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   1  <?php
   2  
   3  /**
   4   * Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
   5   *
   6   * http://www.secg.org/SEC2-Ver-1.0.pdf provides for curves with custom parameters.
   7   * ie. the coefficients can be arbitrary set through specially formatted keys, etc.
   8   * As such, Prime.php is built very generically and it's not able to take full
   9   * advantage of curves with 0 coefficients to produce simplified point doubling,
  10   * point addition. Twisted Edwards curves, in contrast, do not have a way, currently,
  11   * to customize them. As such, we can omit the super generic stuff from this class
  12   * and let the named curves (Ed25519 and Ed448) define their own custom tailored
  13   * point addition and point doubling methods.
  14   *
  15   * More info:
  16   *
  17   * https://en.wikipedia.org/wiki/Twisted_Edwards_curve
  18   *
  19   * PHP version 5 and 7
  20   *
  21   * @category  Crypt
  22   * @package   EC
  23   * @author    Jim Wigginton <[email protected]>
  24   * @copyright 2017 Jim Wigginton
  25   * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
  26   * @link      http://pear.php.net/package/Math_BigInteger
  27   */
  28  
  29  namespace phpseclib3\Crypt\EC\BaseCurves;
  30  
  31  use phpseclib3\Math\BigInteger;
  32  use phpseclib3\Math\PrimeField;
  33  use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
  34  
  35  /**
  36   * Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
  37   *
  38   * @package Prime
  39   * @author  Jim Wigginton <[email protected]>
  40   * @access  public
  41   */
  42  class TwistedEdwards extends Base
  43  {
  44      /**
  45       * The modulo
  46       *
  47       * @var BigInteger
  48       */
  49      protected $modulo;
  50  
  51      /**
  52       * Cofficient for x^2
  53       *
  54       * @var object
  55       */
  56      protected $a;
  57  
  58      /**
  59       * Cofficient for x^2*y^2
  60       *
  61       * @var object
  62       */
  63      protected $d;
  64  
  65      /**
  66       * Base Point
  67       *
  68       * @var object[]
  69       */
  70      protected $p;
  71  
  72      /**
  73       * The number zero over the specified finite field
  74       *
  75       * @var object
  76       */
  77      protected $zero;
  78  
  79      /**
  80       * The number one over the specified finite field
  81       *
  82       * @var object
  83       */
  84      protected $one;
  85  
  86      /**
  87       * The number two over the specified finite field
  88       *
  89       * @var object
  90       */
  91      protected $two;
  92  
  93      /**
  94       * Sets the modulo
  95       */
  96      public function setModulo(BigInteger $modulo)
  97      {
  98          $this->modulo = $modulo;
  99          $this->factory = new PrimeField($modulo);
 100          $this->zero = $this->factory->newInteger(new BigInteger(0));
 101          $this->one = $this->factory->newInteger(new BigInteger(1));
 102          $this->two = $this->factory->newInteger(new BigInteger(2));
 103      }
 104  
 105      /**
 106       * Set coefficients a and b
 107       */
 108      public function setCoefficients(BigInteger $a, BigInteger $d)
 109      {
 110          if (!isset($this->factory)) {
 111              throw new \RuntimeException('setModulo needs to be called before this method');
 112          }
 113          $this->a = $this->factory->newInteger($a);
 114          $this->d = $this->factory->newInteger($d);
 115      }
 116  
 117      /**
 118       * Set x and y coordinates for the base point
 119       */
 120      public function setBasePoint($x, $y)
 121      {
 122          switch (true) {
 123              case !$x instanceof BigInteger && !$x instanceof PrimeInteger:
 124                  throw new \UnexpectedValueException('Argument 1 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
 125              case !$y instanceof BigInteger && !$y instanceof PrimeInteger:
 126                  throw new \UnexpectedValueException('Argument 2 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
 127          }
 128          if (!isset($this->factory)) {
 129              throw new \RuntimeException('setModulo needs to be called before this method');
 130          }
 131          $this->p = [
 132              $x instanceof BigInteger ? $this->factory->newInteger($x) : $x,
 133              $y instanceof BigInteger ? $this->factory->newInteger($y) : $y
 134          ];
 135      }
 136  
 137      /**
 138       * Returns the a coefficient
 139       *
 140       * @return \phpseclib3\Math\PrimeField\Integer
 141       */
 142      public function getA()
 143      {
 144          return $this->a;
 145      }
 146  
 147      /**
 148       * Returns the a coefficient
 149       *
 150       * @return \phpseclib3\Math\PrimeField\Integer
 151       */
 152      public function getD()
 153      {
 154          return $this->d;
 155      }
 156  
 157      /**
 158       * Retrieve the base point as an array
 159       *
 160       * @return array
 161       */
 162      public function getBasePoint()
 163      {
 164          if (!isset($this->factory)) {
 165              throw new \RuntimeException('setModulo needs to be called before this method');
 166          }
 167          /*
 168          if (!isset($this->p)) {
 169              throw new \RuntimeException('setBasePoint needs to be called before this method');
 170          }
 171          */
 172          return $this->p;
 173      }
 174  
 175      /**
 176       * Returns the affine point
 177       *
 178       * @return \phpseclib3\Math\PrimeField\Integer[]
 179       */
 180      public function convertToAffine(array $p)
 181      {
 182          if (!isset($p[2])) {
 183              return $p;
 184          }
 185          list($x, $y, $z) = $p;
 186          $z = $this->one->divide($z);
 187          return [
 188              $x->multiply($z),
 189              $y->multiply($z)
 190          ];
 191      }
 192  
 193      /**
 194       * Returns the modulo
 195       *
 196       * @return \phpseclib3\Math\BigInteger
 197       */
 198      public function getModulo()
 199      {
 200          return $this->modulo;
 201      }
 202  
 203      /**
 204       * Tests whether or not the x / y values satisfy the equation
 205       *
 206       * @return boolean
 207       */
 208      public function verifyPoint(array $p)
 209      {
 210          list($x, $y) = $p;
 211          $x2 = $x->multiply($x);
 212          $y2 = $y->multiply($y);
 213  
 214          $lhs = $this->a->multiply($x2)->add($y2);
 215          $rhs = $this->d->multiply($x2)->multiply($y2)->add($this->one);
 216  
 217          return $lhs->equals($rhs);
 218      }
 219  }