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220 lines
4.4 KiB
PHP
220 lines
4.4 KiB
PHP
<?php
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/**
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* Curve methods common to all curves
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*
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* PHP version 5 and 7
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*
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* @category Crypt
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* @package EC
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* @author Jim Wigginton <terrafrost@php.net>
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* @copyright 2017 Jim Wigginton
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* @license http://www.opensource.org/licenses/mit-license.html MIT License
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* @link http://pear.php.net/package/Math_BigInteger
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*/
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namespace phpseclib\Crypt\EC\BaseCurves;
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use phpseclib\Math\Common\FiniteField;
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use phpseclib\Math\BigInteger;
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/**
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* Base
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*
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* @package Prime
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* @author Jim Wigginton <terrafrost@php.net>
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* @access public
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*/
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abstract class Base
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{
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/**
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* Doubles
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*
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* @var object[]
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*/
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protected $doubles;
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/**
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* NAF Points
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*
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* @var int[]
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*/
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private $naf;
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/**
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* The Order
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*
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* @var BigInteger
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*/
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protected $order;
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/**
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* Finite Field Integer factory
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*
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* @var \phpseclib\Math\FiniteField\Integer
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*/
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protected $factory;
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/**
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* Returns a random integer
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*
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* @return object
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*/
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public function randomInteger()
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{
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return $this->factory->randomInteger();
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}
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/**
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* Converts a BigInteger to a FiniteField integer
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*
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* @return object
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*/
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public function convertInteger(BigInteger $x)
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{
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return $this->factory->newInteger($x);
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}
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/**
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* Returns the length, in bytes, of the modulo
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*
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* @return integer
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*/
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public function getLengthInBytes()
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{
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return $this->factory->getLengthInBytes();
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}
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/**
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* Returns the length, in bits, of the modulo
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*
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* @return integer
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*/
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public function getLength()
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{
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return $this->factory->getLength();
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}
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/**
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* Multiply a point on the curve by a scalar
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*
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* Uses the montgomery ladder technique as described here:
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*
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* https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Montgomery_ladder
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* https://github.com/phpecc/phpecc/issues/16#issuecomment-59176772
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*
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* @return array
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*/
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public function multiplyPoint(array $p, FiniteField\Integer $d)
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{
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$alreadyInternal = isset($p[2]);
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$r = $alreadyInternal ?
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[[], $p] :
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[[], $this->convertToInternal($p)];
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$d = $d->toBits();
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for ($i = 0; $i < strlen($d); $i++) {
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$d_i = (int) $d[$i];
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$r[1 - $d_i] = $this->addPoint($r[0], $r[1]);
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$r[$d_i] = $this->doublePoint($r[$d_i]);
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}
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return $alreadyInternal ? $r[0] : $this->convertToAffine($r[0]);
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}
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/**
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* Creates a random scalar multiplier
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*
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* @return FiniteField
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*/
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public function createRandomMultiplier()
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{
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static $one;
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if (!isset($one)) {
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$one = new BigInteger(1);
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}
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$dA = BigInteger::randomRange($one, $this->order->subtract($one));
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return $this->factory->newInteger($dA);
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}
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/**
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* Sets the Order
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*/
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public function setOrder(BigInteger $order)
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{
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$this->order = $order;
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}
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/**
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* Returns the Order
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*
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* @return \phpseclib\Math\BigInteger
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*/
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public function getOrder()
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{
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return $this->order;
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}
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/**
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* Use a custom defined modular reduction function
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*
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* @return object
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*/
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public function setReduction(callable $func)
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{
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$this->factory->setReduction($func);
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}
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/**
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* Returns the affine point
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*
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* @return object[]
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*/
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public function convertToAffine(array $p)
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{
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return $p;
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}
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/**
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* Converts an affine point to a jacobian coordinate
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*
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* @return object[]
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*/
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public function convertToInternal(array $p)
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{
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return $p;
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}
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/**
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* Negates a point
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*
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* @return object[]
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*/
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public function negatePoint(array $p)
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{
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$temp = [
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$p[0],
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$p[1]->negate()
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];
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if (isset($p[2])) {
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$temp[] = $p[2];
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}
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return $temp;
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}
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/**
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* Multiply and Add Points
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*
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* @return int[]
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*/
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public function multiplyAddPoints(array $points, array $scalars)
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{
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$p1 = $this->convertToInternal($points[0]);
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$p2 = $this->convertToInternal($points[1]);
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$p1 = $this->multiplyPoint($p1, $scalars[0]);
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$p2 = $this->multiplyPoint($p2, $scalars[1]);
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$r = $this->addPoint($p1, $p2);
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return $this->convertToAffine($r);
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}
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} |