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1 <?php 2 3 /** 4 * Generic EC Key Parsing Helper functions 5 * 6 * PHP version 5 7 * 8 * @category Crypt 9 * @package EC 10 * @author Jim Wigginton <[email protected]> 11 * @copyright 2015 Jim Wigginton 12 * @license http://www.opensource.org/licenses/mit-license.html MIT License 13 * @link http://phpseclib.sourceforge.net 14 */ 15 16 namespace phpseclib3\Crypt\EC\Formats\Keys; 17 18 use ParagonIE\ConstantTime\Hex; 19 use phpseclib3\Common\Functions\Strings; 20 use phpseclib3\Crypt\EC\BaseCurves\Base as BaseCurve; 21 use phpseclib3\Crypt\EC\BaseCurves\Binary as BinaryCurve; 22 use phpseclib3\Crypt\EC\BaseCurves\Prime as PrimeCurve; 23 use phpseclib3\Crypt\EC\BaseCurves\TwistedEdwards as TwistedEdwardsCurve; 24 use phpseclib3\Exception\UnsupportedCurveException; 25 use phpseclib3\File\ASN1; 26 use phpseclib3\File\ASN1\Maps; 27 use phpseclib3\Math\BigInteger; 28 29 /** 30 * Generic EC Key Parsing Helper functions 31 * 32 * @package EC 33 * @author Jim Wigginton <[email protected]> 34 * @access public 35 */ 36 trait Common 37 { 38 /** 39 * Curve OIDs 40 * 41 * @var array 42 */ 43 private static $curveOIDs = []; 44 45 /** 46 * Child OIDs loaded 47 * 48 * @var bool 49 */ 50 protected static $childOIDsLoaded = false; 51 52 /** 53 * Use Named Curves 54 * 55 * @var bool 56 */ 57 private static $useNamedCurves = true; 58 59 /** 60 * Initialize static variables 61 */ 62 private static function initialize_static_variables() 63 { 64 if (empty(self::$curveOIDs)) { 65 // the sec* curves are from the standards for efficient cryptography group 66 // sect* curves are curves over binary finite fields 67 // secp* curves are curves over prime finite fields 68 // sec*r* curves are regular curves; sec*k* curves are koblitz curves 69 // brainpool*r* curves are regular prime finite field curves 70 // brainpool*t* curves are twisted versions of the brainpool*r* curves 71 self::$curveOIDs = [ 72 'prime192v1' => '1.2.840.10045.3.1.1', // J.5.1, example 1 (aka secp192r1) 73 'prime192v2' => '1.2.840.10045.3.1.2', // J.5.1, example 2 74 'prime192v3' => '1.2.840.10045.3.1.3', // J.5.1, example 3 75 'prime239v1' => '1.2.840.10045.3.1.4', // J.5.2, example 1 76 'prime239v2' => '1.2.840.10045.3.1.5', // J.5.2, example 2 77 'prime239v3' => '1.2.840.10045.3.1.6', // J.5.2, example 3 78 'prime256v1' => '1.2.840.10045.3.1.7', // J.5.3, example 1 (aka secp256r1) 79 80 // https://tools.ietf.org/html/rfc5656#section-10 81 'nistp256' => '1.2.840.10045.3.1.7', // aka secp256r1 82 'nistp384' => '1.3.132.0.34', // aka secp384r1 83 'nistp521' => '1.3.132.0.35', // aka secp521r1 84 85 'nistk163' => '1.3.132.0.1', // aka sect163k1 86 'nistp192' => '1.2.840.10045.3.1.1', // aka secp192r1 87 'nistp224' => '1.3.132.0.33', // aka secp224r1 88 'nistk233' => '1.3.132.0.26', // aka sect233k1 89 'nistb233' => '1.3.132.0.27', // aka sect233r1 90 'nistk283' => '1.3.132.0.16', // aka sect283k1 91 'nistk409' => '1.3.132.0.36', // aka sect409k1 92 'nistb409' => '1.3.132.0.37', // aka sect409r1 93 'nistt571' => '1.3.132.0.38', // aka sect571k1 94 95 // from https://tools.ietf.org/html/rfc5915 96 'secp192r1' => '1.2.840.10045.3.1.1', // aka prime192v1 97 'sect163k1' => '1.3.132.0.1', 98 'sect163r2' => '1.3.132.0.15', 99 'secp224r1' => '1.3.132.0.33', 100 'sect233k1' => '1.3.132.0.26', 101 'sect233r1' => '1.3.132.0.27', 102 'secp256r1' => '1.2.840.10045.3.1.7', // aka prime256v1 103 'sect283k1' => '1.3.132.0.16', 104 'sect283r1' => '1.3.132.0.17', 105 'secp384r1' => '1.3.132.0.34', 106 'sect409k1' => '1.3.132.0.36', 107 'sect409r1' => '1.3.132.0.37', 108 'secp521r1' => '1.3.132.0.35', 109 'sect571k1' => '1.3.132.0.38', 110 'sect571r1' => '1.3.132.0.39', 111 // from http://www.secg.org/SEC2-Ver-1.0.pdf 112 'secp112r1' => '1.3.132.0.6', 113 'secp112r2' => '1.3.132.0.7', 114 'secp128r1' => '1.3.132.0.28', 115 'secp128r2' => '1.3.132.0.29', 116 'secp160k1' => '1.3.132.0.9', 117 'secp160r1' => '1.3.132.0.8', 118 'secp160r2' => '1.3.132.0.30', 119 'secp192k1' => '1.3.132.0.31', 120 'secp224k1' => '1.3.132.0.32', 121 'secp256k1' => '1.3.132.0.10', 122 123 'sect113r1' => '1.3.132.0.4', 124 'sect113r2' => '1.3.132.0.5', 125 'sect131r1' => '1.3.132.0.22', 126 'sect131r2' => '1.3.132.0.23', 127 'sect163r1' => '1.3.132.0.2', 128 'sect193r1' => '1.3.132.0.24', 129 'sect193r2' => '1.3.132.0.25', 130 'sect239k1' => '1.3.132.0.3', 131 132 // from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.202.2977&rep=rep1&type=pdf#page=36 133 /* 134 'c2pnb163v1' => '1.2.840.10045.3.0.1', // J.4.1, example 1 135 'c2pnb163v2' => '1.2.840.10045.3.0.2', // J.4.1, example 2 136 'c2pnb163v3' => '1.2.840.10045.3.0.3', // J.4.1, example 3 137 'c2pnb172w1' => '1.2.840.10045.3.0.4', // J.4.2, example 1 138 'c2tnb191v1' => '1.2.840.10045.3.0.5', // J.4.3, example 1 139 'c2tnb191v2' => '1.2.840.10045.3.0.6', // J.4.3, example 2 140 'c2tnb191v3' => '1.2.840.10045.3.0.7', // J.4.3, example 3 141 'c2onb191v4' => '1.2.840.10045.3.0.8', // J.4.3, example 4 142 'c2onb191v5' => '1.2.840.10045.3.0.9', // J.4.3, example 5 143 'c2pnb208w1' => '1.2.840.10045.3.0.10', // J.4.4, example 1 144 'c2tnb239v1' => '1.2.840.10045.3.0.11', // J.4.5, example 1 145 'c2tnb239v2' => '1.2.840.10045.3.0.12', // J.4.5, example 2 146 'c2tnb239v3' => '1.2.840.10045.3.0.13', // J.4.5, example 3 147 'c2onb239v4' => '1.2.840.10045.3.0.14', // J.4.5, example 4 148 'c2onb239v5' => '1.2.840.10045.3.0.15', // J.4.5, example 5 149 'c2pnb272w1' => '1.2.840.10045.3.0.16', // J.4.6, example 1 150 'c2pnb304w1' => '1.2.840.10045.3.0.17', // J.4.7, example 1 151 'c2tnb359v1' => '1.2.840.10045.3.0.18', // J.4.8, example 1 152 'c2pnb368w1' => '1.2.840.10045.3.0.19', // J.4.9, example 1 153 'c2tnb431r1' => '1.2.840.10045.3.0.20', // J.4.10, example 1 154 */ 155 156 // http://www.ecc-brainpool.org/download/Domain-parameters.pdf 157 // https://tools.ietf.org/html/rfc5639 158 'brainpoolP160r1' => '1.3.36.3.3.2.8.1.1.1', 159 'brainpoolP160t1' => '1.3.36.3.3.2.8.1.1.2', 160 'brainpoolP192r1' => '1.3.36.3.3.2.8.1.1.3', 161 'brainpoolP192t1' => '1.3.36.3.3.2.8.1.1.4', 162 'brainpoolP224r1' => '1.3.36.3.3.2.8.1.1.5', 163 'brainpoolP224t1' => '1.3.36.3.3.2.8.1.1.6', 164 'brainpoolP256r1' => '1.3.36.3.3.2.8.1.1.7', 165 'brainpoolP256t1' => '1.3.36.3.3.2.8.1.1.8', 166 'brainpoolP320r1' => '1.3.36.3.3.2.8.1.1.9', 167 'brainpoolP320t1' => '1.3.36.3.3.2.8.1.1.10', 168 'brainpoolP384r1' => '1.3.36.3.3.2.8.1.1.11', 169 'brainpoolP384t1' => '1.3.36.3.3.2.8.1.1.12', 170 'brainpoolP512r1' => '1.3.36.3.3.2.8.1.1.13', 171 'brainpoolP512t1' => '1.3.36.3.3.2.8.1.1.14' 172 ]; 173 ASN1::loadOIDs([ 174 'prime-field' => '1.2.840.10045.1.1', 175 'characteristic-two-field' => '1.2.840.10045.1.2', 176 'characteristic-two-basis' => '1.2.840.10045.1.2.3', 177 // per http://www.secg.org/SEC1-Ver-1.0.pdf#page=84, gnBasis "not used here" 178 'gnBasis' => '1.2.840.10045.1.2.3.1', // NULL 179 'tpBasis' => '1.2.840.10045.1.2.3.2', // Trinomial 180 'ppBasis' => '1.2.840.10045.1.2.3.3' // Pentanomial 181 ] + self::$curveOIDs); 182 } 183 } 184 185 /** 186 * Explicitly set the curve 187 * 188 * If the key contains an implicit curve phpseclib needs the curve 189 * to be explicitly provided 190 * 191 * @param \phpseclib3\Crypt\EC\BaseCurves\Base $curve 192 */ 193 public static function setImplicitCurve(BaseCurve $curve) 194 { 195 self::$implicitCurve = $curve; 196 } 197 198 /** 199 * Returns an instance of \phpseclib3\Crypt\EC\BaseCurves\Base based 200 * on the curve parameters 201 * 202 * @param array $params 203 * @return \phpseclib3\Crypt\EC\BaseCurves\Base|false 204 */ 205 protected static function loadCurveByParam(array $params) 206 { 207 if (count($params) > 1) { 208 throw new \RuntimeException('No parameters are present'); 209 } 210 if (isset($params['namedCurve'])) { 211 $curve = '\phpseclib3\Crypt\EC\Curves\\' . $params['namedCurve']; 212 if (!class_exists($curve)) { 213 throw new UnsupportedCurveException('Named Curve of ' . $params['namedCurve'] . ' is not supported'); 214 } 215 return new $curve(); 216 } 217 if (isset($params['implicitCurve'])) { 218 if (!isset(self::$implicitCurve)) { 219 throw new \RuntimeException('Implicit curves can be provided by calling setImplicitCurve'); 220 } 221 return self::$implicitCurve; 222 } 223 if (isset($params['specifiedCurve'])) { 224 $data = $params['specifiedCurve']; 225 switch ($data['fieldID']['fieldType']) { 226 case 'prime-field': 227 $curve = new PrimeCurve(); 228 $curve->setModulo($data['fieldID']['parameters']); 229 $curve->setCoefficients( 230 new BigInteger($data['curve']['a'], 256), 231 new BigInteger($data['curve']['b'], 256) 232 ); 233 $point = self::extractPoint("\0" . $data['base'], $curve); 234 $curve->setBasePoint(...$point); 235 $curve->setOrder($data['order']); 236 return $curve; 237 case 'characteristic-two-field': 238 $curve = new BinaryCurve(); 239 $params = ASN1::decodeBER($data['fieldID']['parameters']); 240 $params = ASN1::asn1map($params[0], Maps\Characteristic_two::MAP); 241 $modulo = [(int) $params['m']->toString()]; 242 switch ($params['basis']) { 243 case 'tpBasis': 244 $modulo[] = (int) $params['parameters']->toString(); 245 break; 246 case 'ppBasis': 247 $temp = ASN1::decodeBER($params['parameters']); 248 $temp = ASN1::asn1map($temp[0], Maps\Pentanomial::MAP); 249 $modulo[] = (int) $temp['k3']->toString(); 250 $modulo[] = (int) $temp['k2']->toString(); 251 $modulo[] = (int) $temp['k1']->toString(); 252 } 253 $modulo[] = 0; 254 $curve->setModulo(...$modulo); 255 $len = ceil($modulo[0] / 8); 256 $curve->setCoefficients( 257 Hex::encode($data['curve']['a']), 258 Hex::encode($data['curve']['b']) 259 ); 260 $point = self::extractPoint("\0" . $data['base'], $curve); 261 $curve->setBasePoint(...$point); 262 $curve->setOrder($data['order']); 263 return $curve; 264 default: 265 throw new UnsupportedCurveException('Field Type of ' . $data['fieldID']['fieldType'] . ' is not supported'); 266 } 267 } 268 throw new \RuntimeException('No valid parameters are present'); 269 } 270 271 /** 272 * Extract points from a string 273 * 274 * Supports both compressed and uncompressed points 275 * 276 * @param string $str 277 * @param \phpseclib3\Crypt\EC\BaseCurves\Base $curve 278 * @return object[] 279 */ 280 public static function extractPoint($str, BaseCurve $curve) 281 { 282 if ($curve instanceof TwistedEdwardsCurve) { 283 // first step of point deciding as discussed at the following URL's: 284 // https://tools.ietf.org/html/rfc8032#section-5.1.3 285 // https://tools.ietf.org/html/rfc8032#section-5.2.3 286 $y = $str; 287 $y = strrev($y); 288 $sign = (bool) (ord($y[0]) & 0x80); 289 $y[0] = $y[0] & chr(0x7F); 290 $y = new BigInteger($y, 256); 291 if ($y->compare($curve->getModulo()) >= 0) { 292 throw new \RuntimeException('The Y coordinate should not be >= the modulo'); 293 } 294 $point = $curve->recoverX($y, $sign); 295 if (!$curve->verifyPoint($point)) { 296 throw new \RuntimeException('Unable to verify that point exists on curve'); 297 } 298 return $point; 299 } 300 301 // the first byte of a bit string represents the number of bits in the last byte that are to be ignored but, 302 // currently, bit strings wanting a non-zero amount of bits trimmed are not supported 303 if (($val = Strings::shift($str)) != "\0") { 304 throw new \UnexpectedValueException('extractPoint expects the first byte to be null - not ' . Hex::encode($val)); 305 } 306 if ($str == "\0") { 307 return []; 308 } 309 310 $keylen = strlen($str); 311 $order = $curve->getLengthInBytes(); 312 // point compression is being used 313 if ($keylen == $order + 1) { 314 return $curve->derivePoint($str); 315 } 316 317 // point compression is not being used 318 if ($keylen == 2 * $order + 1) { 319 preg_match("#(.)(.{{$order}})(.{{$order}})#s", $str, $matches); 320 list(, $w, $x, $y) = $matches; 321 if ($w != "\4") { 322 throw new \UnexpectedValueException('The first byte of an uncompressed point should be 04 - not ' . Hex::encode($val)); 323 } 324 $point = [ 325 $curve->convertInteger(new BigInteger($x, 256)), 326 $curve->convertInteger(new BigInteger($y, 256)) 327 ]; 328 329 if (!$curve->verifyPoint($point)) { 330 throw new \RuntimeException('Unable to verify that point exists on curve'); 331 } 332 333 return $point; 334 } 335 336 throw new \UnexpectedValueException('The string representation of the points is not of an appropriate length'); 337 } 338 339 /** 340 * Encode Parameters 341 * 342 * @todo Maybe at some point this could be moved to __toString() for each of the curves? 343 * @param \phpseclib3\Crypt\EC\BaseCurves\Base $curve 344 * @param bool $returnArray optional 345 * @param array $options optional 346 * @return string|false 347 */ 348 private static function encodeParameters(BaseCurve $curve, $returnArray = false, array $options = []) 349 { 350 $useNamedCurves = isset($options['namedCurve']) ? $options['namedCurve'] : self::$useNamedCurves; 351 352 $reflect = new \ReflectionClass($curve); 353 $name = $reflect->getShortName(); 354 if ($useNamedCurves) { 355 if (isset(self::$curveOIDs[$name])) { 356 if ($reflect->isFinal()) { 357 $reflect = $reflect->getParentClass(); 358 $name = $reflect->getShortName(); 359 } 360 return $returnArray ? 361 ['namedCurve' => $name] : 362 ASN1::encodeDER(['namedCurve' => $name], Maps\ECParameters::MAP); 363 } 364 foreach (new \DirectoryIterator(__DIR__ . '/../../Curves/') as $file) { 365 if ($file->getExtension() != 'php') { 366 continue; 367 } 368 $testName = $file->getBasename('.php'); 369 $class = 'phpseclib3\Crypt\EC\Curves\\' . $testName; 370 $reflect = new \ReflectionClass($class); 371 if ($reflect->isFinal()) { 372 continue; 373 } 374 $candidate = new $class(); 375 switch ($name) { 376 case 'Prime': 377 if (!$candidate instanceof PrimeCurve) { 378 break; 379 } 380 if (!$candidate->getModulo()->equals($curve->getModulo())) { 381 break; 382 } 383 if ($candidate->getA()->toBytes() != $curve->getA()->toBytes()) { 384 break; 385 } 386 if ($candidate->getB()->toBytes() != $curve->getB()->toBytes()) { 387 break; 388 } 389 390 list($candidateX, $candidateY) = $candidate->getBasePoint(); 391 list($curveX, $curveY) = $curve->getBasePoint(); 392 if ($candidateX->toBytes() != $curveX->toBytes()) { 393 break; 394 } 395 if ($candidateY->toBytes() != $curveY->toBytes()) { 396 break; 397 } 398 399 return $returnArray ? 400 ['namedCurve' => $testName] : 401 ASN1::encodeDER(['namedCurve' => $testName], Maps\ECParameters::MAP); 402 case 'Binary': 403 if (!$candidate instanceof BinaryCurve) { 404 break; 405 } 406 if ($candidate->getModulo() != $curve->getModulo()) { 407 break; 408 } 409 if ($candidate->getA()->toBytes() != $curve->getA()->toBytes()) { 410 break; 411 } 412 if ($candidate->getB()->toBytes() != $curve->getB()->toBytes()) { 413 break; 414 } 415 416 list($candidateX, $candidateY) = $candidate->getBasePoint(); 417 list($curveX, $curveY) = $curve->getBasePoint(); 418 if ($candidateX->toBytes() != $curveX->toBytes()) { 419 break; 420 } 421 if ($candidateY->toBytes() != $curveY->toBytes()) { 422 break; 423 } 424 425 return $returnArray ? 426 ['namedCurve' => $testName] : 427 ASN1::encodeDER(['namedCurve' => $testName], Maps\ECParameters::MAP); 428 } 429 } 430 } 431 432 $order = $curve->getOrder(); 433 // we could try to calculate the order thusly: 434 // https://crypto.stackexchange.com/a/27914/4520 435 // https://en.wikipedia.org/wiki/Schoof%E2%80%93Elkies%E2%80%93Atkin_algorithm 436 if (!$order) { 437 throw new \RuntimeException('Specified Curves need the order to be specified'); 438 } 439 $point = $curve->getBasePoint(); 440 $x = $point[0]->toBytes(); 441 $y = $point[1]->toBytes(); 442 443 if ($curve instanceof PrimeCurve) { 444 /* 445 * valid versions are: 446 * 447 * ecdpVer1: 448 * - neither the curve or the base point are generated verifiably randomly. 449 * ecdpVer2: 450 * - curve and base point are generated verifiably at random and curve.seed is present 451 * ecdpVer3: 452 * - base point is generated verifiably at random but curve is not. curve.seed is present 453 */ 454 // other (optional) parameters can be calculated using the methods discused at 455 // https://crypto.stackexchange.com/q/28947/4520 456 $data = [ 457 'version' => 'ecdpVer1', 458 'fieldID' => [ 459 'fieldType' => 'prime-field', 460 'parameters' => $curve->getModulo() 461 ], 462 'curve' => [ 463 'a' => $curve->getA()->toBytes(), 464 'b' => $curve->getB()->toBytes() 465 ], 466 'base' => "\4" . $x . $y, 467 'order' => $order 468 ]; 469 470 return $returnArray ? 471 ['specifiedCurve' => $data] : 472 ASN1::encodeDER(['specifiedCurve' => $data], Maps\ECParameters::MAP); 473 } 474 if ($curve instanceof BinaryCurve) { 475 $modulo = $curve->getModulo(); 476 $basis = count($modulo); 477 $m = array_shift($modulo); 478 array_pop($modulo); // the last parameter should always be 0 479 //rsort($modulo); 480 switch ($basis) { 481 case 3: 482 $basis = 'tpBasis'; 483 $modulo = new BigInteger($modulo[0]); 484 break; 485 case 5: 486 $basis = 'ppBasis'; 487 // these should be in strictly ascending order (hence the commented out rsort above) 488 $modulo = [ 489 'k1' => new BigInteger($modulo[2]), 490 'k2' => new BigInteger($modulo[1]), 491 'k3' => new BigInteger($modulo[0]) 492 ]; 493 $modulo = ASN1::encodeDER($modulo, Maps\Pentanomial::MAP); 494 $modulo = new ASN1\Element($modulo); 495 } 496 $params = ASN1::encodeDER([ 497 'm' => new BigInteger($m), 498 'basis' => $basis, 499 'parameters' => $modulo 500 ], Maps\Characteristic_two::MAP); 501 $params = new ASN1\Element($params); 502 $a = ltrim($curve->getA()->toBytes(), "\0"); 503 if (!strlen($a)) { 504 $a = "\0"; 505 } 506 $b = ltrim($curve->getB()->toBytes(), "\0"); 507 if (!strlen($b)) { 508 $b = "\0"; 509 } 510 $data = [ 511 'version' => 'ecdpVer1', 512 'fieldID' => [ 513 'fieldType' => 'characteristic-two-field', 514 'parameters' => $params 515 ], 516 'curve' => [ 517 'a' => $a, 518 'b' => $b 519 ], 520 'base' => "\4" . $x . $y, 521 'order' => $order 522 ]; 523 524 return $returnArray ? 525 ['specifiedCurve' => $data] : 526 ASN1::encodeDER(['specifiedCurve' => $data], Maps\ECParameters::MAP); 527 } 528 529 throw new UnsupportedCurveException('Curve cannot be serialized'); 530 } 531 532 /** 533 * Use Specified Curve 534 * 535 * A specified curve has all the coefficients, the base points, etc, explicitely included. 536 * A specified curve is a more verbose way of representing a curve 537 */ 538 public static function useSpecifiedCurve() 539 { 540 self::$useNamedCurves = false; 541 } 542 543 /** 544 * Use Named Curve 545 * 546 * A named curve does not include any parameters. It is up to the EC parameters to 547 * know what the coefficients, the base points, etc, are from the name of the curve. 548 * A named curve is a more concise way of representing a curve 549 */ 550 public static function useNamedCurve() 551 { 552 self::$useNamedCurves = true; 553 } 554 }
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