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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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/** |
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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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protected $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 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(CurveFp $curve, \GMP $x, \GMP $y, ?\GMP $order = null, bool $infinity = false) |
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{ |
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$this->adapter = new GmpMath(); |
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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 = null === $order ? gmp_init(0, 10) : $order; |
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$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 (" . $this->adapter->toString($x) . ", " . $this->adapter->toString($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 bool |
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*/ |
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public function isInfinity(): bool |
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{ |
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return (bool) $this->infinity; |
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} |
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/** |
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* @return CurveFp |
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*/ |
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public function getCurve(): CurveFp |
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{ |
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return $this->curve; |
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} |
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/** |
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* @return \GMP |
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*/ |
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public function getOrder(): \GMP |
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{ |
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return $this->order; |
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} |
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/** |
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* @return \GMP |
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*/ |
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public function getX(): \GMP |
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{ |
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return $this->x; |
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} |
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/** |
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* @return \GMP |
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*/ |
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public function getY(): \GMP |
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{ |
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return $this->y; |
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} |
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/** |
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* @param Point $addend |
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* |
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* @return Point |
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*/ |
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public function add(Point $addend): Point |
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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 $addend; |
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} |
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if ($this->adapter->equals($addend->getX(), $this->x)) { |
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if ($this->adapter->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 = $this->modAdapter->div( |
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$this->adapter->sub($addend->getY(), $this->y), |
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$this->adapter->sub($addend->getX(), $this->x) |
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); |
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$xR = $this->modAdapter->sub( |
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$this->adapter->sub($this->adapter->pow($slope, 2), $this->x), |
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$addend->getX() |
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); |
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$yR = $this->modAdapter->sub( |
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$this->adapter->mul($slope, $this->adapter->sub($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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* @param Point $other |
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* |
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* @return int |
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*/ |
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public function cmp(Point $other): int |
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{ |
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if ($other->isInfinity() && $this->isInfinity()) { |
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return 0; |
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} |
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if ($other->isInfinity() || $this->isInfinity()) { |
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return 1; |
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} |
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$equal = ($this->adapter->equals($this->x, $other->getX())); |
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$equal &= ($this->adapter->equals($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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return $equal ? 0 : 1; |
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} |
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/** |
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* @param Point $other |
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* @return bool |
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*/ |
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public function equals(Point $other): bool |
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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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* @param \GMP $n |
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* |
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* @return Point |
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*/ |
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public function mul(\GMP $n): Point |
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{ |
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if ($this->isInfinity()) { |
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return $this->curve->getInfinity(); |
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} |
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/** @var \GMP $zero */ |
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$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(Point $a, Point $b, int $cond) |
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{ |
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$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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private function cswapValue(& $a, & $b, int $cond) |
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{ |
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$isGMP = is_object($a) && $a instanceof \GMP; |
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/** @var \GMP $sa */ |
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$sa = $isGMP ? $a : gmp_init(intval($a), 10); |
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/** @var \GMP $sb */ |
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$sb = $isGMP ? $b : gmp_init(intval($b), 10); |
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$size = max(mb_strlen(gmp_strval($sa, 2), '8bit'), mb_strlen(gmp_strval($sb, 2), '8bit')); |
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$mask = 1 - intval($cond); |
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$mask = str_pad('', $size, $mask, STR_PAD_LEFT); |
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/** @var \GMP $mask */ |
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$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, $this->y)) { |
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throw new \RuntimeException('Invalid point'); |
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} |
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} |
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/** |
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* @return Point |
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*/ |
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public function getDouble(): Point |
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{ |
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if ($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 = $modMath->sub( |
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$math->mul($tangent, $math->sub($this->x, $x3)), |
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$this->y |
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); |
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return $this->curve->getPoint($x3, $y3, $this->order); |
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} |
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} |
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This error could be the result of:
1. Missing dependencies
PHP Analyzer uses your
composer.json
file (if available) to determine the dependencies of your project and to determine all the available classes and functions. It expects thecomposer.json
to be in the root folder of your repository.Are you sure this class is defined by one of your dependencies, or did you maybe not list a dependency in either the
require
orrequire-dev
section?2. Missing use statement
PHP does not complain about undefined classes in
ìnstanceof
checks. For example, the following PHP code will work perfectly fine:If you have not tested against this specific condition, such errors might go unnoticed.