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<?php
/**
* Curve methods common to all curves
*
* PHP version 5 and 7
*
* @category Crypt
* @package EC
* @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\Common\FiniteField;
use phpseclib3\Math\BigInteger;
/**
* Base
*
* @package Prime
* @author Jim Wigginton <terrafrost@php.net>
* @access public
*/
abstract class Base
{
/**
* Doubles
*
* @var object[]
*/
protected $doubles;
/**
* NAF Points
*
* @var int[]
*/
private $naf;
/**
* The Order
*
* @var BigInteger
*/
protected $order;
/**
* Finite Field Integer factory
*
* @var \phpseclib3\Math\FiniteField\Integer
*/
protected $factory;
/**
* Returns a random integer
*
* @return object
*/
public function randomInteger()
{
return $this->factory->randomInteger();
}
/**
* Converts a BigInteger to a FiniteField integer
*
* @return object
*/
public function convertInteger(BigInteger $x)
{
return $this->factory->newInteger($x);
}
/**
* Returns the length, in bytes, of the modulo
*
* @return integer
*/
public function getLengthInBytes()
{
return $this->factory->getLengthInBytes();
}
/**
* Returns the length, in bits, of the modulo
*
* @return integer
*/
public function getLength()
{
return $this->factory->getLength();
}
/**
* 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
*
* @return array
*/
public function multiplyPoint(array $p, FiniteField\Integer $d)
{
$alreadyInternal = isset($p[2]);
$r = $alreadyInternal ?
[[], $p] :
[[], $this->convertToInternal($p)];
$d = $d->toBits();
for ($i = 0; $i < strlen($d); $i++) {
$d_i = (int) $d[$i];
$r[1 - $d_i] = $this->addPoint($r[0], $r[1]);
$r[$d_i] = $this->doublePoint($r[$d_i]);
}
return $alreadyInternal ? $r[0] : $this->convertToAffine($r[0]);
}
/**
* Creates a random scalar multiplier
*
* @return FiniteField
*/
public function createRandomMultiplier()
{
static $one;
if (!isset($one)) {
$one = new BigInteger(1);
}
$dA = BigInteger::randomRange($one, $this->order->subtract($one));
return $this->factory->newInteger($dA);
}
/**
* Sets the Order
*/
public function setOrder(BigInteger $order)
{
$this->order = $order;
}
/**
* Returns the Order
*
* @return \phpseclib3\Math\BigInteger
*/
public function getOrder()
{
return $this->order;
}
/**
* Use a custom defined modular reduction function
*
* @return object
*/
public function setReduction(callable $func)
{
$this->factory->setReduction($func);
}
/**
* Returns the affine point
*
* @return object[]
*/
public function convertToAffine(array $p)
{
return $p;
}
/**
* Converts an affine point to a jacobian coordinate
*
* @return object[]
*/
public function convertToInternal(array $p)
{
return $p;
}
/**
* Negates a point
*
* @return object[]
*/
public function negatePoint(array $p)
{
$temp = [
$p[0],
$p[1]->negate()
];
if (isset($p[2])) {
$temp[] = $p[2];
}
return $temp;
}
/**
* Multiply and Add Points
*
* @return int[]
*/
public function multiplyAddPoints(array $points, array $scalars)
{
$p1 = $this->convertToInternal($points[0]);
$p2 = $this->convertToInternal($points[1]);
$p1 = $this->multiplyPoint($p1, $scalars[0]);
$p2 = $this->multiplyPoint($p2, $scalars[1]);
$r = $this->addPoint($p1, $p2);
return $this->convertToAffine($r);
}
}
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