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   1  <?php
   2  
   3  /**
   4   * brainpoolP160t1
   5   *
   6   * This curve is a twisted version of brainpoolP160r1 with A = -3. With brainpool,
   7   * the curves ending in r1 are the "regular" curves and the curves ending in "t1"
   8   * are the twisted version of the r1 curves. Per https://tools.ietf.org/html/rfc5639#page-7
   9   * you can convert a point on an r1 curve to a point on a t1 curve thusly:
  10   *
  11   *     F(x,y) := (x*Z^2, y*Z^3)
  12   *
  13   * The advantage of A = -3 is that some of the point doubling and point addition can be
  14   * slightly optimized. See http://hyperelliptic.org/EFD/g1p/auto-shortw-projective-3.html
  15   * vs http://hyperelliptic.org/EFD/g1p/auto-shortw-projective.html for example.
  16   *
  17   * phpseclib does not currently take advantage of this optimization opportunity
  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\Curves;
  30  
  31  use phpseclib3\Crypt\EC\BaseCurves\Prime;
  32  use phpseclib3\Math\BigInteger;
  33  
  34  class brainpoolP160t1 extends Prime
  35  {
  36      public function __construct()
  37      {
  38          $this->setModulo(new BigInteger('E95E4A5F737059DC60DFC7AD95B3D8139515620F', 16));
  39          $this->setCoefficients(
  40              new BigInteger('E95E4A5F737059DC60DFC7AD95B3D8139515620C', 16), // eg. -3
  41              new BigInteger('7A556B6DAE535B7B51ED2C4D7DAA7A0B5C55F380', 16)
  42          );
  43          $this->setBasePoint(
  44              new BigInteger('B199B13B9B34EFC1397E64BAEB05ACC265FF2378', 16),
  45              new BigInteger('ADD6718B7C7C1961F0991B842443772152C9E0AD', 16)
  46          );
  47          $this->setOrder(new BigInteger('E95E4A5F737059DC60DF5991D45029409E60FC09', 16));
  48      }
  49  }