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Rev	Author	Line No.	Line
827	daniel-mar	1	<?php
		2
		3	/**
		4	* Curves over ax^2 + y^2 = 1 + dx^2*y^2
		5	*
		6	* http://www.secg.org/SEC2-Ver-1.0.pdf provides for curves with custom parameters.
		7	* ie. the coefficients can be arbitrary set through specially formatted keys, etc.
		8	* As such, Prime.php is built very generically and it's not able to take full
		9	* advantage of curves with 0 coefficients to produce simplified point doubling,
		10	* point addition. Twisted Edwards curves, in contrast, do not have a way, currently,
		11	* to customize them. As such, we can omit the super generic stuff from this class
		12	* and let the named curves (Ed25519 and Ed448) define their own custom tailored
		13	* point addition and point doubling methods.
		14	*
		15	* More info:
		16	*
		17	* https://en.wikipedia.org/wiki/Twisted_Edwards_curve
		18	*
		19	* PHP version 5 and 7
		20	*
874	daniel-mar	21	* @category Crypt
		22	* @package EC
827	daniel-mar	23	* @author Jim Wigginton <terrafrost@php.net>
		24	* @copyright 2017 Jim Wigginton
		25	* @license http://www.opensource.org/licenses/mit-license.html MIT License
		26	* @link http://pear.php.net/package/Math_BigInteger
		27	*/
		28
		29	namespace phpseclib3\Crypt\EC\BaseCurves;
		30
		31	use phpseclib3\Math\BigInteger;
		32	use phpseclib3\Math\PrimeField;
		33	use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
		34
		35	/**
		36	* Curves over ax^2 + y^2 = 1 + dx^2*y^2
		37	*
874	daniel-mar	38	* @package Prime
827	daniel-mar	39	* @author Jim Wigginton <terrafrost@php.net>
874	daniel-mar	40	* @access public
827	daniel-mar	41	*/
		42	class TwistedEdwards extends Base
		43	{
		44	/**
		45	* The modulo
		46	*
		47	* @var BigInteger
		48	*/
		49	protected $modulo;
		50
		51	/**
		52	* Cofficient for x^2
		53	*
		54	* @var object
		55	*/
		56	protected $a;
		57
		58	/**
		59	* Cofficient for x^2*y^2
		60	*
		61	* @var object
		62	*/
		63	protected $d;
		64
		65	/**
		66	* Base Point
		67	*
		68	* @var object[]
		69	*/
		70	protected $p;
		71
		72	/**
		73	* The number zero over the specified finite field
		74	*
		75	* @var object
		76	*/
		77	protected $zero;
		78
		79	/**
		80	* The number one over the specified finite field
		81	*
		82	* @var object
		83	*/
		84	protected $one;
		85
		86	/**
		87	* The number two over the specified finite field
		88	*
		89	* @var object
		90	*/
		91	protected $two;
		92
		93	/**
		94	* Sets the modulo
		95	*/
		96	public function setModulo(BigInteger $modulo)
		97	{
		98	$this->modulo = $modulo;
		99	$this->factory = new PrimeField($modulo);
		100	$this->zero = $this->factory->newInteger(new BigInteger(0));
		101	$this->one = $this->factory->newInteger(new BigInteger(1));
		102	$this->two = $this->factory->newInteger(new BigInteger(2));
		103	}
		104
		105	/**
		106	* Set coefficients a and b
		107	*/
		108	public function setCoefficients(BigInteger $a, BigInteger $d)
		109	{
		110	if (!isset($this->factory)) {
		111	throw new \RuntimeException('setModulo needs to be called before this method');
		112	}
		113	$this->a = $this->factory->newInteger($a);
		114	$this->d = $this->factory->newInteger($d);
		115	}
		116
		117	/**
		118	* Set x and y coordinates for the base point
		119	*/
		120	public function setBasePoint($x, $y)
		121	{
		122	switch (true) {
		123	case !$x instanceof BigInteger && !$x instanceof PrimeInteger:
		124	throw new \UnexpectedValueException('Argument 1 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
		125	case !$y instanceof BigInteger && !$y instanceof PrimeInteger:
		126	throw new \UnexpectedValueException('Argument 2 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
		127	}
		128	if (!isset($this->factory)) {
		129	throw new \RuntimeException('setModulo needs to be called before this method');
		130	}
		131	$this->p = [
		132	$x instanceof BigInteger ? $this->factory->newInteger($x) : $x,
		133	$y instanceof BigInteger ? $this->factory->newInteger($y) : $y
		134	];
		135	}
		136
		137	/**
		138	* Returns the a coefficient
		139	*
		140	* @return \phpseclib3\Math\PrimeField\Integer
		141	*/
		142	public function getA()
		143	{
		144	return $this->a;
		145	}
		146
		147	/**
		148	* Returns the a coefficient
		149	*
		150	* @return \phpseclib3\Math\PrimeField\Integer
		151	*/
		152	public function getD()
		153	{
		154	return $this->d;
		155	}
		156
		157	/**
		158	* Retrieve the base point as an array
		159	*
		160	* @return array
		161	*/
		162	public function getBasePoint()
		163	{
		164	if (!isset($this->factory)) {
		165	throw new \RuntimeException('setModulo needs to be called before this method');
		166	}
		167	/*
		168	if (!isset($this->p)) {
		169	throw new \RuntimeException('setBasePoint needs to be called before this method');
		170	}
		171	*/
		172	return $this->p;
		173	}
		174
		175	/**
		176	* Returns the affine point
		177	*
		178	* @return \phpseclib3\Math\PrimeField\Integer[]
		179	*/
		180	public function convertToAffine(array $p)
		181	{
		182	if (!isset($p[2])) {
		183	return $p;
		184	}
		185	list($x, $y, $z) = $p;
		186	$z = $this->one->divide($z);
		187	return [
		188	$x->multiply($z),
		189	$y->multiply($z)
		190	];
		191	}
		192
		193	/**
		194	* Returns the modulo
		195	*
		196	* @return \phpseclib3\Math\BigInteger
		197	*/
		198	public function getModulo()
		199	{
		200	return $this->modulo;
		201	}
		202
		203	/**
		204	* Tests whether or not the x / y values satisfy the equation
		205	*
		206	* @return boolean
		207	*/
		208	public function verifyPoint(array $p)
		209	{
		210	list($x, $y) = $p;
		211	$x2 = $x->multiply($x);
		212	$y2 = $y->multiply($y);
		213
		214	$lhs = $this->a->multiply($x2)->add($y2);
		215	$rhs = $this->d->multiply($x2)->multiply($y2)->add($this->one);
		216
		217	return $lhs->equals($rhs);
		218	}
		219	}

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oidplus/trunk/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/TwistedEdwards.php – Rev 874