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<?php |
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declare(strict_types=1); |
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/*********************************************************************** |
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Copyright (C) 2012 Matyas Danter |
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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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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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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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namespace Mdanter\Ecc\Primitives; |
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use Mdanter\Ecc\Exception\PointRecoveryException; |
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use Mdanter\Ecc\Exception\SquareRootException; |
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use Mdanter\Ecc\Math\GmpMathInterface; |
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use Mdanter\Ecc\Math\ModularArithmetic; |
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use Mdanter\Ecc\Random\RandomNumberGeneratorInterface; |
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/** |
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* This class is a representation of an EC over a field modulo a prime number |
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* |
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* Important objectives for this class are: |
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* - Does the curve contain a point? |
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* - Comparison of two curves. |
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*/ |
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class CurveFp implements CurveFpInterface |
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{ |
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/** |
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* @var CurveParameters |
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*/ |
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protected $parameters; |
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/** |
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* |
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* @var GmpMathInterface |
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*/ |
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protected $adapter = null; |
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/** |
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* |
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* @var ModularArithmetic |
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*/ |
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protected $modAdapter = null; |
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/** |
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* Constructor that sets up the instance variables. |
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* |
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* @param CurveParameters $parameters |
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* @param GmpMathInterface $adapter |
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*/ |
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public function __construct(CurveParameters $parameters, GmpMathInterface $adapter) |
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{ |
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$this->parameters = $parameters; |
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$this->adapter = $adapter; |
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$this->modAdapter = new ModularArithmetic($this->adapter, $this->parameters->getPrime()); |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::getModAdapter() |
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*/ |
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public function getModAdapter(): ModularArithmetic |
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{ |
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return $this->modAdapter; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::getPoint() |
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*/ |
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public function getPoint(\GMP $x, \GMP $y, \GMP $order = null): PointInterface |
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{ |
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return new Point($this->adapter, $this, $x, $y, $order); |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::getInfinity() |
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*/ |
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public function getInfinity(): PointInterface |
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{ |
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return new Point($this->adapter, $this, gmp_init(0, 10), gmp_init(0, 10), null, true); |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::getGenerator() |
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*/ |
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public function getGenerator(\GMP $x, \GMP $y, \GMP $order, RandomNumberGeneratorInterface $randomGenerator = null): GeneratorPoint |
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{ |
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return new GeneratorPoint($this->adapter, $this, $x, $y, $order, $randomGenerator); |
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} |
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/** |
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* @param bool $wasOdd |
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* @param \GMP $xCoord |
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* @return \GMP |
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*/ |
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public function recoverYfromX(bool $wasOdd, \GMP $xCoord): \GMP |
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{ |
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$math = $this->adapter; |
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$prime = $this->getPrime(); |
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try { |
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$root = $this->adapter->getNumberTheory()->squareRootModP( |
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$math->add( |
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$math->add( |
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$this->modAdapter->pow($xCoord, gmp_init(3, 10)), |
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$math->mul($this->getA(), $xCoord) |
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), |
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$this->getB() |
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), |
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$prime |
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); |
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} catch (SquareRootException $e) { |
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throw new PointRecoveryException("Failed to recover y coordinate for point", 0, $e); |
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} |
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if ($math->equals($math->mod($root, gmp_init(2, 10)), gmp_init(1)) === $wasOdd) { |
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return $root; |
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} else { |
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return $math->sub($prime, $root); |
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} |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::contains() |
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*/ |
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public function contains(\GMP $x, \GMP $y): bool |
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{ |
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$math = $this->adapter; |
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$eq_zero = $math->equals( |
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$this->modAdapter->sub( |
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$math->pow($y, 2), |
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$math->add( |
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$math->add( |
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$math->pow($x, 3), |
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$math->mul($this->getA(), $x) |
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), |
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$this->getB() |
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) |
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), |
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gmp_init(0, 10) |
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); |
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return $eq_zero; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::getA() |
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*/ |
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public function getA(): \GMP |
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{ |
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return $this->parameters->getA(); |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::getB() |
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*/ |
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public function getB(): \GMP |
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{ |
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return $this->parameters->getB(); |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::getPrime() |
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*/ |
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public function getPrime(): \GMP |
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{ |
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return $this->parameters->getPrime(); |
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} |
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/** |
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* @return int |
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*/ |
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public function getSize(): int |
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{ |
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return $this->parameters->getSize(); |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::cmp() |
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*/ |
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public function cmp(CurveFpInterface $other): int |
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{ |
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$math = $this->adapter; |
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$equal = $math->equals($this->getA(), $other->getA()); |
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$equal &= $math->equals($this->getB(), $other->getB()); |
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$equal &= $math->equals($this->getPrime(), $other->getPrime()); |
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return ($equal) ? 0 : 1; |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::equals() |
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*/ |
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public function equals(CurveFpInterface $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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* {@inheritDoc} |
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* @see \Mdanter\Ecc\Primitives\CurveFpInterface::__toString() |
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*/ |
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public function __toString(): string |
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{ |
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return 'curve(' . $this->adapter->toString($this->getA()) . ', ' . $this->adapter->toString($this->getB()) . ', ' . $this->adapter->toString($this->getPrime()) . ')'; |
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} |
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/** |
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* @return array |
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*/ |
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public function __debugInfo() |
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{ |
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return [ |
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'a' => $this->adapter->toString($this->getA()), |
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'b' => $this->adapter->toString($this->getB()), |
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'prime' => $this->adapter->toString($this->getPrime()) |
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]; |
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} |
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} |
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