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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 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\Random\RandomNumberGenerator; |
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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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final class CurveFp |
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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 GmpMath |
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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 GmpMath $adapter |
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*/ |
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public function __construct(CurveParameters $parameters, GmpMath $adapter) |
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{ |
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$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 \Jose\Component\Core\Util\Ecc\CurveFp::getModAdapter() |
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*/ |
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public function getModAdapter() |
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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 \Jose\Component\Core\Util\Ecc\CurveFp::getPoint() |
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*/ |
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public function getPoint(\GMP $x, \GMP $y, \GMP $order = null) |
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{ |
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return new Point($this->adapter, $this, $x, $y, $order); |
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} |
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/** |
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* {@inheritDoc} |
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* @see \Jose\Component\Core\Util\Ecc\CurveFp::getInfinity() |
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*/ |
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public function getInfinity() |
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{ |
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return new Point($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 \Jose\Component\Core\Util\Ecc\CurveFp::getGenerator() |
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*/ |
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public function getGenerator(\GMP $x, \GMP $y, \GMP $order, RandomNumberGenerator $randomGenerator = null) |
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{ |
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return new GeneratorPoint($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 $xCoord |
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* @return \GMP |
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*/ |
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public function recoverYfromX($wasOdd, \GMP $xCoord) |
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{ |
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$math = $this->adapter; |
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$prime = $this->getPrime(); |
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$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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$prime |
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); |
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if ($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 \Jose\Component\Core\Util\Ecc\CurveFp::contains() |
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*/ |
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public function contains(\GMP $x, \GMP $y) |
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{ |
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$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 \Jose\Component\Core\Util\Ecc\CurveFp::getA() |
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*/ |
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public function getA() |
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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 \Jose\Component\Core\Util\Ecc\CurveFp::getB() |
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*/ |
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public function getB() |
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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 \Jose\Component\Core\Util\Ecc\CurveFp::getPrime() |
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*/ |
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public function getPrime() |
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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() |
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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 \Jose\Component\Core\Util\Ecc\CurveFp::cmp() |
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*/ |
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public function cmp(CurveFp $other) |
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{ |
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$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 \Jose\Component\Core\Util\Ecc\CurveFp::equals() |
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*/ |
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public function equals(CurveFp $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\CurveFp::__toString() |
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*/ |
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public function __toString() |
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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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If you return a value from a function or method, it should be a sub-type of the type that is given by the parent type f.e. an interface, or abstract method. This is more formally defined by the Lizkov substitution principle, and guarantees that classes that depend on the parent type can use any instance of a child type interchangably. This principle also belongs to the SOLID principles for object oriented design.
Let’s take a look at an example:
Our function
my_functionexpects aPostobject, and outputs the author of the post. The base classPostreturns a simple string and outputting a simple string will work just fine. However, the child classBlogPostwhich is a sub-type ofPostinstead decided to return anobject, and is therefore violating the SOLID principles. If aBlogPostwere passed tomy_function, PHP would not complain, but ultimately fail when executing thestrtouppercall in its body.