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<?php
/**
* Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
*
* http://www.secg.org/SEC2-Ver-1.0.pdf provides for curves with custom parameters.
* ie. the coefficients can be arbitrary set through specially formatted keys, etc.
* As such, Prime.php is built very generically and it's not able to take full
* advantage of curves with 0 coefficients to produce simplified point doubling,
* point addition. Twisted Edwards curves, in contrast, do not have a way, currently,
* to customize them. As such, we can omit the super generic stuff from this class
* and let the named curves (Ed25519 and Ed448) define their own custom tailored
* point addition and point doubling methods.
*
* More info:
*
* https://en.wikipedia.org/wiki/Twisted_Edwards_curve
*
* PHP version 5 and 7
*
* @author Jim Wigginton <terrafrost@php.net>
* @copyright 2017 Jim Wigginton
* @license http://www.opensource.org/licenses/mit-license.html MIT License
* @link http://pear.php.net/package/Math_BigInteger
*/
namespace phpseclib3\Crypt\EC\BaseCurves;
use phpseclib3\Math\BigInteger;
use phpseclib3\Math\PrimeField;
use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
/**
* Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
*
* @author Jim Wigginton <terrafrost@php.net>
*/
class TwistedEdwards extends Base
{
/**
* The modulo
*
* @var BigInteger
*/
protected $modulo;
/**
* Cofficient for x^2
*
* @var object
*/
protected $a;
/**
* Cofficient for x^2*y^2
*
* @var object
*/
protected $d;
/**
* Base Point
*
* @var object[]
*/
protected $p;
/**
* The number zero over the specified finite field
*
* @var object
*/
protected $zero;
/**
* The number one over the specified finite field
*
* @var object
*/
protected $one;
/**
* The number two over the specified finite field
*
* @var object
*/
protected $two;
/**
* Sets the modulo
*/
public function setModulo(BigInteger $modulo)
{
$this->modulo = $modulo;
$this->factory = new PrimeField($modulo);
$this->zero = $this->factory->newInteger(new BigInteger(0));
$this->one = $this->factory->newInteger(new BigInteger(1));
$this->two = $this->factory->newInteger(new BigInteger(2));
}
/**
* Set coefficients a and b
*/
public function setCoefficients(BigInteger $a, BigInteger $d)
{
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
$this->a = $this->factory->newInteger($a);
$this->d = $this->factory->newInteger($d);
}
/**
* Set x and y coordinates for the base point
*/
public function setBasePoint($x, $y)
{
switch (true) {
case !$x instanceof BigInteger && !$x instanceof PrimeInteger:
throw new \UnexpectedValueException('Argument 1 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
case !$y instanceof BigInteger && !$y instanceof PrimeInteger:
throw new \UnexpectedValueException('Argument 2 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
}
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
$this->p = [
$x instanceof BigInteger ? $this->factory->newInteger($x) : $x,
$y instanceof BigInteger ? $this->factory->newInteger($y) : $y
];
}
/**
* Returns the a coefficient
*
* @return PrimeInteger
*/
public function getA()
{
return $this->a;
}
/**
* Returns the a coefficient
*
* @return PrimeInteger
*/
public function getD()
{
return $this->d;
}
/**
* Retrieve the base point as an array
*
* @return array
*/
public function getBasePoint()
{
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
/*
if (!isset($this->p)) {
throw new \RuntimeException('setBasePoint needs to be called before this method');
}
*/
return $this->p;
}
/**
* Returns the affine point
*
* @return PrimeInteger[]
*/
public function convertToAffine(array $p)
{
if (!isset($p[2])) {
return $p;
}
list($x, $y, $z) = $p;
$z = $this->one->divide($z);
return [
$x->multiply($z),
$y->multiply($z)
];
}
/**
* Returns the modulo
*
* @return BigInteger
*/
public function getModulo()
{
return $this->modulo;
}
/**
* Tests whether or not the x / y values satisfy the equation
*
* @return boolean
*/
public function verifyPoint(array $p)
{
list($x, $y) = $p;
$x2 = $x->multiply($x);
$y2 = $y->multiply($y);
$lhs = $this->a->multiply($x2)->add($y2);
$rhs = $this->d->multiply($x2)->multiply($y2)->add($this->one);
return $lhs->equals($rhs);
}
}
|
