self::mul($a8, $b4, 22) + 3025 self::mul($a9, $b3, 22) + self::mul($a10, $b2, 22) + self::mul($a11, $b1, 22); 3026 $s13 = self::mul($a2, $b11, 22) + self::mul($a3, $b10, 22) + self::mul($a4, $b9, 22) + self::mul($a5, $b8, 22) + 3027 self::mul($a6, $b7, 22) + self::mul($a7, $b6, 22) + self::mul($a8, $b5, 22) + self::mul($a9, $b4, 22) + 3028 self::mul($a10, $b3, 22) + self::mul($a11, $b2, 22); 3029 $s14 = self::mul($a3, $b11, 22) + self::mul($a4, $b10, 22) + self::mul($a5, $b9, 22) + self::mul($a6, $b8, 22) + 3030 self::mul($a7, $b7, 22) + self::mul($a8, $b6, 22) + self::mul($a9, $b5, 22) + self::mul($a10, $b4, 22) + 3031 self::mul($a11, $b3, 22); 3032 $s15 = self::mul($a4, $b11, 22) + self::mul($a5, $b10, 22) + self::mul($a6, $b9, 22) + self::mul($a7, $b8, 22) + 3033 self::mul($a8, $b7, 22) + self::mul($a9, $b6, 22) + self::mul($a10, $b5, 22) + self::mul($a11, $b4, 22); 3034 $s16 = 3035 self::mul($a5, $b11, 22) + self::mul($a6, $b10, 22) + self::mul($a7, $b9, 22) + self::mul($a8, $b8, 22) + 3036 self::mul($a9, $b7, 22) + self::mul($a10, $b6, 22) + self::mul($a11, $b5, 22); 3037 $s17 = self::mul($a6, $b11, 22) + self::mul($a7, $b10, 22) + self::mul($a8, $b9, 22) + self::mul($a9, $b8, 22) + 3038 self::mul($a10, $b7, 22) + self::mul($a11, $b6, 22); 3039 $s18 = self::mul($a7, $b11, 22) + self::mul($a8, $b10, 22) + self::mul($a9, $b9, 22) + self::mul($a10, $b8, 22) 3040 + self::mul($a11, $b7, 22); 3041 $s19 = self::mul($a8, $b11, 22) + self::mul($a9, $b10, 22) + self::mul($a10, $b9, 22) + 3042 self::mul($a11, $b8, 22); 3043 $s20 = self::mul($a9, $b11, 22) + self::mul($a10, $b10, 22) + self::mul($a11, $b9, 22); 3044 $s21 = self::mul($a10, $b11, 22) + self::mul($a11, $b10, 22); 3045 $s22 = self::mul($a11, $b11, 22); 3046 $s23 = 0; 3047 3048 // carry0 = (s0 + (int64_t) (1L << 20)) >> 21; 3049 // s1 += carry0; 3050 // s0 -= carry0 * ((uint64_t) 1L << 21); 3051 $carry0 = ($s0 + (1 << 20)) >> 21; 3052 $s1 += $carry0; 3053 $s0 -= $carry0 << 21; 3054 // carry2 = (s2 + (int64_t) (1L << 20)) >> 21; 3055 // s3 += carry2; 3056 // s2 -= carry2 * ((uint64_t) 1L << 21); 3057 $carry2 = ($s2 + (1 << 20)) >> 21; 3058 $s3 += $carry2; 3059 $s2 -= $carry2 << 21; 3060 // carry4 = (s4 + (int64_t) (1L << 20)) >> 21; 3061 // s5 += carry4; 3062 // s4 -= carry4 * ((uint64_t) 1L << 21); 3063 $carry4 = ($s4 + (1 << 20)) >> 21; 3064 $s5 += $carry4; 3065 $s4 -= $carry4 << 21; 3066 // carry6 = (s6 + (int64_t) (1L << 20)) >> 21; 3067 // s7 += carry6; 3068 // s6 -= carry6 * ((uint64_t) 1L << 21); 3069 $carry6 = ($s6 + (1 << 20)) >> 21; 3070 $s7 += $carry6; 3071 $s6 -= $carry6 << 21; 3072 // carry8 = (s8 + (int64_t) (1L << 20)) >> 21; 3073 // s9 += carry8; 3074 // s8 -= carry8 * ((uint64_t) 1L << 21); 3075 $carry8 = ($s8 + (1 << 20)) >> 21; 3076 $s9 += $carry8; 3077 $s8 -= $carry8 << 21; 3078 // carry10 = (s10 + (int64_t) (1L << 20)) >> 21; 3079 // s11 += carry10; 3080 // s10 -= carry10 * ((uint64_t) 1L << 21); 3081 $carry10 = ($s10 + (1 << 20)) >> 21; 3082 $s11 += $carry10; 3083 $s10 -= $carry10 << 21; 3084 // carry12 = (s12 + (int64_t) (1L << 20)) >> 21; 3085 // s13 += carry12; 3086 // s12 -= carry12 * ((uint64_t) 1L << 21); 3087 $carry12 = ($s12 + (1 << 20)) >> 21; 3088 $s13 += $carry12; 3089 $s12 -= $carry12 << 21; 3090 // carry14 = (s14 + (int64_t) (1L << 20)) >> 21; 3091 // s15 += carry14; 3092 // s14 -= carry14 * ((uint64_t) 1L << 21); 3093 $carry14 = ($s14 + (1 << 20)) >> 21; 3094 $s15 += $carry14; 3095 $s14 -= $carry14 << 21; 3096 // carry16 = (s16 + (int64_t) (1L << 20)) >> 21; 3097 // s17 += carry16; 3098 // s16 -= carry16 * ((uint64_t) 1L << 21); 3099 $carry16 = ($s16 + (1 << 20)) >> 21; 3100 $s17 += $carry16; 3101 $s16 -= $carry16 << 21; 3102 // carry18 = (s18 + (int64_t) (1L << 20)) >> 21; 3103 // s19 += carry18; 3104 // s18 -= carry18 * ((uint64_t) 1L << 21); 3105 $carry18 = ($s18 + (1 << 20)) >> 21; 3106 $s19 += $carry18; 3107 $s18 -= $carry18 << 21; 3108 // carry20 = (s20 + (int64_t) (1L << 20)) >> 21; 3109 // s21 += carry20; 3110 // s20 -= carry20 * ((uint64_t) 1L << 21); 3111 $carry20 = ($s20 + (1 << 20)) >> 21; 3112 $s21 += $carry20; 3113 $s20 -= $carry20 << 21; 3114 // carry22 = (s22 + (int64_t) (1L << 20)) >> 21; 3115 // s23 += carry22; 3116 // s22 -= carry22 * ((uint64_t) 1L << 21); 3117 $carry22 = ($s22 + (1 << 20)) >> 21; 3118 $s23 += $carry22; 3119 $s22 -= $carry22 << 21; 3120 3121 // carry1 = (s1 + (int64_t) (1L << 20)) >> 21; 3122 // s2 += carry1; 3123 // s1 -= carry1 * ((uint64_t) 1L << 21); 3124 $carry1 = ($s1 + (1 << 20)) >> 21; 3125 $s2 += $carry1; 3126 $s1 -= $carry1 << 21; 3127 // carry3 = (s3 + (int64_t) (1L << 20)) >> 21; 3128 // s4 += carry3; 3129 // s3 -= carry3 * ((uint64_t) 1L << 21); 3130 $carry3 = ($s3 + (1 << 20)) >> 21; 3131 $s4 += $carry3; 3132 $s3 -= $carry3 << 21; 3133 // carry5 = (s5 + (int64_t) (1L << 20)) >> 21; 3134 // s6 += carry5; 3135 // s5 -= carry5 * ((uint64_t) 1L << 21); 3136 $carry5 = ($s5 + (1 << 20)) >> 21; 3137 $s6 += $carry5; 3138 $s5 -= $carry5 << 21; 3139 // carry7 = (s7 + (int64_t) (1L << 20)) >> 21; 3140 // s8 += carry7; 3141 // s7 -= carry7 * ((uint64_t) 1L << 21); 3142 $carry7 = ($s7 + (1 << 20)) >> 21; 3143 $s8 += $carry7; 3144 $s7 -= $carry7 << 21; 3145 // carry9 = (s9 + (int64_t) (1L << 20)) >> 21; 3146 // s10 += carry9; 3147 // s9 -= carry9 * ((uint64_t) 1L << 21); 3148 $carry9 = ($s9 + (1 << 20)) >> 21; 3149 $s10 += $carry9; 3150 $s9 -= $carry9 << 21; 3151 // carry11 = (s11 + (int64_t) (1L << 20)) >> 21; 3152 // s12 += carry11; 3153 // s11 -= carry11 * ((uint64_t) 1L << 21); 3154 $carry11 = ($s11 + (1 << 20)) >> 21; 3155 $s12 += $carry11; 3156 $s11 -= $carry11 << 21; 3157 // carry13 = (s13 + (int64_t) (1L << 20)) >> 21; 3158 // s14 += carry13; 3159 // s13 -= carry13 * ((uint64_t) 1L << 21); 3160 $carry13 = ($s13 + (1 << 20)) >> 21; 3161 $s14 += $carry13; 3162 $s13 -= $carry13 << 21; 3163 // carry15 = (s15 + (int64_t) (1L << 20)) >> 21; 3164 // s16 += carry15; 3165 // s15 -= carry15 * ((uint64_t) 1L << 21); 3166 $carry15 = ($s15 + (1 << 20)) >> 21; 3167 $s16 += $carry15; 3168 $s15 -= $carry15 << 21; 3169 // carry17 = (s17 + (int64_t) (1L << 20)) >> 21; 3170 // s18 += carry17; 3171 // s17 -= carry17 * ((uint64_t) 1L << 21); 3172 $carry17 = ($s17 + (1 << 20)) >> 21; 3173 $s18 += $carry17; 3174 $s17 -= $carry17 << 21; 3175 // carry19 = (s19 + (int64_t) (1L << 20)) >> 21; 3176 // s20 += carry19; 3177 // s19 -= carry19 * ((uint64_t) 1L << 21); 3178 $carry19 = ($s19 + (1 << 20)) >> 21; 3179 $s20 += $carry19; 3180 $s19 -= $carry19 << 21; 3181 // carry21 = (s21 + (int64_t) (1L << 20)) >> 21; 3182 // s22 += carry21; 3183 // s21 -= carry21 * ((uint64_t) 1L << 21); 3184 $carry21 = ($s21 + (1 << 20)) >> 21; 3185 $s22 += $carry21; 3186 $s21 -= $carry21 << 21; 3187 3188 // s11 += s23 * 666643; 3189 // s12 += s23 * 470296; 3190 // s13 += s23 * 654183; 3191 // s14 -= s23 * 997805; 3192 // s15 += s23 * 136657; 3193 // s16 -= s23 * 683901; 3194 $s11 += self::mul($s23, 666643, 20); 3195 $s12 += self::mul($s23, 470296, 19); 3196 $s13 += self::mul($s23, 654183, 20); 3197 $s14 -= self::mul($s23, 997805, 20); 3198 $s15 += self::mul($s23, 136657, 18); 3199 $s16 -= self::mul($s23, 683901, 20); 3200 3201 // s10 += s22 * 666643; 3202 // s11 += s22 * 470296; 3203 // s12 += s22 * 654183; 3204 // s13 -= s22 * 997805; 3205 // s14 += s22 * 136657; 3206 // s15 -= s22 * 683901; 3207 $s10 += self::mul($s22, 666643, 20); 3208 $s11 += self::mul($s22, 470296, 19); 3209 $s12 += self::mul($s22, 654183, 20); 3210 $s13 -= self::mul($s22, 997805, 20); 3211 $s14 += self::mul($s22, 136657, 18); 3212 $s15 -= self::mul($s22, 683901, 20); 3213 3214 // s9 += s21 * 666643; 3215 // s10 += s21 * 470296; 3216 // s11 += s21 * 654183; 3217 // s12 -= s21 * 997805; 3218 // s13 += s21 * 136657; 3219 // s14 -= s21 * 683901; 3220 $s9 += self::mul($s21, 666643, 20); 3221 $s10 += self::mul($s21, 470296, 19); 3222 $s11 += self::mul($s21, 654183, 20); 3223 $s12 -= self::mul($s21, 997805, 20); 3224 $s13 += self::mul($s21, 136657, 18); 3225 $s14 -= self::mul($s21, 683901, 20); 3226 3227 // s8 += s20 * 666643; 3228 // s9 += s20 * 470296; 3229 // s10 += s20 * 654183; 3230 // s11 -= s20 * 997805; 3231 // s12 += s20 * 136657; 3232 // s13 -= s20 * 683901; 3233 $s8 += self::mul($s20, 666643, 20); 3234 $s9 += self::mul($s20, 470296, 19); 3235 $s10 += self::mul($s20, 654183, 20); 3236 $s11 -= self::mul($s20, 997805, 20); 3237 $s12 += self::mul($s20, 136657, 18); 3238 $s13 -= self::mul($s20, 683901, 20); 3239 3240 // s7 += s19 * 666643; 3241 // s8 += s19 * 470296; 3242 // s9 += s19 * 654183; 3243 // s10 -= s19 * 997805; 3244 // s11 += s19 * 136657; 3245 // s12 -= s19 * 683901; 3246 $s7 += self::mul($s19, 666643, 20); 3247 $s8 += self::mul($s19, 470296, 19); 3248 $s9 += self::mul($s19, 654183, 20); 3249 $s10 -= self::mul($s19, 997805, 20); 3250 $s11 += self::mul($s19, 136657, 18); 3251 $s12 -= self::mul($s19, 683901, 20); 3252 3253 // s6 += s18 * 666643; 3254 // s7 += s18 * 470296; 3255 // s8 += s18 * 654183; 3256 // s9 -= s18 * 997805; 3257 // s10 += s18 * 136657; 3258 // s11 -= s18 * 683901; 3259 $s6 += self::mul($s18, 666643, 20); 3260 $s7 += self::mul($s18, 470296, 19); 3261 $s8 += self::mul($s18, 654183, 20); 3262 $s9 -= self::mul($s18, 997805, 20); 3263 $s10 += self::mul($s18, 136657, 18); 3264 $s11 -= self::mul($s18, 683901, 20); 3265 3266 // carry6 = (s6 + (int64_t) (1L << 20)) >> 21; 3267 // s7 += carry6; 3268 // s6 -= carry6 * ((uint64_t) 1L << 21); 3269 $carry6 = ($s6 + (1 << 20)) >> 21; 3270 $s7 += $carry6; 3271 $s6 -= $carry6 << 21; 3272 // carry8 = (s8 + (int64_t) (1L << 20)) >> 21; 3273 // s9 += carry8; 3274 // s8 -= carry8 * ((uint64_t) 1L << 21); 3275 $carry8 = ($s8 + (1 << 20)) >> 21; 3276 $s9 += $carry8; 3277 $s8 -= $carry8 << 21; 3278 // carry10 = (s10 + (int64_t) (1L << 20)) >> 21; 3279 // s11 += carry10; 3280 // s10 -= carry10 * ((uint64_t) 1L << 21); 3281 $carry10 = ($s10 + (1 << 20)) >> 21; 3282 $s11 += $carry10; 3283 $s10 -= $carry10 << 21; 3284 // carry12 = (s12 + (int64_t) (1L << 20)) >> 21; 3285 // s13 += carry12; 3286 // s12 -= carry12 * ((uint64_t) 1L << 21); 3287 $carry12 = ($s12 + (1 << 20)) >> 21; 3288 $s13 += $carry12; 3289 $s12 -= $carry12 << 21; 3290 // carry14 = (s14 + (int64_t) (1L << 20)) >> 21; 3291 // s15 += carry14; 3292 // s14 -= carry14 * ((uint64_t) 1L << 21); 3293 $carry14 = ($s14 + (1 << 20)) >> 21; 3294 $s15 += $carry14; 3295 $s14 -= $carry14 << 21; 3296 // carry16 = (s16 + (int64_t) (1L << 20)) >> 21; 3297 // s17 += carry16; 3298 // s16 -= carry16 * ((uint64_t) 1L << 21); 3299 $carry16 = ($s16 + (1 << 20)) >> 21; 3300 $s17 += $carry16; 3301 $s16 -= $carry16 << 21; 3302 3303 // carry7 = (s7 + (int64_t) (1L << 20)) >> 21; 3304 // s8 += carry7; 3305 // s7 -= carry7 * ((uint64_t) 1L << 21); 3306 $carry7 = ($s7 + (1 << 20)) >> 21; 3307 $s8 += $carry7; 3308 $s7 -= $carry7 << 21; 3309 // carry9 = (s9 + (int64_t) (1L << 20)) >> 21; 3310 // s10 += carry9; 3311 // s9 -= carry9 * ((uint64_t) 1L << 21); 3312 $carry9 = ($s9 + (1 << 20)) >> 21; 3313 $s10 += $carry9; 3314 $s9 -= $carry9 << 21; 3315 // carry11 = (s11 + (int64_t) (1L << 20)) >> 21; 3316 // s12 += carry11; 3317 // s11 -= carry11 * ((uint64_t) 1L << 21); 3318 $carry11 = ($s11 + (1 << 20)) >> 21; 3319 $s12 += $carry11; 3320 $s11 -= $carry11 << 21; 3321 // carry13 = (s13 + (int64_t) (1L << 20)) >> 21; 3322 // s14 += carry13; 3323 // s13 -= carry13 * ((uint64_t) 1L << 21); 3324 $carry13 = ($s13 + (1 << 20)) >> 21; 3325 $s14 += $carry13; 3326 $s13 -= $carry13 << 21; 3327 // carry15 = (s15 + (int64_t) (1L << 20)) >> 21; 3328 // s16 += carry15; 3329 // s15 -= carry15 * ((uint64_t) 1L << 21); 3330 $carry15 = ($s15 + (1 << 20)) >> 21; 3331 $s16 += $carry15; 3332 $s15 -= $carry15 << 21; 3333 3334 // s5 += s17 * 666643; 3335 // s6 += s17 * 470296; 3336 // s7 += s17 * 654183; 3337 // s8 -= s17 * 997805; 3338 // s9 += s17 * 136657; 3339 // s10 -= s17 * 683901; 3340 $s5 += self::mul($s17, 666643, 20); 3341 $s6 += self::mul($s17, 470296, 19); 3342 $s7 += self::mul($s17, 654183, 20); 3343 $s8 -= self::mul($s17, 997805, 20); 3344 $s9 += self::mul($s17, 136657, 18); 3345 $s10 -= self::mul($s17, 683901, 20); 3346 3347 // s4 += s16 * 666643; 3348 // s5 += s16 * 470296; 3349 // s6 += s16 * 654183; 3350 // s7 -= s16 * 997805; 3351 // s8 += s16 * 136657; 3352 // s9 -= s16 * 683901; 3353 $s4 += self::mul($s16, 666643, 20); 3354 $s5 += self::mul($s16, 470296, 19); 3355 $s6 += self::mul($s16, 654183, 20); 3356 $s7 -= self::mul($s16, 997805, 20); 3357 $s8 += self::mul($s16, 136657, 18); 3358 $s9 -= self::mul($s16, 683901, 20); 3359 3360 // s3 += s15 * 666643; 3361 // s4 += s15 * 470296; 3362 // s5 += s15 * 654183; 3363 // s6 -= s15 * 997805; 3364 // s7 += s15 * 136657; 3365 // s8 -= s15 * 683901; 3366 $s3 += self::mul($s15, 666643, 20); 3367 $s4 += self::mul($s15, 470296, 19); 3368 $s5 += self::mul($s15, 654183, 20); 3369 $s6 -= self::mul($s15, 997805, 20); 3370 $s7 += self::mul($s15, 136657, 18); 3371 $s8 -= self::mul($s15, 683901, 20); 3372 3373 // s2 += s14 * 666643; 3374 // s3 += s14 * 470296; 3375 // s4 += s14 * 654183; 3376 // s5 -= s14 * 997805; 3377 // s6 += s14 * 136657; 3378 // s7 -= s14 * 683901; 3379 $s2 += self::mul($s14, 666643, 20); 3380 $s3 += self::mul($s14, 470296, 19); 3381 $s4 += self::mul($s14, 654183, 20); 3382 $s5 -= self::mul($s14, 997805, 20); 3383 $s6 += self::mul($s14, 136657, 18); 3384 $s7 -= self::mul($s14, 683901, 20); 3385 3386 // s1 += s13 * 666643; 3387 // s2 += s13 * 470296; 3388 // s3 += s13 * 654183; 3389 // s4 -= s13 * 997805; 3390 // s5 += s13 * 136657; 3391 // s6 -= s13 * 683901; 3392 $s1 += self::mul($s13, 666643, 20); 3393 $s2 += self::mul($s13, 470296, 19); 3394 $s3 += self::mul($s13, 654183, 20); 3395 $s4 -= self::mul($s13, 997805, 20); 3396 $s5 += self::mul($s13, 136657, 18); 3397 $s6 -= self::mul($s13, 683901, 20); 3398 3399 // s0 += s12 * 666643; 3400 // s1 += s12 * 470296; 3401 // s2 += s12 * 654183; 3402 // s3 -= s12 * 997805; 3403 // s4 += s12 * 136657; 3404 // s5 -= s12 * 683901; 3405 // s12 = 0; 3406 $s0 += self::mul($s12, 666643, 20); 3407 $s1 += self::mul($s12, 470296, 19); 3408 $s2 += self::mul($s12, 654183, 20); 3409 $s3 -= self::mul($s12, 997805, 20); 3410 $s4 += self::mul($s12, 136657, 18); 3411 $s5 -= self::mul($s12, 683901, 20); 3412 $s12 = 0; 3413 3414 // carry0 = (s0 + (int64_t) (1L << 20)) >> 21; 3415 // s1 += carry0; 3416 // s0 -= carry0 * ((uint64_t) 1L << 21); 3417 $carry0 = ($s0 + (1 << 20)) >> 21; 3418 $s1 += $carry0; 3419 $s0 -= $carry0 << 21; 3420 // carry2 = (s2 + (int64_t) (1L << 20)) >> 21; 3421 // s3 += carry2; 3422 // s2 -= carry2 * ((uint64_t) 1L << 21); 3423 $carry2 = ($s2 + (1 << 20)) >> 21; 3424 $s3 += $carry2; 3425 $s2 -= $carry2 << 21; 3426 // carry4 = (s4 + (int64_t) (1L << 20)) >> 21; 3427 // s5 += carry4; 3428 // s4 -= carry4 * ((uint64_t) 1L << 21); 3429 $carry4 = ($s4 + (1 << 20)) >> 21; 3430 $s5 += $carry4; 3431 $s4 -= $carry4 << 21; 3432 // carry6 = (s6 + (int64_t) (1L << 20)) >> 21; 3433 // s7 += carry6; 3434 // s6 -= carry6 * ((uint64_t) 1L << 21); 3435 $carry6 = ($s6 + (1 << 20)) >> 21; 3436 $s7 += $carry6; 3437 $s6 -= $carry6 << 21; 3438 // carry8 = (s8 + (int64_t) (1L << 20)) >> 21; 3439 // s9 += carry8; 3440 // s8 -= carry8 * ((uint64_t) 1L << 21); 3441 $carry8 = ($s8 + (1 << 20)) >> 21; 3442 $s9 += $carry8; 3443 $s8 -= $carry8 << 21; 3444 // carry10 = (s10 + (int64_t) (1L << 20)) >> 21; 3445 // s11 += carry10; 3446 // s10 -= carry10 * ((uint64_t) 1L << 21); 3447 $carry10 = ($s10 + (1 << 20)) >> 21; 3448 $s11 += $carry10; 3449 $s10 -= $carry10 << 21; 3450 3451 // carry1 = (s1 + (int64_t) (1L << 20)) >> 21; 3452 // s2 += carry1; 3453 // s1 -= carry1 * ((uint64_t) 1L << 21); 3454 $carry1 = ($s1 + (1 << 20)) >> 21; 3455 $s2 += $carry1; 3456 $s1 -= $carry1 << 21; 3457 // carry3 = (s3 + (int64_t) (1L << 20)) >> 21; 3458 // s4 += carry3; 3459 // s3 -= carry3 * ((uint64_t) 1L << 21); 3460 $carry3 = ($s3 + (1 << 20)) >> 21; 3461 $s4 += $carry3; 3462 $s3 -= $carry3 << 21; 3463 // carry5 = (s5 + (int64_t) (1L << 20)) >> 21; 3464 // s6 += carry5; 3465 // s5 -= carry5 * ((uint64_t) 1L << 21); 3466 $carry5 = ($s5 + (1 << 20)) >> 21; 3467 $s6 += $carry5; 3468 $s5 -= $carry5 << 21; 3469 // carry7 = (s7 + (int64_t) (1L << 20)) >> 21; 3470 // s8 += carry7; 3471 // s7 -= carry7 * ((uint64_t) 1L << 21); 3472 $carry7 = ($s7 + (1 << 20)) >> 21; 3473 $s8 += $carry7; 3474 $s7 -= $carry7 << 21; 3475 // carry9 = (s9 + (int64_t) (1L << 20)) >> 21; 3476 // s10 += carry9; 3477 // s9 -= carry9 * ((uint64_t) 1L << 21); 3478 $carry9 = ($s9 + (1 << 20)) >> 21; 3479 $s10 += $carry9; 3480 $s9 -= $carry9 << 21; 3481 // carry11 = (s11 + (int64_t) (1L << 20)) >> 21; 3482 // s12 += carry11; 3483 // s11 -= carry11 * ((uint64_t) 1L << 21); 3484 $carry11 = ($s11 + (1 << 20)) >> 21; 3485 $s12 += $carry11; 3486 $s11 -= $carry11 << 21; 3487 3488 // s0 += s12 * 666643; 3489 // s1 += s12 * 470296; 3490 // s2 += s12 * 654183; 3491 // s3 -= s12 * 997805; 3492 // s4 += s12 * 136657; 3493 // s5 -= s12 * 683901; 3494 // s12 = 0; 3495 $s0 += self::mul($s12, 666643, 20); 3496 $s1 += self::mul($s12, 470296, 19); 3497 $s2 += self::mul($s12, 654183, 20); 3498 $s3 -= self::mul($s12, 997805, 20); 3499 $s4 += self::mul($s12, 136657, 18); 3500 $s5 -= self::mul($s12, 683901, 20); 3501 $s12 = 0; 3502 3503 // carry0 = s0 >> 21; 3504 // s1 += carry0; 3505 // s0 -= carry0 * ((uint64_t) 1L << 21); 3506 $carry0 = $s0 >> 21; 3507 $s1 += $carry0; 3508 $s0 -= $carry0 << 21; 3509 // carry1 = s1 >> 21; 3510 // s2 += carry1; 3511 // s1 -= carry1 * ((uint64_t) 1L << 21); 3512 $carry1 = $s1 >> 21; 3513 $s2 += $carry1; 3514 $s1 -= $carry1 << 21; 3515 // carry2 = s2 >> 21; 3516 // s3 += carry2; 3517 // s2 -= carry2 * ((uint64_t) 1L << 21); 3518 $carry2 = $s2 >> 21; 3519 $s3 += $carry2; 3520 $s2 -= $carry2 << 21; 3521 // carry3 = s3 >> 21; 3522 // s4 += carry3; 3523 // s3 -= carry3 * ((uint64_t) 1L << 21); 3524 $carry3 = $s3 >> 21; 3525 $s4 += $carry3; 3526 $s3 -= $carry3 << 21; 3527 // carry4 = s4 >> 21; 3528 // s5 += carry4; 3529 // s4 -= carry4 * ((uint64_t) 1L << 21); 3530 $carry4 = $s4 >> 21; 3531 $s5 += $carry4; 3532 $s4 -= $carry4 << 21; 3533 // carry5 = s5 >> 21; 3534 // s6 += carry5; 3535 // s5 -= carry5 * ((uint64_t) 1L << 21); 3536 $carry5 = $s5 >> 21; 3537 $s6 += $carry5; 3538 $s5 -= $carry5 << 21; 3539 // carry6 = s6 >> 21; 3540 // s7 += carry6; 3541 // s6 -= carry6 * ((uint64_t) 1L << 21); 3542 $carry6 = $s6 >> 21; 3543 $s7 += $carry6; 3544 $s6 -= $carry6 << 21; 3545 // carry7 = s7 >> 21; 3546 // s8 += carry7; 3547 // s7 -= carry7 * ((uint64_t) 1L << 21); 3548 $carry7 = $s7 >> 21; 3549 $s8 += $carry7; 3550 $s7 -= $carry7 << 21; 3551 // carry8 = s8 >> 21; 3552 // s9 += carry8; 3553 // s8 -= carry8 * ((uint64_t) 1L << 21); 3554 $carry8 = $s8 >> 21; 3555 $s9 += $carry8; 3556 $s8 -= $carry8 << 21; 3557 // carry9 = s9 >> 21; 3558 // s10 += carry9; 3559 // s9 -= carry9 * ((uint64_t) 1L << 21); 3560 $carry9 = $s9 >> 21; 3561 $s10 += $carry9; 3562 $s9 -= $carry9 << 21; 3563 // carry10 = s10 >> 21; 3564 // s11 += carry10; 3565 // s10 -= carry10 * ((uint64_t) 1L << 21); 3566 $carry10 = $s10 >> 21; 3567 $s11 += $carry10; 3568 $s10 -= $carry10 << 21; 3569 // carry11 = s11 >> 21; 3570 // s12 += carry11; 3571 // s11 -= carry11 * ((uint64_t) 1L << 21); 3572 $carry11 = $s11 >> 21; 3573 $s12 += $carry11; 3574 $s11 -= $carry11 << 21; 3575 3576 // s0 += s12 * 666643; 3577 // s1 += s12 * 470296; 3578 // s2 += s12 * 654183; 3579 // s3 -= s12 * 997805; 3580 // s4 += s12 * 136657; 3581 // s5 -= s12 * 683901; 3582 $s0 += self::mul($s12, 666643, 20); 3583 $s1 += self::mul($s12, 470296, 19); 3584 $s2 += self::mul($s12, 654183, 20); 3585 $s3 -= self::mul($s12, 997805, 20); 3586 $s4 += self::mul($s12, 136657, 18); 3587 $s5 -= self::mul($s12, 683901, 20); 3588 3589 // carry0 = s0 >> 21; 3590 // s1 += carry0; 3591 // s0 -= carry0 * ((uint64_t) 1L << 21); 3592 $carry0 = $s0 >> 21; 3593 $s1 += $carry0; 3594 $s0 -= $carry0 << 21; 3595 // carry1 = s1 >> 21; 3596 // s2 += carry1; 3597 // s1 -= carry1 * ((uint64_t) 1L << 21); 3598 $carry1 = $s1 >> 21; 3599 $s2 += $carry1; 3600 $s1 -= $carry1 << 21; 3601 // carry2 = s2 >> 21; 3602 // s3 += carry2; 3603 // s2 -= carry2 * ((uint64_t) 1L << 21); 3604 $carry2 = $s2 >> 21; 3605 $s3 += $carry2; 3606 $s2 -= $carry2 << 21; 3607 // carry3 = s3 >> 21; 3608 // s4 += carry3; 3609 // s3 -= carry3 * ((uint64_t) 1L << 21); 3610 $carry3 = $s3 >> 21; 3611 $s4 += $carry3; 3612 $s3 -= $carry3 << 21; 3613 // carry4 = s4 >> 21; 3614 // s5 += carry4; 3615 // s4 -= carry4 * ((uint64_t) 1L << 21); 3616 $carry4 = $s4 >> 21; 3617 $s5 += $carry4; 3618 $s4 -= $carry4 << 21; 3619 // carry5 = s5 >> 21; 3620 // s6 += carry5; 3621 // s5 -= carry5 * ((uint64_t) 1L << 21); 3622 $carry5 = $s5 >> 21; 3623 $s6 += $carry5; 3624 $s5 -= $carry5 << 21; 3625 // carry6 = s6 >> 21; 3626 // s7 += carry6; 3627 // s6 -= carry6 * ((uint64_t) 1L << 21); 3628 $carry6 = $s6 >> 21; 3629 $s7 += $carry6; 3630 $s6 -= $carry6 << 21; 3631 // carry7 = s7 >> 21; 3632 // s8 += carry7; 3633 // s7 -= carry7 * ((uint64_t) 1L << 21); 3634 $carry7 = $s7 >> 21; 3635 $s8 += $carry7; 3636 $s7 -= $carry7 << 21; 3637 // carry8 = s8 >> 21; 3638 // s9 += carry8; 3639 // s8 -= carry8 * ((uint64_t) 1L << 21); 3640 $carry8 = $s8 >> 21; 3641 $s9 += $carry8; 3642 $s8 -= $carry8 << 21; 3643 // carry9 = s9 >> 21; 3644 // s10 += carry9; 3645 // s9 -= carry9 * ((uint64_t) 1L << 21); 3646 $carry9 = $s9 >> 21; 3647 $s10 += $carry9; 3648 $s9 -= $carry9 << 21; 3649 // carry10 = s10 >> 21; 3650 // s11 += carry10; 3651 // s10 -= carry10 * ((uint64_t) 1L << 21); 3652 $carry10 = $s10 >> 21; 3653 $s11 += $carry10; 3654 $s10 -= $carry10 << 21; 3655 3656 $s = array_fill(0, 32, 0); 3657 // s[0] = s0 >> 0; 3658 $s[0] = $s0 >> 0; 3659 // s[1] = s0 >> 8; 3660 $s[1] = $s0 >> 8; 3661 // s[2] = (s0 >> 16) | (s1 * ((uint64_t) 1 << 5)); 3662 $s[2] = ($s0 >> 16) | ($s1 << 5); 3663 // s[3] = s1 >> 3; 3664 $s[3] = $s1 >> 3; 3665 // s[4] = s1 >> 11; 3666 $s[4] = $s1 >> 11; 3667 // s[5] = (s1 >> 19) | (s2 * ((uint64_t) 1 << 2)); 3668 $s[5] = ($s1 >> 19) | ($s2 << 2); 3669 // s[6] = s2 >> 6; 3670 $s[6] = $s2 >> 6; 3671 // s[7] = (s2 >> 14) | (s3 * ((uint64_t) 1 << 7)); 3672 $s[7] = ($s2 >> 14) | ($s3 << 7); 3673 // s[8] = s3 >> 1; 3674 $s[8] = $s3 >> 1; 3675 // s[9] = s3 >> 9; 3676 $s[9] = $s3 >> 9; 3677 // s[10] = (s3 >> 17) | (s4 * ((uint64_t) 1 << 4)); 3678 $s[10] = ($s3 >> 17) | ($s4 << 4); 3679 // s[11] = s4 >> 4; 3680 $s[11] = $s4 >> 4; 3681 // s[12] = s4 >> 12; 3682 $s[12] = $s4 >> 12; 3683 // s[13] = (s4 >> 20) | (s5 * ((uint64_t) 1 << 1)); 3684 $s[13] = ($s4 >> 20) | ($s5 << 1); 3685 // s[14] = s5 >> 7; 3686 $s[14] = $s5 >> 7; 3687 // s[15] = (s5 >> 15) | (s6 * ((uint64_t) 1 << 6)); 3688 $s[15] = ($s5 >> 15) | ($s6 << 6); 3689 // s[16] = s6 >> 2; 3690 $s[16] = $s6 >> 2; 3691 // s[17] = s6 >> 10; 3692 $s[17] = $s6 >> 10; 3693 // s[18] = (s6 >> 18) | (s7 * ((uint64_t) 1 << 3)); 3694 $s[18] = ($s6 >> 18) | ($s7 << 3); 3695 // s[19] = s7 >> 5; 3696 $s[19] = $s7 >> 5; 3697 // s[20] = s7 >> 13; 3698 $s[20] = $s7 >> 13; 3699 // s[21] = s8 >> 0; 3700 $s[21] = $s8 >> 0; 3701 // s[22] = s8 >> 8; 3702 $s[22] = $s8 >> 8; 3703 // s[23] = (s8 >> 16) | (s9 * ((uint64_t) 1 << 5)); 3704 $s[23] = ($s8 >> 16) | ($s9 << 5); 3705 // s[24] = s9 >> 3; 3706 $s[24] = $s9 >> 3; 3707 // s[25] = s9 >> 11; 3708 $s[25] = $s9 >> 11; 3709 // s[26] = (s9 >> 19) | (s10 * ((uint64_t) 1 << 2)); 3710 $s[26] = ($s9 >> 19) | ($s10 << 2); 3711 // s[27] = s10 >> 6; 3712 $s[27] = $s10 >> 6; 3713 // s[28] = (s10 >> 14) | (s11 * ((uint64_t) 1 << 7)); 3714 $s[28] = ($s10 >> 14) | ($s11 << 7); 3715 // s[29] = s11 >> 1; 3716 $s[29] = $s11 >> 1; 3717 // s[30] = s11 >> 9; 3718 $s[30] = $s11 >> 9; 3719 // s[31] = s11 >> 17; 3720 $s[31] = $s11 >> 17; 3721 return self::intArrayToString($s); 3722 } 3723 3724 /** 3725 * @param string $s 3726 * @return string 3727 */ 3728 public static function sc25519_sq($s) 3729 { 3730 return self::sc25519_mul($s, $s); 3731 } 3732 3733 /** 3734 * @param string $s 3735 * @param int $n 3736 * @param string $a 3737 * @return string 3738 */ 3739 public static function sc25519_sqmul($s, $n, $a) 3740 { 3741 for ($i = 0; $i < $n; ++$i) { 3742 $s = self::sc25519_sq($s); 3743 } 3744 return self::sc25519_mul($s, $a); 3745 } 3746 3747 /** 3748 * @param string $s 3749 * @return string 3750 */ 3751 public static function sc25519_invert($s) 3752 { 3753 $_10 = self::sc25519_sq($s); 3754 $_11 = self::sc25519_mul($s, $_10); 3755 $_100 = self::sc25519_mul($s, $_11); 3756 $_1000 = self::sc25519_sq($_100); 3757 $_1010 = self::sc25519_mul($_10, $_1000); 3758 $_1011 = self::sc25519_mul($s, $_1010); 3759 $_10000 = self::sc25519_sq($_1000); 3760 $_10110 = self::sc25519_sq($_1011); 3761 $_100000 = self::sc25519_mul($_1010, $_10110); 3762 $_100110 = self::sc25519_mul($_10000, $_10110); 3763 $_1000000 = self::sc25519_sq($_100000); 3764 $_1010000 = self::sc25519_mul($_10000, $_1000000); 3765 $_1010011 = self::sc25519_mul($_11, $_1010000); 3766 $_1100011 = self::sc25519_mul($_10000, $_1010011); 3767 $_1100111 = self::sc25519_mul($_100, $_1100011); 3768 $_1101011 = self::sc25519_mul($_100, $_1100111); 3769 $_10010011 = self::sc25519_mul($_1000000, $_1010011); 3770 $_10010111 = self::sc25519_mul($_100, $_10010011); 3771 $_10111101 = self::sc25519_mul($_100110, $_10010111); 3772 $_11010011 = self::sc25519_mul($_10110, $_10111101); 3773 $_11100111 = self::sc25519_mul($_1010000, $_10010111); 3774 $_11101011 = self::sc25519_mul($_100, $_11100111); 3775 $_11110101 = self::sc25519_mul($_1010, $_11101011); 3776 3777 $recip = self::sc25519_mul($_1011, $_11110101); 3778 $recip = self::sc25519_sqmul($recip, 126, $_1010011); 3779 $recip = self::sc25519_sqmul($recip, 9, $_10); 3780 $recip = self::sc25519_mul($recip, $_11110101); 3781 $recip = self::sc25519_sqmul($recip, 7, $_1100111); 3782 $recip = self::sc25519_sqmul($recip, 9, $_11110101); 3783 $recip = self::sc25519_sqmul($recip, 11, $_10111101); 3784 $recip = self::sc25519_sqmul($recip, 8, $_11100111); 3785 $recip = self::sc25519_sqmul($recip, 9, $_1101011); 3786 $recip = self::sc25519_sqmul($recip, 6, $_1011); 3787 $recip = self::sc25519_sqmul($recip, 14, $_10010011); 3788 $recip = self::sc25519_sqmul($recip, 10, $_1100011); 3789 $recip = self::sc25519_sqmul($recip, 9, $_10010111); 3790 $recip = self::sc25519_sqmul($recip, 10, $_11110101); 3791 $recip = self::sc25519_sqmul($recip, 8, $_11010011); 3792 return self::sc25519_sqmul($recip, 8, $_11101011); 3793 } 3794 3795 /** 3796 * @param string $s 3797 * @return string 3798 */ 3799 public static function clamp($s) 3800 { 3801 $s_ = self::stringToIntArray($s); 3802 $s_[0] &= 248; 3803 $s_[31] |= 64; 3804 $s_[31] &= 127; 3805 return self::intArrayToString($s_); 3806 } 3807 3808 /** 3809 * Ensure limbs are less than 28 bits long to prevent float promotion. 3810 * 3811 * This uses a constant-time conditional swap under the hood. 3812 * 3813 * @param ParagonIE_Sodium_Core_Curve25519_Fe $f 3814 * @return ParagonIE_Sodium_Core_Curve25519_Fe 3815 */ 3816 public static function fe_normalize(ParagonIE_Sodium_Core_Curve25519_Fe $f) 3817 { 3818 $x = (PHP_INT_SIZE << 3) - 1; // 31 or 63 3819 3820 $g = self::fe_copy($f); 3821 $e = array( 3822 $g->e0, $g->e1, $g->e2, $g->e3, $g->e4, 3823 $g->e5, $g->e6, $g->e7, $g->e8, $g->e9 3824 ); 3825 for ($i = 0; $i < 10; ++$i) { 3826 $mask = -(($e[$i] >> $x) & 1); 3827 3828 /* 3829 * Get two candidate normalized values for $e[$i], depending on the sign of $e[$i]: 3830 */ 3831 $a = $e[$i] & 0x7ffffff; 3832 $b = -((-$e[$i]) & 0x7ffffff); 3833 3834 /* 3835 * Return the appropriate candidate value, based on the sign of the original input: 3836 * 3837 * The following is equivalent to this ternary: 3838 * 3839 * $e[$i] = (($e[$i] >> $x) & 1) ? $a : $b; 3840 * 3841 * Except what's written doesn't contain timing leaks. 3842 */ 3843 $e[$i] = ($a ^ (($a ^ $b) & $mask)); 3844 } 3845 $g->e0 = $e[0]; 3846 $g->e1 = $e[1]; 3847 $g->e2 = $e[2]; 3848 $g->e3 = $e[3]; 3849 $g->e4 = $e[4]; 3850 $g->e5 = $e[5]; 3851 $g->e6 = $e[6]; 3852 $g->e7 = $e[7]; 3853 $g->e8 = $e[8]; 3854 $g->e9 = $e[9]; 3855 return $g; 3856 } 3857 }
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| Generated : Mon Oct 20 08:20:05 2025 | Cross-referenced by PHPXref |