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<?php |
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namespace Jose\Component\Core\Util\Ecc\Primitives; |
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use Jose\Component\Core\Util\Ecc\Math\GmpMath; |
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use Jose\Component\Core\Util\Ecc\Math\ModularArithmetic; |
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use Jose\Component\Core\Util\Ecc\Util\BinaryString; |
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/** |
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* ********************************************************************* |
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* Copyright (C) 2012 Matyas Danter |
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* |
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* Permission is hereby granted, free of charge, to any person obtaining |
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* a copy of this software and associated documentation files (the "Software"), |
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* to deal in the Software without restriction, including without limitation |
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* the rights to use, copy, modify, merge, publish, distribute, sublicense, |
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* and/or sell copies of the Software, and to permit persons to whom the |
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* Software is furnished to do so, subject to the following conditions: |
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* |
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* The above copyright notice and this permission notice shall be included |
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* in all copies or substantial portions of the Software. |
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* |
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS |
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* OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
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* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES |
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* OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, |
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* ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR |
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* OTHER DEALINGS IN THE SOFTWARE. |
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* *********************************************************************** |
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*/ |
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/** |
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* This class is where the elliptic curve arithmetic takes place. |
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* The important methods are: |
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* - add: adds two points according to ec arithmetic |
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* - double: doubles a point on the ec field mod p |
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* - mul: uses double and add to achieve multiplication The rest of the methods are there for supporting the ones above. |
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*/ |
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class Point |
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{ |
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/** |
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* @var CurveFp |
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*/ |
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private $curve; |
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/** |
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* @var GmpMath |
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*/ |
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private $adapter; |
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/** |
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* @var ModularArithmetic |
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*/ |
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private $modAdapter; |
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/** |
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* @var \GMP |
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*/ |
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private $x; |
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/** |
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* @var \GMP |
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*/ |
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private $y; |
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/** |
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* @var \GMP |
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*/ |
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private $order; |
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/** |
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* @var bool |
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*/ |
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private $infinity = false; |
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/** |
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* Initialize a new instance |
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* |
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* @param GmpMath $adapter |
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* @param CurveFp $curve |
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* @param \GMP $x |
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* @param \GMP $y |
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* @param \GMP $order |
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* @param bool $infinity |
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* |
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* @throws \RuntimeException when either the curve does not contain the given coordinates or |
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* when order is not null and P(x, y) * order is not equal to infinity. |
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*/ |
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public function __construct(GmpMath $adapter, CurveFp $curve, \GMP $x, \GMP $y, \GMP $order = null, $infinity = false) |
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{ |
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$this->adapter = $adapter; |
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$this->modAdapter = $curve->getModAdapter(); |
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$this->curve = $curve; |
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$this->x = $x; |
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$this->y = $y; |
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$this->order = $order !== null ? $order : gmp_init(0, 10); |
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$this->infinity = (bool) $infinity; |
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if (! $infinity && ! $curve->contains($x, $y)) { |
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throw new \RuntimeException("Curve " . $curve . " does not contain point (" . $adapter->toString($x) . ", " . $adapter->toString($y) . ")"); |
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} |
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if (!is_null($order)) { |
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$mul = $this->mul($order); |
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if (!$mul->isInfinity()) { |
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throw new \RuntimeException("SELF * ORDER MUST EQUAL INFINITY. (" . (string)$mul . " found instead)"); |
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} |
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} |
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} |
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/** |
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* @return GmpMath |
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*/ |
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public function getAdapter() |
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{ |
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return $this->adapter; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::isInfinity() |
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*/ |
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public function isInfinity() |
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{ |
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return (bool) $this->infinity; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::getCurve() |
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*/ |
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public function getCurve() |
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{ |
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return $this->curve; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::getOrder() |
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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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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::getX() |
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*/ |
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public function getX() |
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{ |
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return $this->x; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::getY() |
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*/ |
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public function getY() |
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{ |
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return $this->y; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::add() |
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* @return self |
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*/ |
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public function add(Point $addend) |
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{ |
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if (! $this->curve->equals($addend->getCurve())) { |
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throw new \RuntimeException("The Elliptic Curves do not match."); |
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} |
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if ($addend->isInfinity()) { |
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return clone $this; |
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} |
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if ($this->isInfinity()) { |
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return clone $addend; |
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} |
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$math = $this->adapter; |
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$modMath = $this->modAdapter; |
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if ($math->equals($addend->getX(), $this->x)) { |
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if ($math->equals($addend->getY(), $this->y)) { |
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return $this->getDouble(); |
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} else { |
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return $this->curve->getInfinity(); |
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} |
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} |
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$slope = $modMath->div( |
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$math->sub($addend->getY(), $this->y), |
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$math->sub($addend->getX(), $this->x) |
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); |
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$xR = $modMath->sub( |
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$math->sub($math->pow($slope, 2), $this->x), |
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$addend->getX() |
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); |
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$yR = $modMath->sub( |
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$math->mul($slope, $math->sub($this->x, $xR)), |
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$this->y |
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); |
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return $this->curve->getPoint($xR, $yR, $this->order); |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::cmp() |
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*/ |
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public function cmp(Point $other) |
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{ |
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if ($other->isInfinity() && $this->isInfinity()) { |
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return 0; |
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} |
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if ($other->isInfinity() || $this->isInfinity()) { |
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return 1; |
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} |
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$math = $this->adapter; |
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$equal = ($math->equals($this->x, $other->getX())); |
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$equal &= ($math->equals($this->y, $other->getY())); |
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$equal &= $this->isInfinity() == $other->isInfinity(); |
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$equal &= $this->curve->equals($other->getCurve()); |
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if ($equal) { |
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return 0; |
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} |
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return 1; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::equals() |
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*/ |
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public function equals(Point $other) |
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{ |
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return $this->cmp($other) == 0; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::mul() |
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*/ |
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public function mul(\GMP $n) |
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{ |
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if ($this->isInfinity()) { |
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return $this->curve->getInfinity(); |
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} |
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$zero = gmp_init(0, 10); |
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if ($this->adapter->cmp($this->order, $zero) > 0) { |
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$n = $this->adapter->mod($n, $this->order); |
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} |
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if ($this->adapter->equals($n, $zero)) { |
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return $this->curve->getInfinity(); |
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} |
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/** @var Point[] $r */ |
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$r = [ |
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$this->curve->getInfinity(), |
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clone $this |
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]; |
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$k = $this->curve->getSize(); |
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$n = str_pad($this->adapter->baseConvert($this->adapter->toString($n), 10, 2), $k, '0', STR_PAD_LEFT); |
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for ($i = 0; $i < $k; $i++) { |
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$j = $n[$i]; |
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$this->cswap($r[0], $r[1], $j ^ 1); |
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$r[0] = $r[0]->add($r[1]); |
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$r[1] = $r[1]->getDouble(); |
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$this->cswap($r[0], $r[1], $j ^ 1); |
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} |
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$r[0]->validate(); |
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return $r[0]; |
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} |
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/** |
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* @param Point $a |
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* @param Point $b |
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* @param int $cond |
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*/ |
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private function cswap(self $a, self $b, $cond) |
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{ |
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$this->cswapValue($a->x, $b->x, $cond); |
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$this->cswapValue($a->y, $b->y, $cond); |
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$this->cswapValue($a->order, $b->order, $cond); |
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$this->cswapValue($a->infinity, $b->infinity, $cond); |
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} |
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/** |
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* @param $a |
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* @param $b |
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* @param $cond |
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*/ |
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public function cswapValue(& $a, & $b, $cond) |
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{ |
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$isGMP = is_object($a) && $a instanceof \GMP; |
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$sa = $isGMP ? $a : gmp_init(intval($a), 10); |
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$sb = $isGMP ? $b : gmp_init(intval($b), 10); |
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$size = max(BinaryString::length(gmp_strval($sa, 2)), BinaryString::length(gmp_strval($sb, 2))); |
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$mask = 1 - intval($cond); |
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$mask = str_pad('', $size, $mask, STR_PAD_LEFT); |
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$mask = gmp_init($mask, 2); |
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$taA = $this->adapter->bitwiseAnd($sa, $mask); |
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$taB = $this->adapter->bitwiseAnd($sb, $mask); |
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$sa = $this->adapter->bitwiseXor($this->adapter->bitwiseXor($sa, $sb), $taB); |
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$sb = $this->adapter->bitwiseXor($this->adapter->bitwiseXor($sa, $sb), $taA); |
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$sa = $this->adapter->bitwiseXor($this->adapter->bitwiseXor($sa, $sb), $taB); |
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$a = $isGMP ? $sa : (bool) gmp_strval($sa, 10); |
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$b = $isGMP ? $sb : (bool) gmp_strval($sb, 10); |
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} |
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/** |
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* |
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*/ |
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private function validate() |
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{ |
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if (! $this->infinity && ! $this->curve->contains($this->x, $this->y)) { |
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throw new \RuntimeException('Invalid point'); |
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} |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\Point::getDouble() |
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* @return self |
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*/ |
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public function getDouble() |
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{ |
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if ($this->isInfinity()) { |
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return $this->curve->getInfinity(); |
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} |
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$math = $this->adapter; |
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$modMath = $this->modAdapter; |
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$a = $this->curve->getA(); |
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$threeX2 = $math->mul(gmp_init(3, 10), $math->pow($this->x, 2)); |
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$tangent = $modMath->div( |
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$math->add($threeX2, $a), |
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$math->mul(gmp_init(2, 10), $this->y) |
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); |
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$x3 = $modMath->sub( |
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$math->pow($tangent, 2), |
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$math->mul(gmp_init(2, 10), $this->x) |
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); |
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$y3 = $modMath->sub( |
371
|
|
|
$math->mul($tangent, $math->sub($this->x, $x3)), |
372
|
|
|
$this->y |
373
|
|
|
); |
374
|
|
|
|
375
|
|
|
return $this->curve->getPoint($x3, $y3, $this->order); |
376
|
|
|
} |
377
|
|
|
|
378
|
|
|
/** |
379
|
|
|
* {@inheritDoc} |
380
|
|
|
* @see \Jose\Component\Core\Util\Ecc\Point::__toString() |
381
|
|
|
*/ |
382
|
|
|
public function __toString() |
383
|
|
|
{ |
384
|
|
|
if ($this->infinity) { |
385
|
|
|
return '[ (infinity) on ' . (string) $this->curve . ' ]'; |
386
|
|
|
} |
387
|
|
|
|
388
|
|
|
return "[ (" . $this->adapter->toString($this->x) . "," . $this->adapter->toString($this->y) . ') on ' . (string) $this->curve . ' ]'; |
389
|
|
|
} |
390
|
|
|
|
391
|
|
|
/** |
392
|
|
|
* @return array |
393
|
|
|
*/ |
394
|
|
|
public function __debugInfo() |
395
|
|
|
{ |
396
|
|
|
$info = [ |
397
|
|
|
'x' => $this->adapter->toString($this->x), |
398
|
|
|
'y' => $this->adapter->toString($this->y), |
399
|
|
|
'z' => $this->adapter->toString($this->order), |
400
|
|
|
'curve' => $this->curve |
401
|
|
|
]; |
402
|
|
|
|
403
|
|
|
if ($this->infinity) { |
404
|
|
|
$info['x'] = 'inf (' . $info['x'] . ')'; |
405
|
|
|
$info['y'] = 'inf (' . $info['y'] . ')'; |
406
|
|
|
$info['z'] = 'inf (' . $info['z'] . ')'; |
407
|
|
|
} |
408
|
|
|
|
409
|
|
|
return $info; |
410
|
|
|
} |
411
|
|
|
} |
412
|
|
|
|
If a method or function can return multiple different values and unless you are sure that you only can receive a single value in this context, we recommend to add an additional type check:
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