Viel neues
This commit is contained in:
Sven Steinert
281
qa-tool/htdocs/oidc/phpseclib/Crypt/EC/BaseCurves/Montgomery.php
Normal file
281
qa-tool/htdocs/oidc/phpseclib/Crypt/EC/BaseCurves/Montgomery.php
Normal file
@@ -0,0 +1,281 @@
|
||||
<?php
|
||||
|
||||
/**
|
||||
* Curves over y^2 = x^3 + a*x + x
|
||||
*
|
||||
* Technically, a Montgomery curve has a coefficient for y^2 but for Curve25519 and Curve448 that
|
||||
* coefficient is 1.
|
||||
*
|
||||
* Curve25519 and Curve448 do not make use of the y coordinate, which makes it unsuitable for use
|
||||
* with ECDSA / EdDSA. A few other differences between Curve25519 and Ed25519 are discussed at
|
||||
* https://crypto.stackexchange.com/a/43058/4520
|
||||
*
|
||||
* More info:
|
||||
*
|
||||
* https://en.wikipedia.org/wiki/Montgomery_curve
|
||||
*
|
||||
* PHP version 5 and 7
|
||||
*
|
||||
* @author Jim Wigginton <terrafrost@php.net>
|
||||
* @copyright 2019 Jim Wigginton
|
||||
* @license http://www.opensource.org/licenses/mit-license.html MIT License
|
||||
* @link http://pear.php.net/package/Math_BigInteger
|
||||
*/
|
||||
|
||||
declare(strict_types=1);
|
||||
|
||||
namespace phpseclib3\Crypt\EC\BaseCurves;
|
||||
|
||||
use phpseclib3\Crypt\EC\Curves\Curve25519;
|
||||
use phpseclib3\Exception\RuntimeException;
|
||||
use phpseclib3\Exception\UnexpectedValueException;
|
||||
use phpseclib3\Math\BigInteger;
|
||||
use phpseclib3\Math\PrimeField;
|
||||
use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
|
||||
|
||||
/**
|
||||
* Curves over y^2 = x^3 + a*x + x
|
||||
*
|
||||
* @author Jim Wigginton <terrafrost@php.net>
|
||||
*/
|
||||
class Montgomery extends Base
|
||||
{
|
||||
/**
|
||||
* Prime Field Integer factory
|
||||
*
|
||||
* @var PrimeField
|
||||
*/
|
||||
protected $factory;
|
||||
|
||||
/**
|
||||
* Cofficient for x
|
||||
*
|
||||
* @var object
|
||||
*/
|
||||
protected $a;
|
||||
|
||||
/**
|
||||
* Constant used for point doubling
|
||||
*
|
||||
* @var object
|
||||
*/
|
||||
protected $a24;
|
||||
|
||||
/**
|
||||
* The Number Zero
|
||||
*
|
||||
* @var object
|
||||
*/
|
||||
protected $zero;
|
||||
|
||||
/**
|
||||
* The Number One
|
||||
*
|
||||
* @var object
|
||||
*/
|
||||
protected $one;
|
||||
|
||||
/**
|
||||
* Base Point
|
||||
*
|
||||
* @var object
|
||||
*/
|
||||
protected $p;
|
||||
|
||||
/**
|
||||
* The modulo
|
||||
*
|
||||
* @var BigInteger
|
||||
*/
|
||||
protected $modulo;
|
||||
|
||||
/**
|
||||
* The Order
|
||||
*
|
||||
* @var BigInteger
|
||||
*/
|
||||
protected $order;
|
||||
|
||||
/**
|
||||
* Sets the modulo
|
||||
*/
|
||||
public function setModulo(BigInteger $modulo): void
|
||||
{
|
||||
$this->modulo = $modulo;
|
||||
$this->factory = new PrimeField($modulo);
|
||||
$this->zero = $this->factory->newInteger(new BigInteger());
|
||||
$this->one = $this->factory->newInteger(new BigInteger(1));
|
||||
}
|
||||
|
||||
/**
|
||||
* Set coefficients a
|
||||
*/
|
||||
public function setCoefficients(BigInteger $a): void
|
||||
{
|
||||
if (!isset($this->factory)) {
|
||||
throw new RuntimeException('setModulo needs to be called before this method');
|
||||
}
|
||||
$this->a = $this->factory->newInteger($a);
|
||||
$two = $this->factory->newInteger(new BigInteger(2));
|
||||
$four = $this->factory->newInteger(new BigInteger(4));
|
||||
$this->a24 = $this->a->subtract($two)->divide($four);
|
||||
}
|
||||
|
||||
/**
|
||||
* Set x and y coordinates for the base point
|
||||
*
|
||||
* @param BigInteger|PrimeInteger $x
|
||||
* @param BigInteger|PrimeInteger $y
|
||||
* @return PrimeInteger[]
|
||||
*/
|
||||
public function setBasePoint($x, $y): array
|
||||
{
|
||||
switch (true) {
|
||||
case !$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) : $y,
|
||||
];
|
||||
}
|
||||
|
||||
/**
|
||||
* Retrieve the base point as an array
|
||||
*
|
||||
* @return array
|
||||
*/
|
||||
public function getBasePoint()
|
||||
{
|
||||
if (!isset($this->factory)) {
|
||||
throw new RuntimeException('setModulo needs to be called before this method');
|
||||
}
|
||||
/*
|
||||
if (!isset($this->p)) {
|
||||
throw new \phpseclib3\Exception\RuntimeException('setBasePoint needs to be called before this method');
|
||||
}
|
||||
*/
|
||||
return $this->p;
|
||||
}
|
||||
|
||||
/**
|
||||
* Doubles and adds a point on a curve
|
||||
*
|
||||
* See https://tools.ietf.org/html/draft-ietf-tls-curve25519-01#appendix-A.1.3
|
||||
*
|
||||
* @return FiniteField[][]
|
||||
*/
|
||||
private function doubleAndAddPoint(array $p, array $q, PrimeInteger $x1): array
|
||||
{
|
||||
if (!isset($this->factory)) {
|
||||
throw new RuntimeException('setModulo needs to be called before this method');
|
||||
}
|
||||
|
||||
if (!count($p) || !count($q)) {
|
||||
return [];
|
||||
}
|
||||
|
||||
if (!isset($p[1])) {
|
||||
throw new RuntimeException('Affine coordinates need to be manually converted to XZ coordinates');
|
||||
}
|
||||
|
||||
[$x2, $z2] = $p;
|
||||
[$x3, $z3] = $q;
|
||||
|
||||
$a = $x2->add($z2);
|
||||
$aa = $a->multiply($a);
|
||||
$b = $x2->subtract($z2);
|
||||
$bb = $b->multiply($b);
|
||||
$e = $aa->subtract($bb);
|
||||
$c = $x3->add($z3);
|
||||
$d = $x3->subtract($z3);
|
||||
$da = $d->multiply($a);
|
||||
$cb = $c->multiply($b);
|
||||
$temp = $da->add($cb);
|
||||
$x5 = $temp->multiply($temp);
|
||||
$temp = $da->subtract($cb);
|
||||
$z5 = $x1->multiply($temp->multiply($temp));
|
||||
$x4 = $aa->multiply($bb);
|
||||
$temp = static::class == Curve25519::class ? $bb : $aa;
|
||||
$z4 = $e->multiply($temp->add($this->a24->multiply($e)));
|
||||
|
||||
return [
|
||||
[$x4, $z4],
|
||||
[$x5, $z5],
|
||||
];
|
||||
}
|
||||
|
||||
/**
|
||||
* Multiply a point on the curve by a scalar
|
||||
*
|
||||
* Uses the montgomery ladder technique as described here:
|
||||
*
|
||||
* https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Montgomery_ladder
|
||||
* https://github.com/phpecc/phpecc/issues/16#issuecomment-59176772
|
||||
*/
|
||||
public function multiplyPoint(array $p, BigInteger $d): array
|
||||
{
|
||||
$p1 = [$this->one, $this->zero];
|
||||
$alreadyInternal = isset($x[1]);
|
||||
$p2 = $this->convertToInternal($p);
|
||||
$x = $p[0];
|
||||
|
||||
$b = $d->toBits();
|
||||
$b = str_pad($b, 256, '0', STR_PAD_LEFT);
|
||||
for ($i = 0; $i < strlen($b); $i++) {
|
||||
$b_i = (int) $b[$i];
|
||||
if ($b_i) {
|
||||
[$p2, $p1] = $this->doubleAndAddPoint($p2, $p1, $x);
|
||||
} else {
|
||||
[$p1, $p2] = $this->doubleAndAddPoint($p1, $p2, $x);
|
||||
}
|
||||
}
|
||||
|
||||
return $alreadyInternal ? $p1 : $this->convertToAffine($p1);
|
||||
}
|
||||
|
||||
/**
|
||||
* Converts an affine point to an XZ coordinate
|
||||
*
|
||||
* From https://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html
|
||||
*
|
||||
* XZ coordinates represent x y as X Z satsfying the following equations:
|
||||
*
|
||||
* x=X/Z
|
||||
*
|
||||
* @return PrimeInteger[]
|
||||
*/
|
||||
public function convertToInternal(array $p): array
|
||||
{
|
||||
if (empty($p)) {
|
||||
return [clone $this->zero, clone $this->one];
|
||||
}
|
||||
|
||||
if (isset($p[1])) {
|
||||
return $p;
|
||||
}
|
||||
|
||||
$p[1] = clone $this->one;
|
||||
|
||||
return $p;
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the affine point
|
||||
*
|
||||
* @return PrimeInteger[]
|
||||
*/
|
||||
public function convertToAffine(array $p): array
|
||||
{
|
||||
if (!isset($p[1])) {
|
||||
return $p;
|
||||
}
|
||||
[$x, $z] = $p;
|
||||
return [$x->divide($z)];
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user