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<?php /** * Generic EC Key Parsing Helper functions * * PHP version 5 * * @author Jim Wigginton <terrafrost@php.net> * @copyright 2015 Jim Wigginton * @license http://www.opensource.org/licenses/mit-license.html MIT License * @link http://phpseclib.sourceforge.net */ namespace phpseclib3\Crypt\EC\Formats\Keys; use phpseclib3\Common\Functions\Strings; use phpseclib3\Crypt\EC\BaseCurves\Base as BaseCurve; use phpseclib3\Crypt\EC\BaseCurves\Binary as BinaryCurve; use phpseclib3\Crypt\EC\BaseCurves\Prime as PrimeCurve; use phpseclib3\Crypt\EC\BaseCurves\TwistedEdwards as TwistedEdwardsCurve; use phpseclib3\Exception\UnsupportedCurveException; use phpseclib3\File\ASN1; use phpseclib3\File\ASN1\Maps; use phpseclib3\Math\BigInteger; /** * Generic EC Key Parsing Helper functions * * @author Jim Wigginton <terrafrost@php.net> */ trait Common { /** * Curve OIDs * * @var array */ private static $curveOIDs = []; /** * Child OIDs loaded * * @var bool */ protected static $childOIDsLoaded = false; /** * Use Named Curves * * @var bool */ private static $useNamedCurves = true; /** * Initialize static variables */ private static function initialize_static_variables() { if (empty(self::$curveOIDs)) { // the sec* curves are from the standards for efficient cryptography group // sect* curves are curves over binary finite fields // secp* curves are curves over prime finite fields // sec*r* curves are regular curves; sec*k* curves are koblitz curves // brainpool*r* curves are regular prime finite field curves // brainpool*t* curves are twisted versions of the brainpool*r* curves self::$curveOIDs = [ 'prime192v1' => '1.2.840.10045.3.1.1', // J.5.1, example 1 (aka secp192r1) 'prime192v2' => '1.2.840.10045.3.1.2', // J.5.1, example 2 'prime192v3' => '1.2.840.10045.3.1.3', // J.5.1, example 3 'prime239v1' => '1.2.840.10045.3.1.4', // J.5.2, example 1 'prime239v2' => '1.2.840.10045.3.1.5', // J.5.2, example 2 'prime239v3' => '1.2.840.10045.3.1.6', // J.5.2, example 3 'prime256v1' => '1.2.840.10045.3.1.7', // J.5.3, example 1 (aka secp256r1) // https://tools.ietf.org/html/rfc5656#section-10 'nistp256' => '1.2.840.10045.3.1.7', // aka secp256r1 'nistp384' => '1.3.132.0.34', // aka secp384r1 'nistp521' => '1.3.132.0.35', // aka secp521r1 'nistk163' => '1.3.132.0.1', // aka sect163k1 'nistp192' => '1.2.840.10045.3.1.1', // aka secp192r1 'nistp224' => '1.3.132.0.33', // aka secp224r1 'nistk233' => '1.3.132.0.26', // aka sect233k1 'nistb233' => '1.3.132.0.27', // aka sect233r1 'nistk283' => '1.3.132.0.16', // aka sect283k1 'nistk409' => '1.3.132.0.36', // aka sect409k1 'nistb409' => '1.3.132.0.37', // aka sect409r1 'nistt571' => '1.3.132.0.38', // aka sect571k1 // from https://tools.ietf.org/html/rfc5915 'secp192r1' => '1.2.840.10045.3.1.1', // aka prime192v1 'sect163k1' => '1.3.132.0.1', 'sect163r2' => '1.3.132.0.15', 'secp224r1' => '1.3.132.0.33', 'sect233k1' => '1.3.132.0.26', 'sect233r1' => '1.3.132.0.27', 'secp256r1' => '1.2.840.10045.3.1.7', // aka prime256v1 'sect283k1' => '1.3.132.0.16', 'sect283r1' => '1.3.132.0.17', 'secp384r1' => '1.3.132.0.34', 'sect409k1' => '1.3.132.0.36', 'sect409r1' => '1.3.132.0.37', 'secp521r1' => '1.3.132.0.35', 'sect571k1' => '1.3.132.0.38', 'sect571r1' => '1.3.132.0.39', // from http://www.secg.org/SEC2-Ver-1.0.pdf 'secp112r1' => '1.3.132.0.6', 'secp112r2' => '1.3.132.0.7', 'secp128r1' => '1.3.132.0.28', 'secp128r2' => '1.3.132.0.29', 'secp160k1' => '1.3.132.0.9', 'secp160r1' => '1.3.132.0.8', 'secp160r2' => '1.3.132.0.30', 'secp192k1' => '1.3.132.0.31', 'secp224k1' => '1.3.132.0.32', 'secp256k1' => '1.3.132.0.10', 'sect113r1' => '1.3.132.0.4', 'sect113r2' => '1.3.132.0.5', 'sect131r1' => '1.3.132.0.22', 'sect131r2' => '1.3.132.0.23', 'sect163r1' => '1.3.132.0.2', 'sect193r1' => '1.3.132.0.24', 'sect193r2' => '1.3.132.0.25', 'sect239k1' => '1.3.132.0.3', // from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.202.2977&rep=rep1&type=pdf#page=36 /* 'c2pnb163v1' => '1.2.840.10045.3.0.1', // J.4.1, example 1 'c2pnb163v2' => '1.2.840.10045.3.0.2', // J.4.1, example 2 'c2pnb163v3' => '1.2.840.10045.3.0.3', // J.4.1, example 3 'c2pnb172w1' => '1.2.840.10045.3.0.4', // J.4.2, example 1 'c2tnb191v1' => '1.2.840.10045.3.0.5', // J.4.3, example 1 'c2tnb191v2' => '1.2.840.10045.3.0.6', // J.4.3, example 2 'c2tnb191v3' => '1.2.840.10045.3.0.7', // J.4.3, example 3 'c2onb191v4' => '1.2.840.10045.3.0.8', // J.4.3, example 4 'c2onb191v5' => '1.2.840.10045.3.0.9', // J.4.3, example 5 'c2pnb208w1' => '1.2.840.10045.3.0.10', // J.4.4, example 1 'c2tnb239v1' => '1.2.840.10045.3.0.11', // J.4.5, example 1 'c2tnb239v2' => '1.2.840.10045.3.0.12', // J.4.5, example 2 'c2tnb239v3' => '1.2.840.10045.3.0.13', // J.4.5, example 3 'c2onb239v4' => '1.2.840.10045.3.0.14', // J.4.5, example 4 'c2onb239v5' => '1.2.840.10045.3.0.15', // J.4.5, example 5 'c2pnb272w1' => '1.2.840.10045.3.0.16', // J.4.6, example 1 'c2pnb304w1' => '1.2.840.10045.3.0.17', // J.4.7, example 1 'c2tnb359v1' => '1.2.840.10045.3.0.18', // J.4.8, example 1 'c2pnb368w1' => '1.2.840.10045.3.0.19', // J.4.9, example 1 'c2tnb431r1' => '1.2.840.10045.3.0.20', // J.4.10, example 1 */ // http://www.ecc-brainpool.org/download/Domain-parameters.pdf // https://tools.ietf.org/html/rfc5639 'brainpoolP160r1' => '1.3.36.3.3.2.8.1.1.1', 'brainpoolP160t1' => '1.3.36.3.3.2.8.1.1.2', 'brainpoolP192r1' => '1.3.36.3.3.2.8.1.1.3', 'brainpoolP192t1' => '1.3.36.3.3.2.8.1.1.4', 'brainpoolP224r1' => '1.3.36.3.3.2.8.1.1.5', 'brainpoolP224t1' => '1.3.36.3.3.2.8.1.1.6', 'brainpoolP256r1' => '1.3.36.3.3.2.8.1.1.7', 'brainpoolP256t1' => '1.3.36.3.3.2.8.1.1.8', 'brainpoolP320r1' => '1.3.36.3.3.2.8.1.1.9', 'brainpoolP320t1' => '1.3.36.3.3.2.8.1.1.10', 'brainpoolP384r1' => '1.3.36.3.3.2.8.1.1.11', 'brainpoolP384t1' => '1.3.36.3.3.2.8.1.1.12', 'brainpoolP512r1' => '1.3.36.3.3.2.8.1.1.13', 'brainpoolP512t1' => '1.3.36.3.3.2.8.1.1.14' ]; ASN1::loadOIDs([ 'prime-field' => '1.2.840.10045.1.1', 'characteristic-two-field' => '1.2.840.10045.1.2', 'characteristic-two-basis' => '1.2.840.10045.1.2.3', // per http://www.secg.org/SEC1-Ver-1.0.pdf#page=84, gnBasis "not used here" 'gnBasis' => '1.2.840.10045.1.2.3.1', // NULL 'tpBasis' => '1.2.840.10045.1.2.3.2', // Trinomial 'ppBasis' => '1.2.840.10045.1.2.3.3' // Pentanomial ] + self::$curveOIDs); } } /** * Explicitly set the curve * * If the key contains an implicit curve phpseclib needs the curve * to be explicitly provided * * @param \phpseclib3\Crypt\EC\BaseCurves\Base $curve */ public static function setImplicitCurve(BaseCurve $curve) { self::$implicitCurve = $curve; } /** * Returns an instance of \phpseclib3\Crypt\EC\BaseCurves\Base based * on the curve parameters * * @param array $params * @return \phpseclib3\Crypt\EC\BaseCurves\Base|false */ protected static function loadCurveByParam(array $params) { if (count($params) > 1) { throw new \RuntimeException('No parameters are present'); } if (isset($params['namedCurve'])) { $curve = '\phpseclib3\Crypt\EC\Curves\\' . $params['namedCurve']; if (!class_exists($curve)) { throw new UnsupportedCurveException('Named Curve of ' . $params['namedCurve'] . ' is not supported'); } return new $curve(); } if (isset($params['implicitCurve'])) { if (!isset(self::$implicitCurve)) { throw new \RuntimeException('Implicit curves can be provided by calling setImplicitCurve'); } return self::$implicitCurve; } if (isset($params['specifiedCurve'])) { $data = $params['specifiedCurve']; switch ($data['fieldID']['fieldType']) { case 'prime-field': $curve = new PrimeCurve(); $curve->setModulo($data['fieldID']['parameters']); $curve->setCoefficients( new BigInteger($data['curve']['a'], 256), new BigInteger($data['curve']['b'], 256) ); $point = self::extractPoint("\0" . $data['base'], $curve); $curve->setBasePoint(...$point); $curve->setOrder($data['order']); return $curve; case 'characteristic-two-field': $curve = new BinaryCurve(); $params = ASN1::decodeBER($data['fieldID']['parameters']); $params = ASN1::asn1map($params[0], Maps\Characteristic_two::MAP); $modulo = [(int) $params['m']->toString()]; switch ($params['basis']) { case 'tpBasis': $modulo[] = (int) $params['parameters']->toString(); break; case 'ppBasis': $temp = ASN1::decodeBER($params['parameters']); $temp = ASN1::asn1map($temp[0], Maps\Pentanomial::MAP); $modulo[] = (int) $temp['k3']->toString(); $modulo[] = (int) $temp['k2']->toString(); $modulo[] = (int) $temp['k1']->toString(); } $modulo[] = 0; $curve->setModulo(...$modulo); $len = ceil($modulo[0] / 8); $curve->setCoefficients( Strings::bin2hex($data['curve']['a']), Strings::bin2hex($data['curve']['b']) ); $point = self::extractPoint("\0" . $data['base'], $curve); $curve->setBasePoint(...$point); $curve->setOrder($data['order']); return $curve; default: throw new UnsupportedCurveException('Field Type of ' . $data['fieldID']['fieldType'] . ' is not supported'); } } throw new \RuntimeException('No valid parameters are present'); } /** * Extract points from a string * * Supports both compressed and uncompressed points * * @param string $str * @param \phpseclib3\Crypt\EC\BaseCurves\Base $curve * @return object[] */ public static function extractPoint($str, BaseCurve $curve) { if ($curve instanceof TwistedEdwardsCurve) { // first step of point deciding as discussed at the following URL's: // https://tools.ietf.org/html/rfc8032#section-5.1.3 // https://tools.ietf.org/html/rfc8032#section-5.2.3 $y = $str; $y = strrev($y); $sign = (bool) (ord($y[0]) & 0x80); $y[0] = $y[0] & chr(0x7F); $y = new BigInteger($y, 256); if ($y->compare($curve->getModulo()) >= 0) { throw new \RuntimeException('The Y coordinate should not be >= the modulo'); } $point = $curve->recoverX($y, $sign); if (!$curve->verifyPoint($point)) { throw new \RuntimeException('Unable to verify that point exists on curve'); } return $point; } // the first byte of a bit string represents the number of bits in the last byte that are to be ignored but, // currently, bit strings wanting a non-zero amount of bits trimmed are not supported if (($val = Strings::shift($str)) != "\0") { throw new \UnexpectedValueException('extractPoint expects the first byte to be null - not ' . Strings::bin2hex($val)); } if ($str == "\0") { return []; } $keylen = strlen($str); $order = $curve->getLengthInBytes(); // point compression is being used if ($keylen == $order + 1) { return $curve->derivePoint($str); } // point compression is not being used if ($keylen == 2 * $order + 1) { preg_match("#(.)(.{{$order}})(.{{$order}})#s", $str, $matches); list(, $w, $x, $y) = $matches; if ($w != "\4") { throw new \UnexpectedValueException('The first byte of an uncompressed point should be 04 - not ' . Strings::bin2hex($val)); } $point = [ $curve->convertInteger(new BigInteger($x, 256)), $curve->convertInteger(new BigInteger($y, 256)) ]; if (!$curve->verifyPoint($point)) { throw new \RuntimeException('Unable to verify that point exists on curve'); } return $point; } throw new \UnexpectedValueException('The string representation of the points is not of an appropriate length'); } /** * Encode Parameters * * @todo Maybe at some point this could be moved to __toString() for each of the curves? * @param \phpseclib3\Crypt\EC\BaseCurves\Base $curve * @param bool $returnArray optional * @param array $options optional * @return string|false */ private static function encodeParameters(BaseCurve $curve, $returnArray = false, array $options = []) { $useNamedCurves = isset($options['namedCurve']) ? $options['namedCurve'] : self::$useNamedCurves; $reflect = new \ReflectionClass($curve); $name = $reflect->getShortName(); if ($useNamedCurves) { if (isset(self::$curveOIDs[$name])) { if ($reflect->isFinal()) { $reflect = $reflect->getParentClass(); $name = $reflect->getShortName(); } return $returnArray ? ['namedCurve' => $name] : ASN1::encodeDER(['namedCurve' => $name], Maps\ECParameters::MAP); } foreach (new \DirectoryIterator(__DIR__ . '/../../Curves/') as $file) { if ($file->getExtension() != 'php') { continue; } $testName = $file->getBasename('.php'); $class = 'phpseclib3\Crypt\EC\Curves\\' . $testName; $reflect = new \ReflectionClass($class); if ($reflect->isFinal()) { continue; } $candidate = new $class(); switch ($name) { case 'Prime': if (!$candidate instanceof PrimeCurve) { break; } if (!$candidate->getModulo()->equals($curve->getModulo())) { break; } if ($candidate->getA()->toBytes() != $curve->getA()->toBytes()) { break; } if ($candidate->getB()->toBytes() != $curve->getB()->toBytes()) { break; } list($candidateX, $candidateY) = $candidate->getBasePoint(); list($curveX, $curveY) = $curve->getBasePoint(); if ($candidateX->toBytes() != $curveX->toBytes()) { break; } if ($candidateY->toBytes() != $curveY->toBytes()) { break; } return $returnArray ? ['namedCurve' => $testName] : ASN1::encodeDER(['namedCurve' => $testName], Maps\ECParameters::MAP); case 'Binary': if (!$candidate instanceof BinaryCurve) { break; } if ($candidate->getModulo() != $curve->getModulo()) { break; } if ($candidate->getA()->toBytes() != $curve->getA()->toBytes()) { break; } if ($candidate->getB()->toBytes() != $curve->getB()->toBytes()) { break; } list($candidateX, $candidateY) = $candidate->getBasePoint(); list($curveX, $curveY) = $curve->getBasePoint(); if ($candidateX->toBytes() != $curveX->toBytes()) { break; } if ($candidateY->toBytes() != $curveY->toBytes()) { break; } return $returnArray ? ['namedCurve' => $testName] : ASN1::encodeDER(['namedCurve' => $testName], Maps\ECParameters::MAP); } } } $order = $curve->getOrder(); // we could try to calculate the order thusly: // https://crypto.stackexchange.com/a/27914/4520 // https://en.wikipedia.org/wiki/Schoof%E2%80%93Elkies%E2%80%93Atkin_algorithm if (!$order) { throw new \RuntimeException('Specified Curves need the order to be specified'); } $point = $curve->getBasePoint(); $x = $point[0]->toBytes(); $y = $point[1]->toBytes(); if ($curve instanceof PrimeCurve) { /* * valid versions are: * * ecdpVer1: * - neither the curve or the base point are generated verifiably randomly. * ecdpVer2: * - curve and base point are generated verifiably at random and curve.seed is present * ecdpVer3: * - base point is generated verifiably at random but curve is not. curve.seed is present */ // other (optional) parameters can be calculated using the methods discused at // https://crypto.stackexchange.com/q/28947/4520 $data = [ 'version' => 'ecdpVer1', 'fieldID' => [ 'fieldType' => 'prime-field', 'parameters' => $curve->getModulo() ], 'curve' => [ 'a' => $curve->getA()->toBytes(), 'b' => $curve->getB()->toBytes() ], 'base' => "\4" . $x . $y, 'order' => $order ]; return $returnArray ? ['specifiedCurve' => $data] : ASN1::encodeDER(['specifiedCurve' => $data], Maps\ECParameters::MAP); } if ($curve instanceof BinaryCurve) { $modulo = $curve->getModulo(); $basis = count($modulo); $m = array_shift($modulo); array_pop($modulo); // the last parameter should always be 0 //rsort($modulo); switch ($basis) { case 3: $basis = 'tpBasis'; $modulo = new BigInteger($modulo[0]); break; case 5: $basis = 'ppBasis'; // these should be in strictly ascending order (hence the commented out rsort above) $modulo = [ 'k1' => new BigInteger($modulo[2]), 'k2' => new BigInteger($modulo[1]), 'k3' => new BigInteger($modulo[0]) ]; $modulo = ASN1::encodeDER($modulo, Maps\Pentanomial::MAP); $modulo = new ASN1\Element($modulo); } $params = ASN1::encodeDER([ 'm' => new BigInteger($m), 'basis' => $basis, 'parameters' => $modulo ], Maps\Characteristic_two::MAP); $params = new ASN1\Element($params); $a = ltrim($curve->getA()->toBytes(), "\0"); if (!strlen($a)) { $a = "\0"; } $b = ltrim($curve->getB()->toBytes(), "\0"); if (!strlen($b)) { $b = "\0"; } $data = [ 'version' => 'ecdpVer1', 'fieldID' => [ 'fieldType' => 'characteristic-two-field', 'parameters' => $params ], 'curve' => [ 'a' => $a, 'b' => $b ], 'base' => "\4" . $x . $y, 'order' => $order ]; return $returnArray ? ['specifiedCurve' => $data] : ASN1::encodeDER(['specifiedCurve' => $data], Maps\ECParameters::MAP); } throw new UnsupportedCurveException('Curve cannot be serialized'); } /** * Use Specified Curve * * A specified curve has all the coefficients, the base points, etc, explicitely included. * A specified curve is a more verbose way of representing a curve */ public static function useSpecifiedCurve() { self::$useNamedCurves = false; } /** * Use Named Curve * * A named curve does not include any parameters. It is up to the EC parameters to * know what the coefficients, the base points, etc, are from the name of the curve. * A named curve is a more concise way of representing a curve */ public static function useNamedCurve() { self::$useNamedCurves = true; } }

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