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<?php
/**
* Generic EC Key Parsing Helper functions
*
* PHP version 5
*
* @category Crypt
* @package EC
* @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 ParagonIE\ConstantTime\Hex;
use phpseclib3\Crypt\EC\BaseCurves\Base as BaseCurve;
use phpseclib3\Crypt\EC\BaseCurves\Prime as PrimeCurve;
use phpseclib3\Crypt\EC\BaseCurves\Binary as BinaryCurve;
use phpseclib3\Crypt\EC\BaseCurves\TwistedEdwards as TwistedEdwardsCurve;
use phpseclib3\Common\Functions\Strings;
use phpseclib3\Math\BigInteger;
use phpseclib3\Math\PrimeField;
use phpseclib3\File\ASN1;
use phpseclib3\File\ASN1\Maps;
use phpseclib3\Exception\UnsupportedCurveException;
/**
* Generic EC Key Parsing Helper functions
*
* @package EC
* @author Jim Wigginton <terrafrost@php.net>
* @access public
*/
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);
$curve->setCoefficients(
Hex::encode($data['curve']['a']),
Hex::encode($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($str)) != "\0") {
throw new \UnexpectedValueException('extractPoint expects the first byte to be null - not ' . Hex::encode($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 ' . Hex::encode($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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