init
This commit is contained in:
@@ -0,0 +1,321 @@
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<?php
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namespace Elliptic\Curve;
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use Elliptic\Utils;
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use \Exception;
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use BN\BN;
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abstract class BaseCurve
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{
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public $type;
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public $p;
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public $red;
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public $zero;
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public $one;
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public $two;
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public $n;
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public $g;
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protected $_wnafT1;
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protected $_wnafT2;
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protected $_wnafT3;
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protected $_wnafT4;
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public $redN;
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public $_maxwellTrick;
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function __construct($type, $conf)
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{
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$this->type = $type;
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$this->p = new BN($conf["p"], 16);
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//Use Montgomery, when there is no fast reduction for the prime
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$this->red = isset($conf["prime"]) ? BN::red($conf["prime"]) : BN::mont($this->p);
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//Useful for many curves
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$this->zero = (new BN(0))->toRed($this->red);
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$this->one = (new BN(1))->toRed($this->red);
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$this->two = (new BN(2))->toRed($this->red);
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//Curve configuration, optional
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$this->n = isset($conf["n"]) ? new BN($conf["n"], 16) : null;
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$this->g = isset($conf["g"]) ? $this->pointFromJSON($conf["g"], isset($conf["gRed"]) ? $conf["gRed"] : null) : null;
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//Temporary arrays
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$this->_wnafT1 = array(0,0,0,0);
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$this->_wnafT2 = array(0,0,0,0);
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$this->_wnafT3 = array(0,0,0,0);
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$this->_wnafT4 = array(0,0,0,0);
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//Generalized Greg Maxwell's trick
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$adjustCount = $this->n != null ? $this->p->div($this->n) : null;
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if( $adjustCount == null || $adjustCount->cmpn(100) > 0 )
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{
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$this->redN = null;
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$this->_maxwellTrick = false;
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}
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else
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{
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$this->redN = $this->n->toRed($this->red);
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$this->_maxwellTrick = true;
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}
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}
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abstract public function point($x, $z);
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abstract public function validate($point);
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public function _fixedNafMul($p, $k)
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{
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assert(isset($p->precomputed));
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$doubles = $p->_getDoubles();
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$naf = Utils::getNAF($k, 1);
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$I = (1 << ($doubles["step"] + 1)) - ($doubles["step"] % 2 == 0 ? 2 : 1);
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$I = $I / 3;
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//Translate to more windowed form
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$repr = array();
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for($j = 0; $j < count($naf); $j += $doubles["step"])
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{
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$nafW = 0;
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for($k = $j + $doubles["step"] - 1; $k >= $j; $k--)
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$nafW = ($nafW << 1) + (isset($naf[$k]) ? $naf[$k] : 0);
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array_push($repr, $nafW);
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}
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$a = $this->jpoint(null, null, null);
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$b = $this->jpoint(null, null, null);
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for($i = $I; $i > 0; $i--)
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{
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for($j = 0; $j < count($repr); $j++)
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{
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$nafW = $repr[$j];
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if ($nafW == $i) {
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$b = $b->mixedAdd($doubles["points"][$j]);
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} else if($nafW == -$i) {
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$b = $b->mixedAdd($doubles["points"][$j]->neg());
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}
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}
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$a = $a->add($b);
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}
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return $a->toP();
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}
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public function _wnafMul($p, $k)
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{
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$w = 4;
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//Precompute window
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$nafPoints = $p->_getNAFPoints($w);
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$w = $nafPoints["wnd"];
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$wnd = $nafPoints["points"];
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//Get NAF form
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$naf = Utils::getNAF($k, $w);
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//Add `this`*(N+1) for every w-NAF index
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$acc = $this->jpoint(null, null, null);
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for($i = count($naf) - 1; $i >= 0; $i--)
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{
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//Count zeros
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for($k = 0; $i >= 0 && $naf[$i] == 0; $i--)
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$k++;
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if($i >= 0)
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$k++;
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$acc = $acc->dblp($k);
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if($i < 0)
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break;
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$z = $naf[$i];
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assert($z != 0);
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if( $p->type == "affine" )
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{
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//J +- P
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if( $z > 0 )
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$acc = $acc->mixedAdd($wnd[($z - 1) >> 1]);
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else
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$acc = $acc->mixedAdd($wnd[(-$z - 1) >> 1]->neg());
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}
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else
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{
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//J +- J
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if( $z > 0 )
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$acc = $acc->add($wnd[($z - 1) >> 1]);
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else
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$acc = $acc->add($wnd[(-$z - 1) >> 1]->neg());
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}
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}
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return $p->type == "affine" ? $acc->toP() : $acc;
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}
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public function _wnafMulAdd($defW, $points, $coeffs, $len, $jacobianResult = false)
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{
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$wndWidth = &$this->_wnafT1;
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$wnd = &$this->_wnafT2;
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$naf = &$this->_wnafT3;
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//Fill all arrays
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$max = 0;
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for($i = 0; $i < $len; $i++)
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{
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$p = $points[$i];
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$nafPoints = $p->_getNAFPoints($defW);
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$wndWidth[$i] = $nafPoints["wnd"];
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$wnd[$i] = $nafPoints["points"];
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}
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//Comb all window NAFs
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for($i = $len - 1; $i >= 1; $i -= 2)
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{
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$a = $i - 1;
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$b = $i;
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if( $wndWidth[$a] != 1 || $wndWidth[$b] != 1 )
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{
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$naf[$a] = Utils::getNAF($coeffs[$a], $wndWidth[$a]);
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$naf[$b] = Utils::getNAF($coeffs[$b], $wndWidth[$b]);
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$max = max(count($naf[$a]), $max);
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$max = max(count($naf[$b]), $max);
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continue;
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}
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$comb = array(
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$points[$a], /* 1 */
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null, /* 3 */
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null, /* 5 */
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$points[$b] /* 7 */
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);
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//Try to avoid Projective points, if possible
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if( $points[$a]->y->cmp($points[$b]->y) == 0 )
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{
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$comb[1] = $points[$a]->add($points[$b]);
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$comb[2] = $points[$a]->toJ()->mixedAdd($points[$b]->neg());
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}
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elseif( $points[$a]->y->cmp($points[$b]->y->redNeg()) == 0 )
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{
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$comb[1] = $points[$a]->toJ()->mixedAdd($points[$b]);
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$comb[2] = $points[$a]->add($points[$b]->neg());
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}
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else
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{
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$comb[1] = $points[$a]->toJ()->mixedAdd($points[$b]);
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$comb[2] = $points[$a]->toJ()->mixedAdd($points[$b]->neg());
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}
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$index = array(
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-3, /* -1 -1 */
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-1, /* -1 0 */
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-5, /* -1 1 */
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-7, /* 0 -1 */
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0, /* 0 0 */
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7, /* 0 1 */
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5, /* 1 -1 */
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1, /* 1 0 */
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3 /* 1 1 */
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);
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$jsf = Utils::getJSF($coeffs[$a], $coeffs[$b]);
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$max = max(count($jsf[0]), $max);
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if ($max > 0) {
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$naf[$a] = array_fill(0, $max, 0);
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$naf[$b] = array_fill(0, $max, 0);
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} else {
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$naf[$a] = [];
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$naf[$b] = [];
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}
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for($j = 0; $j < $max; $j++)
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{
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$ja = isset($jsf[0][$j]) ? $jsf[0][$j] : 0;
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$jb = isset($jsf[1][$j]) ? $jsf[1][$j] : 0;
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$naf[$a][$j] = $index[($ja + 1) * 3 + ($jb + 1)];
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$naf[$b][$j] = 0;
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$wnd[$a] = $comb;
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}
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}
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$acc = $this->jpoint(null, null, null);
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$tmp = &$this->_wnafT4;
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for($i = $max; $i >= 0; $i--)
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{
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$k = 0;
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while($i >= 0)
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{
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$zero = true;
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for($j = 0; $j < $len; $j++)
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{
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$tmp[$j] = isset($naf[$j][$i]) ? $naf[$j][$i] : 0;
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if( $tmp[$j] != 0 )
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$zero = false;
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}
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if( !$zero )
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break;
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$k++;
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$i--;
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}
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if( $i >=0 )
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$k++;
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$acc = $acc->dblp($k);
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if( $i < 0 )
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break;
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for($j = 0; $j < $len; $j++)
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{
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$z = $tmp[$j];
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$p = null;
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if( $z == 0 )
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continue;
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elseif( $z > 0 )
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$p = $wnd[$j][($z - 1) >> 1];
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elseif( $z < 0 )
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$p = $wnd[$j][(-$z - 1) >> 1]->neg();
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if( $p->type == "affine" )
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$acc = $acc->mixedAdd($p);
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else
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$acc = $acc->add($p);
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}
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}
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//Zeroify references
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for($i = 0; $i < $len; $i++)
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$wnd[$i] = null;
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if( $jacobianResult )
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return $acc;
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else
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return $acc->toP();
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}
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public function decodePoint($bytes, $enc = false)
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{
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$bytes = Utils::toArray($bytes, $enc);
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$len = $this->p->byteLength();
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$count = count($bytes);
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//uncompressed, hybrid-odd, hybrid-even
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if(($bytes[0] == 0x04 || $bytes[0] == 0x06 || $bytes[0] == 0x07) && ($count - 1) == (2 * $len) )
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{
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if( $bytes[0] == 0x06 )
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assert($bytes[$count - 1] % 2 == 0);
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elseif( $bytes[0] == 0x07 )
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assert($bytes[$count - 1] % 2 == 1);
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return $this->point(array_slice($bytes, 1, $len), array_slice($bytes, 1 + $len, $len));
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}
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if( ($bytes[0] == 0x02 || $bytes[0] == 0x03) && ($count - 1) == $len )
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return $this->pointFromX(array_slice($bytes, 1, $len), $bytes[0] == 0x03);
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throw new Exception("Unknown point format");
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}
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}
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?>
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@@ -0,0 +1,120 @@
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<?php
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namespace Elliptic\Curve\BaseCurve;
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use Elliptic\Utils;
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abstract class Point
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{
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public $curve;
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public $type;
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public $precomputed;
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function __construct($curve, $type)
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{
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$this->curve = $curve;
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$this->type = $type;
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$this->precomputed = null;
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}
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abstract public function eq($other);
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public function validate() {
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return $this->curve->validate($this);
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}
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public function encodeCompressed($enc) {
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return $this->encode($enc, true);
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}
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public function encode($enc, $compact = false) {
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return Utils::encode($this->_encode($compact), $enc);
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}
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protected function _encode($compact)
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{
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$len = $this->curve->p->byteLength();
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$x = $this->getX()->toArray("be", $len);
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if( $compact )
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{
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array_unshift($x, ($this->getY()->isEven() ? 0x02 : 0x03));
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return $x;
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}
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return array_merge(array(0x04), $x, $this->getY()->toArray("be", $len));
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}
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public function precompute($power = null)
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{
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if( isset($this->precomputed) )
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return $this;
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$this->precomputed = array(
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"naf" => $this->_getNAFPoints(8),
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"doubles" => $this->_getDoubles(4, $power),
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"beta" => $this->_getBeta()
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);
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return $this;
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}
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protected function _hasDoubles($k)
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{
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if( !isset($this->precomputed) || !isset($this->precomputed["doubles"]) )
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return false;
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return count($this->precomputed["doubles"]["points"]) >= ceil(($k->bitLength() + 1) / $this->precomputed["doubles"]["step"]);
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}
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public function _getDoubles($step = null, $power = null)
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{
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if( isset($this->precomputed) && isset($this->precomputed["doubles"]) )
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return $this->precomputed["doubles"];
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$doubles = array( $this );
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$acc = $this;
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for($i = 0; $i < $power; $i += $step)
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{
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for($j = 0; $j < $step; $j++)
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$acc = $acc->dbl();
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array_push($doubles, $acc);
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}
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return array(
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"step" => $step,
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"points" => $doubles
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);
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}
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public function _getNAFPoints($wnd)
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{
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if( isset($this->precomputed) && isset($this->precomputed["naf"]) )
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return $this->precomputed["naf"];
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$res = array( $this );
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$max = (1 << $wnd) - 1;
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$dbl = $max === 1 ? null : $this->dbl();
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for($i = 1; $i < $max; $i++)
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array_push($res, $res[$i - 1]->add($dbl));
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return array(
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"wnd" => $wnd,
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"points" => $res
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);
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}
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public function _getBeta() {
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return null;
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}
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public function dblp($k)
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{
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$r = $this;
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for($i = 0; $i < $k; $i++)
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$r = $r->dbl();
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return $r;
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}
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}
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||||
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?>
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@@ -0,0 +1,131 @@
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<?php
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namespace Elliptic\Curve;
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use Elliptic\Curve\EdwardsCurve\Point;
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use Elliptic\Utils;
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use BN\BN;
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class EdwardsCurve extends BaseCurve
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{
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public $twisted;
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public $mOneA;
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public $extended;
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public $a;
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public $c;
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public $c2;
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public $d;
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public $d2;
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public $dd;
|
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public $oneC;
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function __construct($conf)
|
||||
{
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// NOTE: Important as we are creating point in Base.call()
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$this->twisted = ($conf["a"] | 0) != 1;
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$this->mOneA = $this->twisted && ($conf["a"] | 0) == -1;
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$this->extended = $this->mOneA;
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parent::__construct("edward", $conf);
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$this->a = (new BN($conf["a"], 16))->umod($this->red->m);
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$this->a = $this->a->toRed($this->red);
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$this->c = (new BN($conf["c"], 16))->toRed($this->red);
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$this->c2 = $this->c->redSqr();
|
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$this->d = (new BN($conf["d"], 16))->toRed($this->red);
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$this->dd = $this->d->redAdd($this->d);
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if (Utils::$ASSERT_ENABLED) {
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assert(!$this->twisted || $this->c->fromRed()->cmpn(1) == 0);
|
||||
}
|
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$this->oneC = ($conf["c"] | 0) == 1;
|
||||
}
|
||||
|
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public function _mulA($num) {
|
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if ($this->mOneA)
|
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return $num->redNeg();
|
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else
|
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return $this->a->redMul($num);
|
||||
}
|
||||
|
||||
public function _mulC($num) {
|
||||
if ($this->oneC)
|
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return $num;
|
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else
|
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return $this->c->redMul($num);
|
||||
}
|
||||
|
||||
// Just for compatibility with Short curve
|
||||
public function jpoint($x, $y, $z, $t = null) {
|
||||
return $this->point($x, $y, $z, $t);
|
||||
}
|
||||
|
||||
public function pointFromX($x, $odd = false) {
|
||||
$x = new BN($x, 16);
|
||||
if (!$x->red)
|
||||
$x = $x->toRed($this->red);
|
||||
|
||||
$x2 = $x->redSqr();
|
||||
$rhs = $this->c2->redSub($this->a->redMul($x2));
|
||||
$lhs = $this->one->redSub($this->c2->redMul($this->d)->redMul($x2));
|
||||
|
||||
$y2 = $rhs->redMul($lhs->redInvm());
|
||||
$y = $y2->redSqrt();
|
||||
if ($y->redSqr()->redSub($y2)->cmp($this->zero) != 0)
|
||||
throw new \Exception('invalid point');
|
||||
|
||||
$isOdd = $y->fromRed()->isOdd();
|
||||
if ($odd && !$isOdd || !$odd && $isOdd)
|
||||
$y = $y->redNeg();
|
||||
|
||||
return $this->point($x, $y);
|
||||
}
|
||||
|
||||
public function pointFromY($y, $odd = false) {
|
||||
$y = new BN($y, 16);
|
||||
if (!$y->red)
|
||||
$y = $y->toRed($this->red);
|
||||
|
||||
// x^2 = (y^2 - 1) / (d y^2 + 1)
|
||||
$y2 = $y->redSqr();
|
||||
$lhs = $y2->redSub($this->one);
|
||||
$rhs = $y2->redMul($this->d)->redAdd($this->one);
|
||||
$x2 = $lhs->redMul($rhs->redInvm());
|
||||
|
||||
if ($x2->cmp($this->zero) == 0) {
|
||||
if ($odd)
|
||||
throw new \Exception('invalid point');
|
||||
else
|
||||
return $this->point($this->zero, $y);
|
||||
}
|
||||
|
||||
$x = $x2->redSqrt();
|
||||
if ($x->redSqr()->redSub($x2)->cmp($this->zero) != 0)
|
||||
throw new \Exception('invalid point');
|
||||
|
||||
if ($x->isOdd() != $odd)
|
||||
$x = $x->redNeg();
|
||||
|
||||
return $this->point($x, $y);
|
||||
}
|
||||
|
||||
public function validate($point) {
|
||||
if ($point->isInfinity())
|
||||
return true;
|
||||
|
||||
// Curve: A * X^2 + Y^2 = C^2 * (1 + D * X^2 * Y^2)
|
||||
$point->normalize();
|
||||
|
||||
$x2 = $point->x->redSqr();
|
||||
$y2 = $point->y->redSqr();
|
||||
$lhs = $x2->redMul($this->a)->redAdd($y2);
|
||||
$rhs = $this->c2->redMul($this->one->redAdd($this->d->redMul($x2)->redMul($y2)));
|
||||
|
||||
return $lhs->cmp($rhs) == 0;
|
||||
}
|
||||
|
||||
public function pointFromJSON($obj) {
|
||||
return Point::fromJSON($this, $obj);
|
||||
}
|
||||
|
||||
public function point($x = null, $y = null, $z = null, $t = null) {
|
||||
return new Point($this, $x, $y, $z, $t);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,323 @@
|
||||
<?php
|
||||
namespace Elliptic\Curve\EdwardsCurve;
|
||||
|
||||
use BN\BN;
|
||||
|
||||
class Point extends \Elliptic\Curve\BaseCurve\Point
|
||||
{
|
||||
public $x;
|
||||
public $y;
|
||||
public $z;
|
||||
public $t;
|
||||
public $zOne;
|
||||
|
||||
function __construct($curve, $x = null, $y = null, $z = null, $t = null) {
|
||||
parent::__construct($curve, 'projective');
|
||||
if ($x == null && $y == null && $z == null) {
|
||||
$this->x = $this->curve->zero;
|
||||
$this->y = $this->curve->one;
|
||||
$this->z = $this->curve->one;
|
||||
$this->t = $this->curve->zero;
|
||||
$this->zOne = true;
|
||||
} else {
|
||||
$this->x = new BN($x, 16);
|
||||
$this->y = new BN($y, 16);
|
||||
$this->z = $z ? new BN($z, 16) : $this->curve->one;
|
||||
$this->t = $t ? new BN($t, 16) : null;
|
||||
if (!$this->x->red)
|
||||
$this->x = $this->x->toRed($this->curve->red);
|
||||
if (!$this->y->red)
|
||||
$this->y = $this->y->toRed($this->curve->red);
|
||||
if (!$this->z->red)
|
||||
$this->z = $this->z->toRed($this->curve->red);
|
||||
if ($this->t && !$this->t->red)
|
||||
$this->t = $this->t->toRed($this->curve->red);
|
||||
$this->zOne = $this->z == $this->curve->one;
|
||||
|
||||
// Use extended coordinates
|
||||
if ($this->curve->extended && !$this->t) {
|
||||
$this->t = $this->x->redMul($this->y);
|
||||
if (!$this->zOne)
|
||||
$this->t = $this->t->redMul($this->z->redInvm());
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
public static function fromJSON($curve, $obj) {
|
||||
return new Point($curve,
|
||||
isset($obj[0]) ? $obj[0] : null,
|
||||
isset($obj[1]) ? $obj[1] : null,
|
||||
isset($obj[2]) ? $obj[2] : null
|
||||
);
|
||||
}
|
||||
|
||||
public function inspect() {
|
||||
if ($this->isInfinity())
|
||||
return '<EC Point Infinity>';
|
||||
return '<EC Point x: ' . $this->x->fromRed()->toString(16, 2) .
|
||||
' y: ' . $this->y->fromRed()->toString(16, 2) .
|
||||
' z: ' . $this->z->fromRed()->toString(16, 2) . '>';
|
||||
}
|
||||
|
||||
public function isInfinity() {
|
||||
// XXX This code assumes that zero is always zero in red
|
||||
return $this->x->cmpn(0) == 0 &&
|
||||
$this->y->cmp($this->z) == 0;
|
||||
}
|
||||
|
||||
public function _extDbl() {
|
||||
// hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
|
||||
// #doubling-dbl-2008-hwcd
|
||||
// 4M + 4S
|
||||
|
||||
// A = X1^2
|
||||
$a = $this->x->redSqr();
|
||||
// B = Y1^2
|
||||
$b = $this->y->redSqr();
|
||||
// C = 2 * Z1^2
|
||||
$c = $this->z->redSqr();
|
||||
$c = $c->redIAdd($c);
|
||||
// D = a * A
|
||||
$d = $this->curve->_mulA($a);
|
||||
// E = (X1 + Y1)^2 - A - B
|
||||
$e = $this->x->redAdd($this->y)->redSqr()->redISub($a)->redISub($b);
|
||||
// G = D + B
|
||||
$g = $d->redAdd($b);
|
||||
// F = G - C
|
||||
$f = $g->redSub($c);
|
||||
// H = D - B
|
||||
$h = $d->redSub($b);
|
||||
// X3 = E * F
|
||||
$nx = $e->redMul($f);
|
||||
// Y3 = G * H
|
||||
$ny = $g->redMul($h);
|
||||
// T3 = E * H
|
||||
$nt = $e->redMul($h);
|
||||
// Z3 = F * G
|
||||
$nz = $f->redMul($g);
|
||||
return $this->curve->point($nx, $ny, $nz, $nt);
|
||||
}
|
||||
|
||||
public function _projDbl() {
|
||||
// hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
|
||||
// #doubling-dbl-2008-bbjlp
|
||||
// #doubling-dbl-2007-bl
|
||||
// and others
|
||||
// Generally 3M + 4S or 2M + 4S
|
||||
|
||||
// B = (X1 + Y1)^2
|
||||
$b = $this->x->redAdd($this->y)->redSqr();
|
||||
// C = X1^2
|
||||
$c = $this->x->redSqr();
|
||||
// D = Y1^2
|
||||
$d = $this->y->redSqr();
|
||||
|
||||
if ($this->curve->twisted) {
|
||||
// E = a * C
|
||||
$e = $this->curve->_mulA($c);
|
||||
// F = E + D
|
||||
$f = $e->redAdd($d);
|
||||
if ($this->zOne) {
|
||||
// X3 = (B - C - D) * (F - 2)
|
||||
$nx = $b->redSub($c)->redSub($d)->redMul($f->redSub($this->curve->two));
|
||||
// Y3 = F * (E - D)
|
||||
$ny = $f->redMul($e->redSub($d));
|
||||
// Z3 = F^2 - 2 * F
|
||||
$nz = $f->redSqr()->redSub($f)->redSub($f);
|
||||
} else {
|
||||
// H = Z1^2
|
||||
$h = $this->z->redSqr();
|
||||
// J = F - 2 * H
|
||||
$j = $f->redSub($h)->redISub($h);
|
||||
// X3 = (B-C-D)*J
|
||||
$nx = $b->redSub($c)->redISub($d)->redMul($j);
|
||||
// Y3 = F * (E - D)
|
||||
$ny = $f->redMul($e->redSub($d));
|
||||
// Z3 = F * J
|
||||
$nz = $f->redMul($j);
|
||||
}
|
||||
} else {
|
||||
// E = C + D
|
||||
$e = $c->redAdd($d);
|
||||
// H = (c * Z1)^2
|
||||
$h = $this->curve->_mulC($this->c->redMul($this->z))->redSqr();
|
||||
// J = E - 2 * H
|
||||
$j = $e->redSub($h)->redSub($h);
|
||||
// X3 = c * (B - E) * J
|
||||
$nx = $this->curve->_mulC($b->redISub($e))->redMul($j);
|
||||
// Y3 = c * E * (C - D)
|
||||
$ny = $this->curve->_mulC($e)->redMul($c->redISub($d));
|
||||
// Z3 = E * J
|
||||
$nz = $e->redMul($j);
|
||||
}
|
||||
return $this->curve->point($nx, $ny, $nz);
|
||||
}
|
||||
|
||||
public function dbl() {
|
||||
if ($this->isInfinity())
|
||||
return $this;
|
||||
|
||||
// Double in extended coordinates
|
||||
if ($this->curve->extended)
|
||||
return $this->_extDbl();
|
||||
else
|
||||
return $this->_projDbl();
|
||||
}
|
||||
|
||||
public function _extAdd($p) {
|
||||
// hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
|
||||
// #addition-add-2008-hwcd-3
|
||||
// 8M
|
||||
|
||||
// A = (Y1 - X1) * (Y2 - X2)
|
||||
$a = $this->y->redSub($this->x)->redMul($p->y->redSub($p->x));
|
||||
// B = (Y1 + X1) * (Y2 + X2)
|
||||
$b = $this->y->redAdd($this->x)->redMul($p->y->redAdd($p->x));
|
||||
// C = T1 * k * T2
|
||||
$c = $this->t->redMul($this->curve->dd)->redMul($p->t);
|
||||
// D = Z1 * 2 * Z2
|
||||
$d = $this->z->redMul($p->z->redAdd($p->z));
|
||||
// E = B - A
|
||||
$e = $b->redSub($a);
|
||||
// F = D - C
|
||||
$f = $d->redSub($c);
|
||||
// G = D + C
|
||||
$g = $d->redAdd($c);
|
||||
// H = B + A
|
||||
$h = $b->redAdd($a);
|
||||
// X3 = E * F
|
||||
$nx = $e->redMul($f);
|
||||
// Y3 = G * H
|
||||
$ny = $g->redMul($h);
|
||||
// T3 = E * H
|
||||
$nt = $e->redMul($h);
|
||||
// Z3 = F * G
|
||||
$nz = $f->redMul($g);
|
||||
return $this->curve->point($nx, $ny, $nz, $nt);
|
||||
}
|
||||
|
||||
public function _projAdd($p) {
|
||||
// hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
|
||||
// #addition-add-2008-bbjlp
|
||||
// #addition-add-2007-bl
|
||||
// 10M + 1S
|
||||
|
||||
// A = Z1 * Z2
|
||||
$a = $this->z->redMul($p->z);
|
||||
// B = A^2
|
||||
$b = $a->redSqr();
|
||||
// C = X1 * X2
|
||||
$c = $this->x->redMul($p->x);
|
||||
// D = Y1 * Y2
|
||||
$d = $this->y->redMul($p->y);
|
||||
// E = d * C * D
|
||||
$e = $this->curve->d->redMul($c)->redMul($d);
|
||||
// F = B - E
|
||||
$f = $b->redSub($e);
|
||||
// G = B + E
|
||||
$g = $b->redAdd($e);
|
||||
// X3 = A * F * ((X1 + Y1) * (X2 + Y2) - C - D)
|
||||
$tmp = $this->x->redAdd($this->y)->redMul($p->x->redAdd($p->y))->redISub($c)->redISub($d);
|
||||
$nx = $a->redMul($f)->redMul($tmp);
|
||||
if ($this->curve->twisted) {
|
||||
// Y3 = A * G * (D - a * C)
|
||||
$ny = $a->redMul($g)->redMul($d->redSub($this->curve->_mulA($c)));
|
||||
// Z3 = F * G
|
||||
$nz = $f->redMul($g);
|
||||
} else {
|
||||
// Y3 = A * G * (D - C)
|
||||
$ny = $a->redMul($g)->redMul($d->redSub($c));
|
||||
// Z3 = c * F * G
|
||||
$nz = $this->curve->_mulC($f)->redMul($g);
|
||||
}
|
||||
return $this->curve->point($nx, $ny, $nz);
|
||||
}
|
||||
|
||||
public function add($p) {
|
||||
if ($this->isInfinity())
|
||||
return $p;
|
||||
if ($p->isInfinity())
|
||||
return $this;
|
||||
|
||||
if ($this->curve->extended)
|
||||
return $this->_extAdd($p);
|
||||
else
|
||||
return $this->_projAdd($p);
|
||||
}
|
||||
|
||||
public function mul($k) {
|
||||
if ($this->_hasDoubles($k))
|
||||
return $this->curve->_fixedNafMul($this, $k);
|
||||
else
|
||||
return $this->curve->_wnafMul($this, $k);
|
||||
}
|
||||
|
||||
public function mulAdd($k1, $p, $k2) {
|
||||
return $this->curve->_wnafMulAdd(1, [ $this, $p ], [ $k1, $k2 ], 2, false);
|
||||
}
|
||||
|
||||
public function jmulAdd($k1, $p, $k2) {
|
||||
return $this->curve->_wnafMulAdd(1, [ $this, $p ], [ $k1, $k2 ], 2, true);
|
||||
}
|
||||
|
||||
public function normalize() {
|
||||
if ($this->zOne)
|
||||
return $this;
|
||||
|
||||
// Normalize coordinates
|
||||
$zi = $this->z->redInvm();
|
||||
$this->x = $this->x->redMul($zi);
|
||||
$this->y = $this->y->redMul($zi);
|
||||
if ($this->t)
|
||||
$this->t = $this->t->redMul($zi);
|
||||
$this->z = $this->curve->one;
|
||||
$this->zOne = true;
|
||||
return $this;
|
||||
}
|
||||
|
||||
public function neg() {
|
||||
return $this->curve->point($this->x->redNeg(),
|
||||
$this->y,
|
||||
$this->z,
|
||||
($this->t != null) ? $this->t->redNeg() : null);
|
||||
}
|
||||
|
||||
public function getX() {
|
||||
$this->normalize();
|
||||
return $this->x->fromRed();
|
||||
}
|
||||
|
||||
public function getY() {
|
||||
$this->normalize();
|
||||
return $this->y->fromRed();
|
||||
}
|
||||
|
||||
public function eq($other) {
|
||||
return $this == $other ||
|
||||
$this->getX()->cmp($other->getX()) == 0 &&
|
||||
$this->getY()->cmp($other->getY()) == 0;
|
||||
}
|
||||
|
||||
public function eqXToP($x) {
|
||||
$rx = $x->toRed($this->curve->red)->redMul($this->z);
|
||||
if ($this->x->cmp($rx) == 0)
|
||||
return true;
|
||||
|
||||
$xc = $x->_clone();
|
||||
$t = $this->curve->redN->redMul($this->z);
|
||||
for (;;) {
|
||||
$xc->iadd($this->curve->n);
|
||||
if ($xc->cmp($this->curve->p) >= 0)
|
||||
return false;
|
||||
|
||||
$rx->redIAdd($t);
|
||||
if ($this->x->cmp($rx) == 0)
|
||||
return true;
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
||||
// Compatibility with BaseCurve
|
||||
public function toP() { return $this->normalize(); }
|
||||
public function mixedAdd($p) { return $this->add($p); }
|
||||
}
|
||||
@@ -0,0 +1,49 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic\Curve;
|
||||
|
||||
use Elliptic\Curve\MontCurve\Point;
|
||||
use Elliptic\Utils;
|
||||
use BN\BN;
|
||||
|
||||
class MontCurve extends BaseCurve
|
||||
{
|
||||
public $a;
|
||||
public $b;
|
||||
public $i4;
|
||||
public $a24;
|
||||
|
||||
function __construct($conf)
|
||||
{
|
||||
parent::__construct("mont", $conf);
|
||||
|
||||
$this->a = (new BN($conf["a"], 16))->toRed($this->red);
|
||||
$this->b = (new BN($conf["b"], 16))->toRed($this->red);
|
||||
$this->i4 = (new BN(4))->toRed($this->red)->redInvm();
|
||||
$this->a24 = $this->i4->redMul($this->a->redAdd($this->two));
|
||||
}
|
||||
|
||||
public function validate($point)
|
||||
{
|
||||
$x = $point->normalize()->x;
|
||||
$x2 = $x->redSqr();
|
||||
$rhs = $x2->redMul($x)->redAdd($x2->redMul($this->a))->redAdd($x);
|
||||
$y = $rhs->redSqr();
|
||||
|
||||
return $y->redSqr()->cmp($rhs) ===0;
|
||||
}
|
||||
|
||||
public function decodePoint($bytes, $enc = false) {
|
||||
return $this->point(Utils::toArray($bytes, $enc), 1);
|
||||
}
|
||||
|
||||
public function point($x, $z) {
|
||||
return new Point($this, $x, $z);
|
||||
}
|
||||
|
||||
public function pointFromJSON($obj) {
|
||||
return Point::fromJSON($this, $obj);
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
@@ -0,0 +1,160 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic\Curve\MontCurve;
|
||||
|
||||
use BN\BN;
|
||||
|
||||
class Point extends \Elliptic\Curve\BaseCurve\Point
|
||||
{
|
||||
public $x;
|
||||
public $z;
|
||||
|
||||
function __construct($curve, $x, $z)
|
||||
{
|
||||
parent::__construct($curve, "projective");
|
||||
if( $x == null && $z == null )
|
||||
{
|
||||
$this->x = $this->curve->one;
|
||||
$this->z = $this->curve->zero;
|
||||
}
|
||||
else
|
||||
{
|
||||
$this->x = new BN($x, 16);
|
||||
$this->z = new BN($z, 16);
|
||||
if( !$this->x->red )
|
||||
$this->x = $this->x->toRed($this->curve->red);
|
||||
if( !$this->z->red )
|
||||
$this->z = $this->z->toRed($this->curve->red);
|
||||
}
|
||||
}
|
||||
|
||||
public function precompute($power = null) {
|
||||
// No-op
|
||||
}
|
||||
|
||||
protected function _encode($compact) {
|
||||
return $this->getX()->toArray("be", $this->curve->p->byteLength());
|
||||
}
|
||||
|
||||
public static function fromJSON($curve, $obj) {
|
||||
return new Point($curve, $obj[0], isset($obj[1]) ? $obj[1] : $curve->one);
|
||||
}
|
||||
|
||||
public function inspect()
|
||||
{
|
||||
if( $this->isInfinity() )
|
||||
return "<EC Point Infinity>";
|
||||
return "<EC Point x: " . $this->x->fromRed()->toString(16, 2) .
|
||||
" z: " . $this->z->fromRed()->toString(16, 2) . ">";
|
||||
}
|
||||
|
||||
public function isInfinity() {
|
||||
// XXX This code assumes that zero is always zero in red
|
||||
return $this->z->isZero();
|
||||
}
|
||||
|
||||
public function dbl()
|
||||
{
|
||||
// http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#doubling-dbl-1987-m-3
|
||||
// 2M + 2S + 4A
|
||||
|
||||
// A = X1 + Z1
|
||||
$a = $this->x->redAdd($this->z);
|
||||
// AA = A^2
|
||||
$aa = $a->redSqr();
|
||||
// B = X1 - Z1
|
||||
$b = $this->x->redSub($this->z);
|
||||
// BB = B^2
|
||||
$bb = $b->redSqr();
|
||||
// C = AA - BB
|
||||
$c = $aa->redSub($bb);
|
||||
// X3 = AA * BB
|
||||
$nx = $aa->redMul($bb);
|
||||
// Z3 = C * (BB + A24 * C)
|
||||
$nz = $c->redMul( $bb->redAdd($this->curve->a24->redMul($c)) );
|
||||
return $this->curve->point($nx, $nz);
|
||||
}
|
||||
|
||||
public function add($p) {
|
||||
throw new \Exception('Not supported on Montgomery curve');
|
||||
}
|
||||
|
||||
public function diffAdd($p, $diff)
|
||||
{
|
||||
// http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#diffadd-dadd-1987-m-3
|
||||
// 4M + 2S + 6A
|
||||
|
||||
// A = X2 + Z2
|
||||
$a = $this->x->redAdd($this->z);
|
||||
// B = X2 - Z2
|
||||
$b = $this->x->redSub($this->z);
|
||||
// C = X3 + Z3
|
||||
$c = $p->x->redAdd($p->z);
|
||||
// D = X3 - Z3
|
||||
$d = $p->x->redSub($p->z);
|
||||
// DA = D * A
|
||||
$da = $d->redMul($a);
|
||||
// CB = C * B
|
||||
$cb = $c->redMul($b);
|
||||
// X5 = Z1 * (DA + CB)^2
|
||||
$nx = $diff->z->redMul($da->redAdd($cb)->redSqr());
|
||||
// Z5 = X1 * (DA - CB)^2
|
||||
$nz = $diff->x->redMul($da->redSub($cb)->redSqr());
|
||||
|
||||
return $this->curve->point($nx, $nz);
|
||||
}
|
||||
|
||||
public function mul($k)
|
||||
{
|
||||
$t = $k->_clone();
|
||||
$a = $this; // (N / 2) * Q + Q
|
||||
$b = $this->curve->point(null, null); // (N / 2) * Q
|
||||
$c = $this; // Q
|
||||
|
||||
$bits = array();
|
||||
while( !$t->isZero() )
|
||||
{
|
||||
// TODO: Maybe it is faster to use toString(2)?
|
||||
array_push($bits, $t->andln(1));
|
||||
$t->iushrn(1);
|
||||
}
|
||||
|
||||
for($i = count($bits) - 1; $i >= 0; $i--)
|
||||
{
|
||||
if( $bits[$i] === 0 )
|
||||
{
|
||||
// N * Q + Q = ((N / 2) * Q + Q)) + (N / 2) * Q
|
||||
$a = $a->diffAdd($b, $c);
|
||||
// N * Q = 2 * ((N / 2) * Q + Q))
|
||||
$b = $b->dbl();
|
||||
}
|
||||
else
|
||||
{
|
||||
// N * Q = ((N / 2) * Q + Q) + ((N / 2) * Q)
|
||||
$b = $a->diffAdd($b, $c);
|
||||
// N * Q + Q = 2 * ((N / 2) * Q + Q)
|
||||
$a = $a->dbl();
|
||||
}
|
||||
}
|
||||
|
||||
return $b;
|
||||
}
|
||||
|
||||
public function eq($other) {
|
||||
return $this->getX()->cmp($other->getX()) === 0;
|
||||
}
|
||||
|
||||
public function normalize()
|
||||
{
|
||||
$this->x = $this->x->redMul($this->z->redInvm());
|
||||
$this->z = $this->curve->one;
|
||||
return $this;
|
||||
}
|
||||
|
||||
public function getX() {
|
||||
$this->normalize();
|
||||
return $this->x->fromRed();
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
@@ -0,0 +1,27 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic\Curve;
|
||||
|
||||
class PresetCurve
|
||||
{
|
||||
public $curve;
|
||||
public $g;
|
||||
public $n;
|
||||
public $hash;
|
||||
|
||||
function __construct($options)
|
||||
{
|
||||
if ( $options["type"] === "short" )
|
||||
$this->curve = new ShortCurve($options);
|
||||
elseif ( $options["type"] === "edwards" )
|
||||
$this->curve = new EdwardsCurve($options);
|
||||
else
|
||||
$this->curve = new MontCurve($options);
|
||||
|
||||
$this->g = $this->curve->g;
|
||||
$this->n = $this->curve->n;
|
||||
$this->hash = isset($options["hash"]) ? $options["hash"] : null;
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
@@ -0,0 +1,305 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic\Curve;
|
||||
|
||||
use Elliptic\Curve\ShortCurve\Point;
|
||||
use Elliptic\Curve\ShortCurve\JPoint;
|
||||
use Elliptic\Utils;
|
||||
use BN\BN;
|
||||
use \Exception;
|
||||
|
||||
class ShortCurve extends BaseCurve
|
||||
{
|
||||
public $a;
|
||||
public $b;
|
||||
public $tinv;
|
||||
public $zeroA;
|
||||
public $threeA;
|
||||
public $endo;
|
||||
private $_endoWnafT1;
|
||||
private $_endoWnafT2;
|
||||
|
||||
function __construct($conf)
|
||||
{
|
||||
parent::__construct("short", $conf);
|
||||
|
||||
$this->a = (new BN($conf["a"], 16))->toRed($this->red);
|
||||
$this->b = (new BN($conf["b"], 16))->toRed($this->red);
|
||||
$this->tinv = $this->two->redInvm();
|
||||
|
||||
$this->zeroA = $this->a->fromRed()->isZero();
|
||||
$this->threeA = $this->a->fromRed()->sub($this->p)->cmpn(-3) === 0;
|
||||
|
||||
// If curve is endomorphic, precalculate beta and lambda
|
||||
$this->endo = $this->_getEndomorphism($conf);
|
||||
$this->_endoWnafT1 = array(0,0,0,0);
|
||||
$this->_endoWnafT2 = array(0,0,0,0);
|
||||
}
|
||||
|
||||
private function _getEndomorphism($conf)
|
||||
{
|
||||
// No efficient endomorphism
|
||||
if( !$this->zeroA || !isset($this->g) || !isset($this->n) || $this->p->modn(3) != 1 )
|
||||
return null;
|
||||
|
||||
// Compute beta and lambda, that lambda * P = (beta * Px; Py)
|
||||
$beta = null;
|
||||
$lambda = null;
|
||||
if( isset($conf["beta"]) )
|
||||
$beta = (new BN($conf["beta"], 16))->toRed($this->red);
|
||||
else
|
||||
{
|
||||
$betas = $this->_getEndoRoots($this->p);
|
||||
// Choose smallest beta
|
||||
$beta = $betas[0]->cmp($betas[1]) < 0 ? $betas[0] : $betas[1];
|
||||
$beta = $beta->toRed($this->red);
|
||||
}
|
||||
|
||||
if( isset($conf["lambda"]) )
|
||||
$lambda = new BN($conf["lambda"], 16);
|
||||
else
|
||||
{
|
||||
// Choose the lambda that is matching selected beta
|
||||
$lambdas = $this->_getEndoRoots($this->n);
|
||||
if( $this->g->mul($lambdas[0])->x->cmp($this->g->x->redMul($beta)) == 0 )
|
||||
$lambda = $lambdas[0];
|
||||
else
|
||||
{
|
||||
$lambda = $lambdas[1];
|
||||
if (Utils::$ASSERT_ENABLED) {
|
||||
assert($this->g->mul($lambda)->x->cmp($this->g->x->redMul($beta)) === 0);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Get basis vectors, used for balanced length-two representation
|
||||
$basis = null;
|
||||
if( !isset($conf["basis"]) )
|
||||
$basis = $this->_getEndoBasis($lambda);
|
||||
else
|
||||
{
|
||||
$callback = function($vector) {
|
||||
return array(
|
||||
"a" => new BN($vector["a"], 16),
|
||||
"b" => new BN($vector["b"], 16)
|
||||
);
|
||||
};
|
||||
$basis = array_map($callback, $conf["basis"]);
|
||||
}
|
||||
|
||||
return array(
|
||||
"beta" => $beta,
|
||||
"lambda" => $lambda,
|
||||
"basis" => $basis
|
||||
);
|
||||
}
|
||||
|
||||
private function _getEndoRoots($num)
|
||||
{
|
||||
// Find roots of for x^2 + x + 1 in F
|
||||
// Root = (-1 +- Sqrt(-3)) / 2
|
||||
//
|
||||
$red = $num === $this->p ? $this->red : BN::mont($num);
|
||||
$tinv = (new BN(2))->toRed($red)->redInvm();
|
||||
$ntinv = $tinv->redNeg();
|
||||
|
||||
$s = (new BN(3))->toRed($red)->redNeg()->redSqrt()->redMul($tinv);
|
||||
|
||||
return array(
|
||||
$ntinv->redAdd($s)->fromRed(),
|
||||
$ntinv->redSub($s)->fromRed()
|
||||
);
|
||||
}
|
||||
|
||||
private function _getEndoBasis($lambda)
|
||||
{
|
||||
// aprxSqrt >= sqrt(this.n)
|
||||
$aprxSqrt = $this->n->ushrn(intval($this->n->bitLength() / 2));
|
||||
|
||||
// 3.74
|
||||
// Run EGCD, until r(L + 1) < aprxSqrt
|
||||
$u = $lambda;
|
||||
$v = $this->n->_clone();
|
||||
$x1 = new BN(1);
|
||||
$y1 = new BN(0);
|
||||
$x2 = new BN(0);
|
||||
$y2 = new BN(1);
|
||||
|
||||
// NOTE: all vectors are roots of: a + b * lambda = 0 (mod n)
|
||||
$a0 = 0;
|
||||
$b0 = 0;
|
||||
// First vector
|
||||
$a1 = 0;
|
||||
$b1 = 0;
|
||||
// Second vector
|
||||
$a2 = 0;
|
||||
$b2 = 0;
|
||||
|
||||
$prevR = 0;
|
||||
$i = 0;
|
||||
$r = 0;
|
||||
$x = 0;
|
||||
|
||||
while( ! $u->isZero() )
|
||||
{
|
||||
$q = $v->div($u);
|
||||
$r = $v->sub($q->mul($u));
|
||||
$x = $x2->sub($q->mul($x1));
|
||||
$y = $y2->sub($q->mul($y2));
|
||||
|
||||
if( !$a1 && $r->cmp($aprxSqrt) < 0 )
|
||||
{
|
||||
$a0 = $prevR->neg();
|
||||
$b0 = $x1;
|
||||
$a1 = $r->neg();
|
||||
$b1 = $x;
|
||||
}
|
||||
elseif($a1 && ++$i === 2)
|
||||
break;
|
||||
|
||||
$prevR = $r;
|
||||
$v = $u;
|
||||
$u = $r;
|
||||
$x2 = $x1;
|
||||
$x1 = $x;
|
||||
$y2 = $y1;
|
||||
$y1 = $y;
|
||||
}
|
||||
$a2 = $r->neg();
|
||||
$b2 = $x;
|
||||
|
||||
$len1 = $a1->sqr()->add($b1->sqr());
|
||||
$len2 = $a2->sqr()->add($b2->sqr());
|
||||
if( $len2->cmp($len1) >= 0 )
|
||||
{
|
||||
$a2 = $a0;
|
||||
$b2 = $b0;
|
||||
}
|
||||
|
||||
// Normalize signs
|
||||
if( $a1->negative() )
|
||||
{
|
||||
$a1 = $a1->neg();
|
||||
$b1 = $b1->neg();
|
||||
}
|
||||
|
||||
if( $a2->negative() )
|
||||
{
|
||||
$a2 = $a2->neg();
|
||||
$b2 = $b2->neg();
|
||||
}
|
||||
|
||||
return array(
|
||||
array( "a" => $a1, "b" => $b1 ),
|
||||
array( "a" => $a2, "b" => $b2 ),
|
||||
);
|
||||
}
|
||||
|
||||
public function _endoSplit($k)
|
||||
{
|
||||
$basis = $this->endo["basis"];
|
||||
$v1 = $basis[0];
|
||||
$v2 = $basis[1];
|
||||
|
||||
$c1 = $v2["b"]->mul($k)->divRound($this->n);
|
||||
$c2 = $v1["b"]->neg()->mul($k)->divRound($this->n);
|
||||
|
||||
$p1 = $c1->mul($v1["a"]);
|
||||
$p2 = $c2->mul($v2["a"]);
|
||||
$q1 = $c1->mul($v1["b"]);
|
||||
$q2 = $c2->mul($v2["b"]);
|
||||
|
||||
//Calculate answer
|
||||
$k1 = $k->sub($p1)->sub($p2);
|
||||
$k2 = $q1->add($q2)->neg();
|
||||
|
||||
return array( "k1" => $k1, "k2" => $k2 );
|
||||
}
|
||||
|
||||
public function pointFromX($x, $odd)
|
||||
{
|
||||
$x = new BN($x, 16);
|
||||
if( !$x->red )
|
||||
$x = $x->toRed($this->red);
|
||||
|
||||
$y2 = $x->redSqr()->redMul($x)->redIAdd($x->redMul($this->a))->redIAdd($this->b);
|
||||
$y = $y2->redSqrt();
|
||||
if( $y->redSqr()->redSub($y2)->cmp($this->zero) !== 0 )
|
||||
throw new Exception("Invalid point");
|
||||
|
||||
// XXX Is there any way to tell if the number is odd without converting it
|
||||
// to non-red form?
|
||||
$isOdd = $y->fromRed()->isOdd();
|
||||
if( $odd != $isOdd )
|
||||
$y = $y->redNeg();
|
||||
|
||||
return $this->point($x, $y);
|
||||
}
|
||||
|
||||
public function validate($point)
|
||||
{
|
||||
if( $point->inf )
|
||||
return true;
|
||||
|
||||
$x = $point->x;
|
||||
$y = $point->y;
|
||||
|
||||
$ax = $this->a->redMul($x);
|
||||
$rhs = $x->redSqr()->redMul($x)->redIAdd($ax)->redIAdd($this->b);
|
||||
return $y->redSqr()->redISub($rhs)->isZero();
|
||||
}
|
||||
|
||||
public function _endoWnafMulAdd($points, $coeffs, $jacobianResult = false)
|
||||
{
|
||||
$npoints = &$this->_endoWnafT1;
|
||||
$ncoeffs = &$this->_endoWnafT2;
|
||||
|
||||
for($i = 0; $i < count($points); $i++)
|
||||
{
|
||||
$split = $this->_endoSplit($coeffs[$i]);
|
||||
$p = $points[$i];
|
||||
$beta = $p->_getBeta();
|
||||
|
||||
if( $split["k1"]->negative() )
|
||||
{
|
||||
$split["k1"]->ineg();
|
||||
$p = $p->neg(true);
|
||||
}
|
||||
|
||||
if( $split["k2"]->negative() )
|
||||
{
|
||||
$split["k2"]->ineg();
|
||||
$beta = $beta->neg(true);
|
||||
}
|
||||
|
||||
$npoints[$i * 2] = $p;
|
||||
$npoints[$i * 2 + 1] = $beta;
|
||||
$ncoeffs[$i * 2] = $split["k1"];
|
||||
$ncoeffs[$i * 2 + 1] = $split["k2"];
|
||||
}
|
||||
$res = $this->_wnafMulAdd(1, $npoints, $ncoeffs, $i * 2, $jacobianResult);
|
||||
|
||||
// Clean-up references to points and coefficients
|
||||
for($j = 0; $j < 2 * $i; $j++)
|
||||
{
|
||||
$npoints[$j] = null;
|
||||
$ncoeffs[$j] = null;
|
||||
}
|
||||
|
||||
return $res;
|
||||
}
|
||||
|
||||
public function point($x, $y, $isRed = false) {
|
||||
return new Point($this, $x, $y, $isRed);
|
||||
}
|
||||
|
||||
public function pointFromJSON($obj, $red) {
|
||||
return Point::fromJSON($this, $obj, $red);
|
||||
}
|
||||
|
||||
public function jpoint($x, $y, $z) {
|
||||
return new JPoint($this, $x, $y, $z);
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
@@ -0,0 +1,488 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic\Curve\ShortCurve;
|
||||
|
||||
use BN\BN;
|
||||
|
||||
class JPoint extends \Elliptic\Curve\BaseCurve\Point
|
||||
{
|
||||
public $x;
|
||||
public $y;
|
||||
public $z;
|
||||
public $zOne;
|
||||
|
||||
function __construct($curve, $x, $y, $z)
|
||||
{
|
||||
parent::__construct($curve, "jacobian");
|
||||
|
||||
if( $x == null && $y == null && $z == null )
|
||||
{
|
||||
$this->x = $this->curve->one;
|
||||
$this->y = $this->curve->one;
|
||||
$this->z = new BN(0);
|
||||
}
|
||||
else
|
||||
{
|
||||
$this->x = new BN($x, 16);
|
||||
$this->y = new BN($y, 16);
|
||||
$this->z = new BN($z, 16);
|
||||
}
|
||||
|
||||
if( !$this->x->red )
|
||||
$this->x = $this->x->toRed($this->curve->red);
|
||||
if( !$this->y->red )
|
||||
$this->y = $this->y->toRed($this->curve->red);
|
||||
if( !$this->z->red )
|
||||
$this->z = $this->z->toRed($this->curve->red);
|
||||
|
||||
return $this->zOne = $this->z == $this->curve->one;
|
||||
}
|
||||
|
||||
public function toP()
|
||||
{
|
||||
if( $this->isInfinity() )
|
||||
return $this->curve->point(null, null);
|
||||
|
||||
$zinv = $this->z->redInvm();
|
||||
$zinv2 = $zinv->redSqr();
|
||||
$ax = $this->x->redMul($zinv2);
|
||||
$ay = $this->y->redMul($zinv2)->redMul($zinv);
|
||||
|
||||
return $this->curve->point($ax, $ay);
|
||||
}
|
||||
|
||||
public function neg() {
|
||||
return $this->curve->jpoint($this->x, $this->y->redNeg(), $this->z);
|
||||
}
|
||||
|
||||
public function add($p)
|
||||
{
|
||||
// O + P = P
|
||||
if( $this->isInfinity() )
|
||||
return $p;
|
||||
|
||||
// P + O = P
|
||||
if( $p->isInfinity() )
|
||||
return $this;
|
||||
|
||||
// 12M + 4S + 7A
|
||||
$pz2 = $p->z->redSqr();
|
||||
$z2 = $this->z->redSqr();
|
||||
$u1 = $this->x->redMul($pz2);
|
||||
$u2 = $p->x->redMul($z2);
|
||||
$s1 = $this->y->redMul($pz2->redMul($p->z));
|
||||
$s2 = $p->y->redMul($z2->redMul($this->z));
|
||||
|
||||
$h = $u1->redSub($u2);
|
||||
$r = $s1->redSub($s2);
|
||||
|
||||
if( $h->isZero() )
|
||||
{
|
||||
if( ! $r->isZero() )
|
||||
return $this->curve->jpoint(null, null, null);
|
||||
else
|
||||
return $this->dbl();
|
||||
}
|
||||
|
||||
$h2 = $h->redSqr();
|
||||
$h3 = $h2->redMul($h);
|
||||
$v = $u1->redMul($h2);
|
||||
|
||||
$nx = $r->redSqr()->redIAdd($h3)->redISub($v)->redISub($v);
|
||||
$ny = $r->redMul($v->redISub($nx))->redISub($s1->redMul($h3));
|
||||
$nz = $this->z->redMul($p->z)->redMul($h);
|
||||
|
||||
return $this->curve->jpoint($nx, $ny, $nz);
|
||||
}
|
||||
|
||||
public function mixedAdd($p)
|
||||
{
|
||||
// O + P = P
|
||||
if( $this->isInfinity() )
|
||||
return $p->toJ();
|
||||
|
||||
// P + O = P
|
||||
if( $p->isInfinity() )
|
||||
return $this;
|
||||
|
||||
// 8M + 3S + 7A
|
||||
$z2 = $this->z->redSqr();
|
||||
$u1 = $this->x;
|
||||
$u2 = $p->x->redMul($z2);
|
||||
$s1 = $this->y;
|
||||
$s2 = $p->y->redMul($z2)->redMul($this->z);
|
||||
|
||||
$h = $u1->redSub($u2);
|
||||
$r = $s1->redSub($s2);
|
||||
|
||||
if( $h->isZero() )
|
||||
{
|
||||
if( ! $r->isZero() )
|
||||
return $this->curve->jpoint(null, null, null);
|
||||
else
|
||||
return $this->dbl();
|
||||
}
|
||||
|
||||
$h2 = $h->redSqr();
|
||||
$h3 = $h2->redMul($h);
|
||||
$v = $u1->redMul($h2);
|
||||
|
||||
$nx = $r->redSqr()->redIAdd($h3)->redISub($v)->redISub($v);
|
||||
$ny = $r->redMul($v->redISub($nx))->redISub($s1->redMul($h3));
|
||||
$nz = $this->z->redMul($h);
|
||||
|
||||
return $this->curve->jpoint($nx, $ny, $nz);
|
||||
}
|
||||
|
||||
public function dblp($pow = null)
|
||||
{
|
||||
if( $pow == 0 || $this->isInfinity() )
|
||||
return $this;
|
||||
|
||||
if( $pow == null )
|
||||
return $this->dbl();
|
||||
|
||||
if( $this->curve->zeroA || $this->curve->threeA )
|
||||
{
|
||||
$r = $this;
|
||||
for($i = 0; $i < $pow; $i++)
|
||||
$r = $r->dbl();
|
||||
return $r;
|
||||
}
|
||||
|
||||
// 1M + 2S + 1A + N * (4S + 5M + 8A)
|
||||
// N = 1 => 6M + 6S + 9A
|
||||
$jx = $this->x;
|
||||
$jy = $this->y;
|
||||
$jz = $this->z;
|
||||
$jz4 = $jz->redSqr()->redSqr();
|
||||
|
||||
//Reuse results
|
||||
$jyd = $jy->redAdd($jy);
|
||||
for($i = 0; $i < $pow; $i++)
|
||||
{
|
||||
$jx2 = $jx->redSqr();
|
||||
$jyd2 = $jyd->redSqr();
|
||||
$jyd4 = $jyd2->redSqr();
|
||||
$c = $jx2->redAdd($jx2)->redIAdd($jx2)->redIAdd($this->curve->a->redMul($jz4));
|
||||
|
||||
$t1 = $jx->redMul($jyd2);
|
||||
$nx = $c->redSqr()->redISub($t1->redAdd($t1));
|
||||
$t2 = $t1->redISub($nx);
|
||||
$dny = $c->redMul($t2);
|
||||
$dny = $dny->redIAdd($dny)->redISub($jyd4);
|
||||
$nz = $jyd->redMul($jz);
|
||||
if( ($i + 1) < $pow)
|
||||
$jz4 = $jz4->redMul($jyd4);
|
||||
|
||||
$jx = $nx;
|
||||
$jz = $nz;
|
||||
$jyd = $dny;
|
||||
}
|
||||
|
||||
return $this->curve->jpoint($jx, $jyd->redMul($this->curve->tinv), $jz);
|
||||
}
|
||||
|
||||
public function dbl()
|
||||
{
|
||||
if( $this->isInfinity() )
|
||||
return $this;
|
||||
|
||||
if( $this->curve->zeroA )
|
||||
return $this->_zeroDbl();
|
||||
elseif( $this->curve->threeA )
|
||||
return $this->_threeDbl();
|
||||
return $this->_dbl();
|
||||
}
|
||||
|
||||
private function _zOneDbl($withA)
|
||||
{
|
||||
$xx = $this->x->redSqr();
|
||||
$yy = $this->y->redSqr();
|
||||
$yyyy = $yy->redSqr();
|
||||
|
||||
// S = 2 * ((X1 + YY)^2 - XX - YYYY)
|
||||
$s = $this->x->redAdd($yy)->redSqr()->redISub($xx)->redISub($yyyy);
|
||||
$s = $s->redIAdd($s);
|
||||
|
||||
// M = 3 * XX + a; a = 0
|
||||
$m = null;
|
||||
if( $withA )
|
||||
$m = $xx->redAdd($xx)->redIAdd($xx)->redIAdd($this->curve->a);
|
||||
else
|
||||
$m = $xx->redAdd($xx)->redIAdd($xx);
|
||||
|
||||
// T = M ^ 2 - 2*S
|
||||
$t = $m->redSqr()->redISub($s)->redISub($s);
|
||||
|
||||
$yyyy8 = $yyyy->redIAdd($yyyy);
|
||||
$yyyy8 = $yyyy8->redIAdd($yyyy8);
|
||||
$yyyy8 = $yyyy8->redIAdd($yyyy8);
|
||||
|
||||
$ny = $m->redMul($s->redISub($t))->redISub($yyyy8);
|
||||
$nz = $this->y->redAdd($this->y);
|
||||
return $this->curve->jpoint($t, $ny, $nz);
|
||||
}
|
||||
|
||||
private function _zeroDbl()
|
||||
{
|
||||
// Z = 1
|
||||
if( $this->zOne )
|
||||
{
|
||||
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
|
||||
// #doubling-mdbl-2007-bl
|
||||
// 1M + 5S + 14A
|
||||
return $this->_zOneDbl(false);
|
||||
}
|
||||
|
||||
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
|
||||
// #doubling-dbl-2009-l
|
||||
// 2M + 5S + 13A
|
||||
|
||||
$a = $this->x->redSqr();
|
||||
$b = $this->y->redSqr();
|
||||
$c = $b->redSqr();
|
||||
// D = 2 * ((X1 + B)^2 - A - C)
|
||||
$d = $this->x->redAdd($b)->redSqr()->redISub($a)->redISub($c);
|
||||
$d = $d->redIAdd($d);
|
||||
$e = $a->redAdd($a)->redIAdd($a);
|
||||
$f = $e->redSqr();
|
||||
|
||||
$c8 = $c->redIAdd($c);
|
||||
$c8 = $c8->redIAdd($c8);
|
||||
$c8 = $c8->redIAdd($c8);
|
||||
|
||||
// X3 = F - 2 * D
|
||||
$nx = $f->redISub($d)->redISub($d);
|
||||
// Y3 = E * (D - X3) - 8 * C
|
||||
$ny = $e->redMul($d->redISub($nx))->redISub($c8);
|
||||
// Z3 = 2 * Y1 * Z1
|
||||
$nz = $this->y->redMul($this->z);
|
||||
$nz = $nz->redIAdd($nz);
|
||||
|
||||
return $this->curve->jpoint($nx, $ny, $nz);
|
||||
}
|
||||
|
||||
private function _threeDbl()
|
||||
{
|
||||
if( $this->zOne )
|
||||
{
|
||||
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html
|
||||
// #doubling-mdbl-2007-bl
|
||||
// 1M + 5S + 15A
|
||||
|
||||
// XX = X1^2
|
||||
$xx = $this->x->redSqr();
|
||||
// YY = Y1^2
|
||||
$yy = $this->y->redSqr();
|
||||
// YYYY = YY^2
|
||||
$yyyy = $yy->redSqr();
|
||||
// S = 2 * ((X1 + YY)^2 - XX - YYYY)
|
||||
$s = $this->x->redAdd($yy)->redSqr()->redISub($xx)->redISub($yyyy);
|
||||
$s = $s->redIAdd($s);
|
||||
// M = 3 * XX + a
|
||||
$m = $xx->redAdd($xx)->redIAdd($xx)->redIAdd($this->curve->a);
|
||||
// T = M^2 - 2 * S
|
||||
$t = $m->redSqr()->redISub($s)->redISub($s);
|
||||
// X3 = T
|
||||
$nx = $t;
|
||||
// Y3 = M * (S - T) - 8 * YYYY
|
||||
$yyyy8 = $yyyy->redIAdd($yyyy);
|
||||
$yyyy8 = $yyyy8->redIAdd($yyyy8);
|
||||
$yyyy8 = $yyyy8->redIAdd($yyyy8);
|
||||
$ny = $m->redMul($s->redISub($t))->redISub($yyyy8);
|
||||
// Z3 = 2 * Y1
|
||||
$nz = $this->y->redAdd($this->y);
|
||||
} else {
|
||||
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
|
||||
// 3M + 5S
|
||||
|
||||
// delta = Z1^2
|
||||
$delta = $this->z->redSqr();
|
||||
// gamma = Y1^2
|
||||
$gamma = $this->y->redSqr();
|
||||
// beta = X1 * gamma
|
||||
$beta = $this->x->redMul($gamma);
|
||||
// alpha = 3 * (X1 - delta) * (X1 + delta)
|
||||
$alpha = $this->x->redSub($delta)->redMul($this->x->redAdd($delta));
|
||||
$alpha = $alpha->redAdd($alpha)->redIAdd($alpha);
|
||||
// X3 = alpha^2 - 8 * beta
|
||||
$beta4 = $beta->redIAdd($beta);
|
||||
$beta4 = $beta4->redIAdd($beta4);
|
||||
$beta8 = $beta4->redAdd($beta4);
|
||||
$nx = $alpha->redSqr()->redISub($beta8);
|
||||
// Z3 = (Y1 + Z1)^2 - gamma - delta
|
||||
$nz = $this->y->redAdd($this->z)->redSqr()->redISub($gamma)->redISub($delta);
|
||||
|
||||
$ggamma8 = $gamma->redSqr();
|
||||
$ggamma8 = $ggamma8->redIAdd($ggamma8);
|
||||
$ggamma8 = $ggamma8->redIAdd($ggamma8);
|
||||
$ggamma8 = $ggamma8->redIAdd($ggamma8);
|
||||
// Y3 = alpha * (4 * beta - X3) - 8 * gamma^2
|
||||
$ny = $alpha->redMul($beta4->redISub($nx))->redISub($ggamma8);
|
||||
}
|
||||
return $this->curve->jpoint($nx, $ny, $nz);
|
||||
}
|
||||
|
||||
private function _dbl()
|
||||
{
|
||||
// 4M + 6S + 10A
|
||||
$jx = $this->x;
|
||||
$jy = $this->y;
|
||||
$jz = $this->z;
|
||||
$jz4 = $jz->redSqr()->redSqr();
|
||||
|
||||
$jx2 = $jx->redSqr();
|
||||
$jy2 = $jy->redSqr();
|
||||
|
||||
$c = $jx2->redAdd($jx2)->redIAdd($jx2)->redIAdd($this->curve->a->redMul($jz4));
|
||||
$jxd4 = $jx->redAdd($jx);
|
||||
$jxd4 = $jxd4->redIAdd($jxd4);
|
||||
$t1 = $jxd4->redMul($jy2);
|
||||
$nx = $c->redSqr()->redISub($t1->redAdd($t1));
|
||||
$t2 = $t1->redISub($nx);
|
||||
|
||||
$jyd8 = $jy2->redSqr();
|
||||
$jyd8 = $jyd8->redIAdd($jyd8);
|
||||
$jyd8 = $jyd8->redIAdd($jyd8);
|
||||
$jyd8 = $jyd8->redIAdd($jyd8);
|
||||
|
||||
$ny = $c->redMul($t2)->redISub($jyd8);
|
||||
$nz = $jy->redAdd($jy)->redMul($jz);
|
||||
|
||||
return $this->curve->jpoint($nx, $ny, $nz);
|
||||
}
|
||||
|
||||
public function trpl()
|
||||
{
|
||||
if( !$this->curve->zeroA )
|
||||
return $this->dbl()->add($this);
|
||||
|
||||
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#tripling-tpl-2007-bl
|
||||
// 5M + 10S + ...
|
||||
|
||||
$xx = $this->x->redSqr();
|
||||
$yy = $this->y->redSqr();
|
||||
$zz = $this->z->redSqr();
|
||||
// YYYY = YY^2
|
||||
$yyyy = $yy->redSqr();
|
||||
|
||||
// M = 3 * XX + a * ZZ2; a = 0
|
||||
$m = $xx->redAdd($xx)->redIAdd($xx);
|
||||
// MM = M^2
|
||||
$mm = $m->redSqr();
|
||||
|
||||
// E = 6 * ((X1 + YY)^2 - XX - YYYY) - MM
|
||||
$e = $this->x->redAdd($yy)->redSqr()->redISub($xx)->redISub($yyyy);
|
||||
$e = $e->redIAdd($e);
|
||||
$e = $e->redAdd($e)->redIAdd($e);
|
||||
$e = $e->redISub($mm);
|
||||
|
||||
$ee = $e->redSqr();
|
||||
// T = 16*YYYY
|
||||
$t = $yyyy->redIAdd($yyyy);
|
||||
$t = $t->redIAdd($t);
|
||||
$t = $t->redIAdd($t);
|
||||
$t = $t->redIAdd($t);
|
||||
|
||||
// U = (M + E)^2 - MM - EE - T
|
||||
$u = $m->redAdd($e)->redSqr()->redISub($mm)->redISub($ee)->redISub($t);
|
||||
|
||||
$yyu4 = $yy->redMul($u);
|
||||
$yyu4 = $yyu4->redIAdd($yyu4);
|
||||
$yyu4 = $yyu4->redIAdd($yyu4);
|
||||
|
||||
// X3 = 4 * (X1 * EE - 4 * YY * U)
|
||||
$nx = $this->x->redMul($ee)->redISub($yyu4);
|
||||
$nx = $nx->redIAdd($nx);
|
||||
$nx = $nx->redIAdd($nx);
|
||||
|
||||
// Y3 = 8 * Y1 * (U * (T - U) - E * EE)
|
||||
$ny = $this->y->redMul($u->redMul($t->redISub($u))->redISub($e->redMul($ee)));
|
||||
$ny = $ny->redIAdd($ny);
|
||||
$ny = $ny->redIAdd($ny);
|
||||
$ny = $ny->redIAdd($ny);
|
||||
|
||||
// Z3 = (Z1 + E)^2 - ZZ - EE
|
||||
$nz = $this->z->redAdd($e)->redSqr()->redISub($zz)->redISub($ee);
|
||||
|
||||
return $this->curve->jpoint($nx, $ny, $nz);
|
||||
}
|
||||
|
||||
public function mul($k, $kbase) {
|
||||
return $this->curve->_wnafMul($this, new BN($k, $kbase));
|
||||
}
|
||||
|
||||
public function eq($p)
|
||||
{
|
||||
if( $p->type == "affine" )
|
||||
return $this->eq($p->toJ());
|
||||
|
||||
if( $this == $p )
|
||||
return true;
|
||||
|
||||
// x1 * z2^2 == x2 * z1^2
|
||||
$z2 = $this->z->redSqr();
|
||||
$pz2 = $p->z->redSqr();
|
||||
if( ! $this->x->redMul($pz2)->redISub($p->x->redMul($z2))->isZero() )
|
||||
return false;
|
||||
|
||||
// y1 * z2^3 == y2 * z1^3
|
||||
$z3 = $z2->redMul($this->z);
|
||||
$pz3 = $pz2->redMul($p->z);
|
||||
|
||||
return $this->y->redMul($pz3)->redISub($p->y->redMul($z3))->isZero();
|
||||
}
|
||||
|
||||
public function eqXToP($x)
|
||||
{
|
||||
$zs = $this->z->redSqr();
|
||||
$rx = $x->toRed($this->curve->red)->redMul($zs);
|
||||
if( $this->x->cmp($rx) == 0 )
|
||||
return true;
|
||||
|
||||
$xc = $x->_clone();
|
||||
$t = $this->curve->redN->redMul($zs);
|
||||
|
||||
while(true)
|
||||
{
|
||||
$xc->iadd($this->curve->n);
|
||||
if( $xc->cmp($this->curve->p) >= 0 )
|
||||
return false;
|
||||
|
||||
$rx->redIAdd($t);
|
||||
if( $this->x->cmp($rx) == 0 )
|
||||
return true;
|
||||
}
|
||||
}
|
||||
|
||||
public function inspect()
|
||||
{
|
||||
if( $this->isInfinity() )
|
||||
return "<EC JPoint Infinity>";
|
||||
|
||||
return "<EC JPoint x: " . $this->x->toString(16, 2) .
|
||||
" y: " . $this->y->toString(16, 2) .
|
||||
" z: " . $this->z->toString(16, 2) . ">";
|
||||
}
|
||||
|
||||
public function __debugInfo() {
|
||||
return [
|
||||
"EC JPoint" => ($this->isInfinity() ?
|
||||
"Infinity" :
|
||||
[
|
||||
"x" => $this->x->toString(16,2),
|
||||
"y" => $this->y->toString(16,2),
|
||||
"z" => $this->z->toString(16,2)
|
||||
]
|
||||
)
|
||||
];
|
||||
}
|
||||
|
||||
public function isInfinity() {
|
||||
// XXX This code assumes that zero is always zero in red
|
||||
return $this->z->isZero();
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
@@ -0,0 +1,317 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic\Curve\ShortCurve;
|
||||
|
||||
use JsonSerializable;
|
||||
use BN\BN;
|
||||
|
||||
class Point extends \Elliptic\Curve\BaseCurve\Point implements JsonSerializable
|
||||
{
|
||||
public $x;
|
||||
public $y;
|
||||
public $inf;
|
||||
|
||||
function __construct($curve, $x, $y, $isRed)
|
||||
{
|
||||
parent::__construct($curve, 'affine');
|
||||
|
||||
if( $x == null && $y == null )
|
||||
{
|
||||
$this->x = null;
|
||||
$this->y = null;
|
||||
$this->inf = true;
|
||||
}
|
||||
else
|
||||
{
|
||||
$this->x = new BN($x, 16);
|
||||
$this->y = new BN($y, 16);
|
||||
// Force redgomery representation when loading from JSON
|
||||
if( $isRed )
|
||||
{
|
||||
$this->x->forceRed($this->curve->red);
|
||||
$this->y->forceRed($this->curve->red);
|
||||
}
|
||||
|
||||
if( !$this->x->red )
|
||||
$this->x = $this->x->toRed($this->curve->red);
|
||||
if( !$this->y->red )
|
||||
$this->y = $this->y->toRed($this->curve->red);
|
||||
$this->inf = false;
|
||||
}
|
||||
}
|
||||
|
||||
public function _getBeta()
|
||||
{
|
||||
if( !isset($this->curve->endo) )
|
||||
return null;
|
||||
|
||||
if( isset($this->precomputed) && isset($this->precomputed["beta"]) )
|
||||
return $this->precomputed["beta"];
|
||||
|
||||
$beta = $this->curve->point($this->x->redMul($this->curve->endo["beta"]), $this->y);
|
||||
if( isset($this->precomputed) )
|
||||
{
|
||||
$endoMul = function($p) {
|
||||
return $this->curve->point($p->x->redMul($this->curve->endo["beta"]), $p->y);
|
||||
};
|
||||
$beta->precomputed = array(
|
||||
"beta" => null,
|
||||
"naf" => null,
|
||||
"doubles" => null
|
||||
);
|
||||
|
||||
if( isset($this->precomputed["naf"]) )
|
||||
{
|
||||
$beta->precomputed["naf"] = array(
|
||||
"wnd" => $this->precomputed["naf"]["wnd"],
|
||||
"points" => array_map($endoMul, $this->precomputed["naf"]["points"])
|
||||
);
|
||||
}
|
||||
|
||||
if( isset($this->precomputed["doubles"]) )
|
||||
{
|
||||
$beta->precomputed["doubles"] = array(
|
||||
"step" => $this->precomputed["doubles"]["step"],
|
||||
"points" => array_map($endoMul, $this->precomputed["doubles"]["points"])
|
||||
);
|
||||
}
|
||||
$this->precomputed["beta"] = $beta;
|
||||
}
|
||||
return $beta;
|
||||
}
|
||||
|
||||
//toJSON()
|
||||
#[\ReturnTypeWillChange]
|
||||
public function jsonSerialize()
|
||||
{
|
||||
$res = array($this->x, $this->y);
|
||||
|
||||
if( !isset($this->precomputed) )
|
||||
return $res;
|
||||
|
||||
$pre = array();
|
||||
$addPre = false;
|
||||
if( isset($this->precomputed["doubles"]) )
|
||||
{
|
||||
$pre["doubles"] = array(
|
||||
"step" => $this->precomputed["doubles"]["step"],
|
||||
"points" => array_slice($this->precomputed["doubles"]["points"], 1)
|
||||
);
|
||||
$addPre = true;
|
||||
}
|
||||
|
||||
if( isset($this->precomputed["naf"]) )
|
||||
{
|
||||
$pre["naf"] = array(
|
||||
"naf" => $this->precomputed["naf"]["wnd"],
|
||||
"points" => array_slice($this->precomputed["naf"]["points"], 1)
|
||||
);
|
||||
$addPre = true;
|
||||
}
|
||||
|
||||
if( $addPre )
|
||||
array_push($res, $pre);
|
||||
|
||||
return $res;
|
||||
}
|
||||
|
||||
public static function fromJSON($curve, $obj, $red)
|
||||
{
|
||||
if( is_string($obj) )
|
||||
$obj = json_decode($obj);
|
||||
|
||||
$point = $curve->point($obj[0], $obj[1], $red);
|
||||
if( count($obj) === 2 )
|
||||
return $point;
|
||||
|
||||
$pre = $obj[2];
|
||||
$point->precomputed = array("beta" => null);
|
||||
$obj2point = function($obj) use ($curve, $red) {
|
||||
return $curve->point($obj[0], $obj[1], $red);
|
||||
};
|
||||
|
||||
if( isset($pre["doubles"]) )
|
||||
{
|
||||
$tmp = array_map($obj2point, $pre["doubles"]["points"]);
|
||||
array_unshift($tmp, $point);
|
||||
$point->precomputed["doubles"] = array(
|
||||
"step" => $pre["doubles"]["step"],
|
||||
"points" => $tmp
|
||||
);
|
||||
}
|
||||
|
||||
if( isset($pre["naf"]) )
|
||||
{
|
||||
$tmp = array_map($obj2point, $pre["naf"]["points"]);
|
||||
array_unshift($tmp, $point);
|
||||
$point->precomputed["naf"] = array(
|
||||
"wnd" => $pre["naf"]["wnd"],
|
||||
"points" => $tmp
|
||||
);
|
||||
}
|
||||
|
||||
return $point;
|
||||
}
|
||||
|
||||
public function inspect()
|
||||
{
|
||||
if( $this->isInfinity() )
|
||||
return "<EC Point Infinity>";
|
||||
|
||||
return "<EC Point x: " . $this->x->fromRed()->toString(16, 2) .
|
||||
" y: " . $this->y->fromRed()->toString(16, 2) . ">";
|
||||
}
|
||||
|
||||
public function __debugInfo() {
|
||||
return [
|
||||
"EC Point" => ($this->isInfinity() ?
|
||||
"Infinity" :
|
||||
[
|
||||
"x" => $this->x->fromRed()->toString(16, 2),
|
||||
"y" => $this->y->fromRed()->toString(16, 2)
|
||||
])
|
||||
];
|
||||
}
|
||||
public function isInfinity() {
|
||||
return $this->inf;
|
||||
}
|
||||
|
||||
public function add($point)
|
||||
{
|
||||
// O + P = P
|
||||
if( $this->inf )
|
||||
return $point;
|
||||
|
||||
// P + O = P
|
||||
if( $point->inf )
|
||||
return $this;
|
||||
|
||||
// P + P = 2P
|
||||
if( $this->eq($point) )
|
||||
return $this->dbl();
|
||||
|
||||
// P + (-P) = O
|
||||
if( $this->neg()->eq($point) )
|
||||
return $this->curve->point(null, null);
|
||||
|
||||
// P + Q = O
|
||||
if( $this->x->cmp($point->x) === 0 )
|
||||
return $this->curve->point(null, null);
|
||||
|
||||
$c = $this->y->redSub($point->y);
|
||||
if( ! $c->isZero() )
|
||||
$c = $c->redMul($this->x->redSub($point->x)->redInvm());
|
||||
$nx = $c->redSqr()->redISub($this->x)->redISub($point->x);
|
||||
$ny = $c->redMul($this->x->redSub($nx))->redISub($this->y);
|
||||
|
||||
return $this->curve->point($nx, $ny);
|
||||
}
|
||||
|
||||
public function dbl()
|
||||
{
|
||||
if( $this->inf )
|
||||
return $this;
|
||||
|
||||
// 2P = 0
|
||||
$ys1 = $this->y->redAdd($this->y);
|
||||
if( $ys1->isZero() )
|
||||
return $this->curve->point(null, null);
|
||||
|
||||
$x2 = $this->x->redSqr();
|
||||
$dyinv = $ys1->redInvm();
|
||||
$c = $x2->redAdd($x2)->redIAdd($x2)->redIAdd($this->curve->a)->redMul($dyinv);
|
||||
|
||||
$nx = $c->redSqr()->redISub($this->x->redAdd($this->x));
|
||||
$ny = $c->redMul($this->x->redSub($nx))->redISub($this->y);
|
||||
|
||||
return $this->curve->point($nx, $ny);
|
||||
}
|
||||
|
||||
public function getX() {
|
||||
return $this->x->fromRed();
|
||||
}
|
||||
|
||||
public function getY() {
|
||||
return $this->y->fromRed();
|
||||
}
|
||||
|
||||
public function mul($k)
|
||||
{
|
||||
$k = new BN($k, 16);
|
||||
|
||||
if( $this->_hasDoubles($k) )
|
||||
return $this->curve->_fixedNafMul($this, $k);
|
||||
elseif( isset($this->curve->endo) )
|
||||
return $this->curve->_endoWnafMulAdd(array($this), array($k));
|
||||
|
||||
return $this->curve->_wnafMul($this, $k);
|
||||
}
|
||||
|
||||
public function mulAdd($k1, $p2, $k2, $j = false)
|
||||
{
|
||||
$points = array($this, $p2);
|
||||
$coeffs = array($k1, $k2);
|
||||
|
||||
if( isset($this->curve->endo) )
|
||||
return $this->curve->_endoWnafMulAdd($points, $coeffs, $j);
|
||||
|
||||
return $this->curve->_wnafMulAdd(1, $points, $coeffs, 2, $j);
|
||||
}
|
||||
|
||||
public function jmulAdd($k1, $p2, $k2) {
|
||||
return $this->mulAdd($k1, $p2, $k2, true);
|
||||
}
|
||||
|
||||
public function eq($point)
|
||||
{
|
||||
return (
|
||||
$this === $point ||
|
||||
$this->inf === $point->inf &&
|
||||
($this->inf || $this->x->cmp($point->x) === 0 && $this->y->cmp($point->y) === 0)
|
||||
);
|
||||
}
|
||||
|
||||
public function neg($precompute = false)
|
||||
{
|
||||
if( $this->inf )
|
||||
return $this;
|
||||
|
||||
$res = $this->curve->point($this->x, $this->y->redNeg());
|
||||
if( $precompute && isset($this->precomputed) )
|
||||
{
|
||||
$res->precomputed = array();
|
||||
$pre = $this->precomputed;
|
||||
$negate = function($point) {
|
||||
return $point->neg();
|
||||
};
|
||||
|
||||
if( isset($pre["naf"]) )
|
||||
{
|
||||
$res->precomputed["naf"] = array(
|
||||
"wnd" => $pre["naf"]["wnd"],
|
||||
"points" => array_map($negate, $pre["naf"]["points"])
|
||||
);
|
||||
}
|
||||
|
||||
if( isset($pre["doubles"]) )
|
||||
{
|
||||
$res->precomputed["doubles"] = array(
|
||||
"step" => $pre["doubles"]["step"],
|
||||
"points" => array_map($negate, $pre["doubles"]["points"])
|
||||
);
|
||||
}
|
||||
|
||||
}
|
||||
return $res;
|
||||
}
|
||||
|
||||
public function toJ()
|
||||
{
|
||||
if( $this->inf )
|
||||
return $this->curve->jpoint(null, null, null);
|
||||
|
||||
return $this->curve->jpoint($this->x, $this->y, $this->curve->one);
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
+990
@@ -0,0 +1,990 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic;
|
||||
|
||||
use Elliptic\Curve\PresetCurve;
|
||||
|
||||
class Curves
|
||||
{
|
||||
private static $curves;
|
||||
|
||||
public static function hasCurve($name) {
|
||||
return isset(self::$curves[$name]);
|
||||
}
|
||||
public static function getCurve($name) {
|
||||
if (!isset(self::$curves[$name])) {
|
||||
throw new \Exception('Unknown curve ' . $name);
|
||||
}
|
||||
return self::$curves[$name];
|
||||
}
|
||||
|
||||
public static function defineCurve($name, $options)
|
||||
{
|
||||
self::$curves[$name] = new PresetCurve($options);
|
||||
}
|
||||
}
|
||||
|
||||
$sha256 = [ "blockSize" => 512, "outSize" => 256, "hmacStrength" => 192, "padLength" => 64, "algo" => 'sha256' ];
|
||||
$sha224 = [ "blockSize" => 512, "outSize" => 224, "hmacStrength" => 192, "padLength" => 64, "algo" => 'sha224' ];
|
||||
$sha512 = [ "blockSize" => 1024, "outSize" => 512, "hmacStrength" => 192, "padLength" => 128, "algo" => 'sha512' ];
|
||||
$sha384 = [ "blockSize" => 1024, "outSize" => 384, "hmacStrength" => 192, "padLength" => 128, "algo" => 'sha384' ];
|
||||
$sha1 = [ "blockSize" => 512, "outSize" => 160, "hmacStrength" => 80, "padLength" => 64, "algo" => 'sha1' ];
|
||||
|
||||
Curves::defineCurve("p192", array(
|
||||
"type" => "short",
|
||||
"prime" => "p192",
|
||||
"p" => "ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff",
|
||||
"a" => "ffffffff ffffffff ffffffff fffffffe ffffffff fffffffc",
|
||||
"b" => "64210519 e59c80e7 0fa7e9ab 72243049 feb8deec c146b9b1",
|
||||
"n" => "ffffffff ffffffff ffffffff 99def836 146bc9b1 b4d22831",
|
||||
"hash" => $sha256,
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"188da80e b03090f6 7cbf20eb 43a18800 f4ff0afd 82ff1012",
|
||||
"07192b95 ffc8da78 631011ed 6b24cdd5 73f977a1 1e794811"
|
||||
)
|
||||
));
|
||||
|
||||
Curves::defineCurve("p224", array(
|
||||
"type" => "short",
|
||||
"prime" => "p224",
|
||||
"p" => "ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001",
|
||||
"a" => "ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff fffffffe",
|
||||
"b" => "b4050a85 0c04b3ab f5413256 5044b0b7 d7bfd8ba 270b3943 2355ffb4",
|
||||
"n" => "ffffffff ffffffff ffffffff ffff16a2 e0b8f03e 13dd2945 5c5c2a3d",
|
||||
"hash" => $sha256,
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"b70e0cbd 6bb4bf7f 321390b9 4a03c1d3 56c21122 343280d6 115c1d21",
|
||||
"bd376388 b5f723fb 4c22dfe6 cd4375a0 5a074764 44d58199 85007e34"
|
||||
)
|
||||
));
|
||||
|
||||
Curves::defineCurve("p256", array(
|
||||
"type" => "short",
|
||||
"prime" => null,
|
||||
"p" => "ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff",
|
||||
"a" => "ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff fffffffc",
|
||||
"b" => "5ac635d8 aa3a93e7 b3ebbd55 769886bc 651d06b0 cc53b0f6 3bce3c3e 27d2604b",
|
||||
"n" => "ffffffff 00000000 ffffffff ffffffff bce6faad a7179e84 f3b9cac2 fc632551",
|
||||
"hash" => $sha256,
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"6b17d1f2 e12c4247 f8bce6e5 63a440f2 77037d81 2deb33a0 f4a13945 d898c296",
|
||||
"4fe342e2 fe1a7f9b 8ee7eb4a 7c0f9e16 2bce3357 6b315ece cbb64068 37bf51f5"
|
||||
)
|
||||
));
|
||||
|
||||
Curves::defineCurve("p384", array(
|
||||
"type" => "short",
|
||||
"prime" => null,
|
||||
"p" => "ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff " .
|
||||
"fffffffe ffffffff 00000000 00000000 ffffffff",
|
||||
"a" => "ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff " .
|
||||
"fffffffe ffffffff 00000000 00000000 fffffffc",
|
||||
"b" => "b3312fa7 e23ee7e4 988e056b e3f82d19 181d9c6e fe814112 0314088f " .
|
||||
"5013875a c656398d 8a2ed19d 2a85c8ed d3ec2aef",
|
||||
"n" => "ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff c7634d81 " .
|
||||
"f4372ddf 581a0db2 48b0a77a ecec196a ccc52973",
|
||||
"hash" => $sha384,
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"aa87ca22 be8b0537 8eb1c71e f320ad74 6e1d3b62 8ba79b98 59f741e0 82542a38 " .
|
||||
"5502f25d bf55296c 3a545e38 72760ab7",
|
||||
"3617de4a 96262c6f 5d9e98bf 9292dc29 f8f41dbd 289a147c e9da3113 b5f0b8c0 " .
|
||||
"0a60b1ce 1d7e819d 7a431d7c 90ea0e5f"
|
||||
)
|
||||
));
|
||||
|
||||
Curves::defineCurve("p521", array(
|
||||
"type" => "short",
|
||||
"prime" => null,
|
||||
"p" => "000001ff ffffffff ffffffff ffffffff ffffffff ffffffff " .
|
||||
"ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff " .
|
||||
"ffffffff ffffffff ffffffff ffffffff ffffffff",
|
||||
"a" => "000001ff ffffffff ffffffff ffffffff ffffffff ffffffff " .
|
||||
"ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff " .
|
||||
"ffffffff ffffffff ffffffff ffffffff fffffffc",
|
||||
"b" => "00000051 953eb961 8e1c9a1f 929a21a0 b68540ee a2da725b " .
|
||||
"99b315f3 b8b48991 8ef109e1 56193951 ec7e937b 1652c0bd " .
|
||||
"3bb1bf07 3573df88 3d2c34f1 ef451fd4 6b503f00",
|
||||
"n" => "000001ff ffffffff ffffffff ffffffff ffffffff ffffffff " .
|
||||
"ffffffff ffffffff fffffffa 51868783 bf2f966b 7fcc0148 " .
|
||||
"f709a5d0 3bb5c9b8 899c47ae bb6fb71e 91386409",
|
||||
"hash" => $sha512,
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"000000c6 858e06b7 0404e9cd 9e3ecb66 2395b442 9c648139 " .
|
||||
"053fb521 f828af60 6b4d3dba a14b5e77 efe75928 fe1dc127 " .
|
||||
"a2ffa8de 3348b3c1 856a429b f97e7e31 c2e5bd66",
|
||||
"00000118 39296a78 9a3bc004 5c8a5fb4 2c7d1bd9 98f54449 " .
|
||||
"579b4468 17afbd17 273e662c 97ee7299 5ef42640 c550b901 " .
|
||||
"3fad0761 353c7086 a272c240 88be9476 9fd16650"
|
||||
)
|
||||
));
|
||||
|
||||
Curves::defineCurve("curve25519", array(
|
||||
"type" => "mont",
|
||||
"prime" => "p25519",
|
||||
"p" => "7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed",
|
||||
"a" => "76d06",
|
||||
"b" => "0",
|
||||
"n" => "1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed",
|
||||
"hash" => $sha256,
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"9"
|
||||
)
|
||||
));
|
||||
|
||||
Curves:: defineCurve("curve25519-weier", array(
|
||||
"type" => "short",
|
||||
"prime" => "p25519",
|
||||
"p" => "7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed",
|
||||
"a" => "2aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa aaaaaa984914a144",
|
||||
"b" => "7b425ed097b425ed 097b425ed097b425 ed097b425ed097b4 260b5e9c7710c864",
|
||||
"n" => "1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed",
|
||||
"hash" => $sha256,
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaad245a",
|
||||
"20ae19a1b8a086b4e01edd2c7748d14c923d4d7e6d7c61b229e9c5a27eced3d9"
|
||||
)
|
||||
));
|
||||
|
||||
Curves::defineCurve("ed25519", array(
|
||||
"type" => "edwards",
|
||||
"prime" => "p25519",
|
||||
"p" => "7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed",
|
||||
"a" => "-1",
|
||||
"c" => "1",
|
||||
// -121665 * (121666^(-1)) (mod P)
|
||||
"d" => "52036cee2b6ffe73 8cc740797779e898 00700a4d4141d8ab 75eb4dca135978a3",
|
||||
"n" => "1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed",
|
||||
"hash" => $sha256,
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a",
|
||||
// 4/5
|
||||
"6666666666666666666666666666666666666666666666666666666666666658"
|
||||
)
|
||||
));
|
||||
|
||||
$pre = array(
|
||||
"doubles" => array(
|
||||
"step" => 4,
|
||||
"points" => array(
|
||||
array(
|
||||
"e60fce93b59e9ec53011aabc21c23e97b2a31369b87a5ae9c44ee89e2a6dec0a",
|
||||
"f7e3507399e595929db99f34f57937101296891e44d23f0be1f32cce69616821"
|
||||
),
|
||||
array(
|
||||
"8282263212c609d9ea2a6e3e172de238d8c39cabd5ac1ca10646e23fd5f51508",
|
||||
"11f8a8098557dfe45e8256e830b60ace62d613ac2f7b17bed31b6eaff6e26caf"
|
||||
),
|
||||
array(
|
||||
"175e159f728b865a72f99cc6c6fc846de0b93833fd2222ed73fce5b551e5b739",
|
||||
"d3506e0d9e3c79eba4ef97a51ff71f5eacb5955add24345c6efa6ffee9fed695"
|
||||
),
|
||||
array(
|
||||
"363d90d447b00c9c99ceac05b6262ee053441c7e55552ffe526bad8f83ff4640",
|
||||
"4e273adfc732221953b445397f3363145b9a89008199ecb62003c7f3bee9de9"
|
||||
),
|
||||
array(
|
||||
"8b4b5f165df3c2be8c6244b5b745638843e4a781a15bcd1b69f79a55dffdf80c",
|
||||
"4aad0a6f68d308b4b3fbd7813ab0da04f9e336546162ee56b3eff0c65fd4fd36"
|
||||
),
|
||||
array(
|
||||
"723cbaa6e5db996d6bf771c00bd548c7b700dbffa6c0e77bcb6115925232fcda",
|
||||
"96e867b5595cc498a921137488824d6e2660a0653779494801dc069d9eb39f5f"
|
||||
),
|
||||
array(
|
||||
"eebfa4d493bebf98ba5feec812c2d3b50947961237a919839a533eca0e7dd7fa",
|
||||
"5d9a8ca3970ef0f269ee7edaf178089d9ae4cdc3a711f712ddfd4fdae1de8999"
|
||||
),
|
||||
array(
|
||||
"100f44da696e71672791d0a09b7bde459f1215a29b3c03bfefd7835b39a48db0",
|
||||
"cdd9e13192a00b772ec8f3300c090666b7ff4a18ff5195ac0fbd5cd62bc65a09"
|
||||
),
|
||||
array(
|
||||
"e1031be262c7ed1b1dc9227a4a04c017a77f8d4464f3b3852c8acde6e534fd2d",
|
||||
"9d7061928940405e6bb6a4176597535af292dd419e1ced79a44f18f29456a00d"
|
||||
),
|
||||
array(
|
||||
"feea6cae46d55b530ac2839f143bd7ec5cf8b266a41d6af52d5e688d9094696d",
|
||||
"e57c6b6c97dce1bab06e4e12bf3ecd5c981c8957cc41442d3155debf18090088"
|
||||
),
|
||||
array(
|
||||
"da67a91d91049cdcb367be4be6ffca3cfeed657d808583de33fa978bc1ec6cb1",
|
||||
"9bacaa35481642bc41f463f7ec9780e5dec7adc508f740a17e9ea8e27a68be1d"
|
||||
),
|
||||
array(
|
||||
"53904faa0b334cdda6e000935ef22151ec08d0f7bb11069f57545ccc1a37b7c0",
|
||||
"5bc087d0bc80106d88c9eccac20d3c1c13999981e14434699dcb096b022771c8"
|
||||
),
|
||||
array(
|
||||
"8e7bcd0bd35983a7719cca7764ca906779b53a043a9b8bcaeff959f43ad86047",
|
||||
"10b7770b2a3da4b3940310420ca9514579e88e2e47fd68b3ea10047e8460372a"
|
||||
),
|
||||
array(
|
||||
"385eed34c1cdff21e6d0818689b81bde71a7f4f18397e6690a841e1599c43862",
|
||||
"283bebc3e8ea23f56701de19e9ebf4576b304eec2086dc8cc0458fe5542e5453"
|
||||
),
|
||||
array(
|
||||
"6f9d9b803ecf191637c73a4413dfa180fddf84a5947fbc9c606ed86c3fac3a7",
|
||||
"7c80c68e603059ba69b8e2a30e45c4d47ea4dd2f5c281002d86890603a842160"
|
||||
),
|
||||
array(
|
||||
"3322d401243c4e2582a2147c104d6ecbf774d163db0f5e5313b7e0e742d0e6bd",
|
||||
"56e70797e9664ef5bfb019bc4ddaf9b72805f63ea2873af624f3a2e96c28b2a0"
|
||||
),
|
||||
array(
|
||||
"85672c7d2de0b7da2bd1770d89665868741b3f9af7643397721d74d28134ab83",
|
||||
"7c481b9b5b43b2eb6374049bfa62c2e5e77f17fcc5298f44c8e3094f790313a6"
|
||||
),
|
||||
array(
|
||||
"948bf809b1988a46b06c9f1919413b10f9226c60f668832ffd959af60c82a0a",
|
||||
"53a562856dcb6646dc6b74c5d1c3418c6d4dff08c97cd2bed4cb7f88d8c8e589"
|
||||
),
|
||||
array(
|
||||
"6260ce7f461801c34f067ce0f02873a8f1b0e44dfc69752accecd819f38fd8e8",
|
||||
"bc2da82b6fa5b571a7f09049776a1ef7ecd292238051c198c1a84e95b2b4ae17"
|
||||
),
|
||||
array(
|
||||
"e5037de0afc1d8d43d8348414bbf4103043ec8f575bfdc432953cc8d2037fa2d",
|
||||
"4571534baa94d3b5f9f98d09fb990bddbd5f5b03ec481f10e0e5dc841d755bda"
|
||||
),
|
||||
array(
|
||||
"e06372b0f4a207adf5ea905e8f1771b4e7e8dbd1c6a6c5b725866a0ae4fce725",
|
||||
"7a908974bce18cfe12a27bb2ad5a488cd7484a7787104870b27034f94eee31dd"
|
||||
),
|
||||
array(
|
||||
"213c7a715cd5d45358d0bbf9dc0ce02204b10bdde2a3f58540ad6908d0559754",
|
||||
"4b6dad0b5ae462507013ad06245ba190bb4850f5f36a7eeddff2c27534b458f2"
|
||||
),
|
||||
array(
|
||||
"4e7c272a7af4b34e8dbb9352a5419a87e2838c70adc62cddf0cc3a3b08fbd53c",
|
||||
"17749c766c9d0b18e16fd09f6def681b530b9614bff7dd33e0b3941817dcaae6"
|
||||
),
|
||||
array(
|
||||
"fea74e3dbe778b1b10f238ad61686aa5c76e3db2be43057632427e2840fb27b6",
|
||||
"6e0568db9b0b13297cf674deccb6af93126b596b973f7b77701d3db7f23cb96f"
|
||||
),
|
||||
array(
|
||||
"76e64113f677cf0e10a2570d599968d31544e179b760432952c02a4417bdde39",
|
||||
"c90ddf8dee4e95cf577066d70681f0d35e2a33d2b56d2032b4b1752d1901ac01"
|
||||
),
|
||||
array(
|
||||
"c738c56b03b2abe1e8281baa743f8f9a8f7cc643df26cbee3ab150242bcbb891",
|
||||
"893fb578951ad2537f718f2eacbfbbbb82314eef7880cfe917e735d9699a84c3"
|
||||
),
|
||||
array(
|
||||
"d895626548b65b81e264c7637c972877d1d72e5f3a925014372e9f6588f6c14b",
|
||||
"febfaa38f2bc7eae728ec60818c340eb03428d632bb067e179363ed75d7d991f"
|
||||
),
|
||||
array(
|
||||
"b8da94032a957518eb0f6433571e8761ceffc73693e84edd49150a564f676e03",
|
||||
"2804dfa44805a1e4d7c99cc9762808b092cc584d95ff3b511488e4e74efdf6e7"
|
||||
),
|
||||
array(
|
||||
"e80fea14441fb33a7d8adab9475d7fab2019effb5156a792f1a11778e3c0df5d",
|
||||
"eed1de7f638e00771e89768ca3ca94472d155e80af322ea9fcb4291b6ac9ec78"
|
||||
),
|
||||
array(
|
||||
"a301697bdfcd704313ba48e51d567543f2a182031efd6915ddc07bbcc4e16070",
|
||||
"7370f91cfb67e4f5081809fa25d40f9b1735dbf7c0a11a130c0d1a041e177ea1"
|
||||
),
|
||||
array(
|
||||
"90ad85b389d6b936463f9d0512678de208cc330b11307fffab7ac63e3fb04ed4",
|
||||
"e507a3620a38261affdcbd9427222b839aefabe1582894d991d4d48cb6ef150"
|
||||
),
|
||||
array(
|
||||
"8f68b9d2f63b5f339239c1ad981f162ee88c5678723ea3351b7b444c9ec4c0da",
|
||||
"662a9f2dba063986de1d90c2b6be215dbbea2cfe95510bfdf23cbf79501fff82"
|
||||
),
|
||||
array(
|
||||
"e4f3fb0176af85d65ff99ff9198c36091f48e86503681e3e6686fd5053231e11",
|
||||
"1e63633ad0ef4f1c1661a6d0ea02b7286cc7e74ec951d1c9822c38576feb73bc"
|
||||
),
|
||||
array(
|
||||
"8c00fa9b18ebf331eb961537a45a4266c7034f2f0d4e1d0716fb6eae20eae29e",
|
||||
"efa47267fea521a1a9dc343a3736c974c2fadafa81e36c54e7d2a4c66702414b"
|
||||
),
|
||||
array(
|
||||
"e7a26ce69dd4829f3e10cec0a9e98ed3143d084f308b92c0997fddfc60cb3e41",
|
||||
"2a758e300fa7984b471b006a1aafbb18d0a6b2c0420e83e20e8a9421cf2cfd51"
|
||||
),
|
||||
array(
|
||||
"b6459e0ee3662ec8d23540c223bcbdc571cbcb967d79424f3cf29eb3de6b80ef",
|
||||
"67c876d06f3e06de1dadf16e5661db3c4b3ae6d48e35b2ff30bf0b61a71ba45"
|
||||
),
|
||||
array(
|
||||
"d68a80c8280bb840793234aa118f06231d6f1fc67e73c5a5deda0f5b496943e8",
|
||||
"db8ba9fff4b586d00c4b1f9177b0e28b5b0e7b8f7845295a294c84266b133120"
|
||||
),
|
||||
array(
|
||||
"324aed7df65c804252dc0270907a30b09612aeb973449cea4095980fc28d3d5d",
|
||||
"648a365774b61f2ff130c0c35aec1f4f19213b0c7e332843967224af96ab7c84"
|
||||
),
|
||||
array(
|
||||
"4df9c14919cde61f6d51dfdbe5fee5dceec4143ba8d1ca888e8bd373fd054c96",
|
||||
"35ec51092d8728050974c23a1d85d4b5d506cdc288490192ebac06cad10d5d"
|
||||
),
|
||||
array(
|
||||
"9c3919a84a474870faed8a9c1cc66021523489054d7f0308cbfc99c8ac1f98cd",
|
||||
"ddb84f0f4a4ddd57584f044bf260e641905326f76c64c8e6be7e5e03d4fc599d"
|
||||
),
|
||||
array(
|
||||
"6057170b1dd12fdf8de05f281d8e06bb91e1493a8b91d4cc5a21382120a959e5",
|
||||
"9a1af0b26a6a4807add9a2daf71df262465152bc3ee24c65e899be932385a2a8"
|
||||
),
|
||||
array(
|
||||
"a576df8e23a08411421439a4518da31880cef0fba7d4df12b1a6973eecb94266",
|
||||
"40a6bf20e76640b2c92b97afe58cd82c432e10a7f514d9f3ee8be11ae1b28ec8"
|
||||
),
|
||||
array(
|
||||
"7778a78c28dec3e30a05fe9629de8c38bb30d1f5cf9a3a208f763889be58ad71",
|
||||
"34626d9ab5a5b22ff7098e12f2ff580087b38411ff24ac563b513fc1fd9f43ac"
|
||||
),
|
||||
array(
|
||||
"928955ee637a84463729fd30e7afd2ed5f96274e5ad7e5cb09eda9c06d903ac",
|
||||
"c25621003d3f42a827b78a13093a95eeac3d26efa8a8d83fc5180e935bcd091f"
|
||||
),
|
||||
array(
|
||||
"85d0fef3ec6db109399064f3a0e3b2855645b4a907ad354527aae75163d82751",
|
||||
"1f03648413a38c0be29d496e582cf5663e8751e96877331582c237a24eb1f962"
|
||||
),
|
||||
array(
|
||||
"ff2b0dce97eece97c1c9b6041798b85dfdfb6d8882da20308f5404824526087e",
|
||||
"493d13fef524ba188af4c4dc54d07936c7b7ed6fb90e2ceb2c951e01f0c29907"
|
||||
),
|
||||
array(
|
||||
"827fbbe4b1e880ea9ed2b2e6301b212b57f1ee148cd6dd28780e5e2cf856e241",
|
||||
"c60f9c923c727b0b71bef2c67d1d12687ff7a63186903166d605b68baec293ec"
|
||||
),
|
||||
array(
|
||||
"eaa649f21f51bdbae7be4ae34ce6e5217a58fdce7f47f9aa7f3b58fa2120e2b3",
|
||||
"be3279ed5bbbb03ac69a80f89879aa5a01a6b965f13f7e59d47a5305ba5ad93d"
|
||||
),
|
||||
array(
|
||||
"e4a42d43c5cf169d9391df6decf42ee541b6d8f0c9a137401e23632dda34d24f",
|
||||
"4d9f92e716d1c73526fc99ccfb8ad34ce886eedfa8d8e4f13a7f7131deba9414"
|
||||
),
|
||||
array(
|
||||
"1ec80fef360cbdd954160fadab352b6b92b53576a88fea4947173b9d4300bf19",
|
||||
"aeefe93756b5340d2f3a4958a7abbf5e0146e77f6295a07b671cdc1cc107cefd"
|
||||
),
|
||||
array(
|
||||
"146a778c04670c2f91b00af4680dfa8bce3490717d58ba889ddb5928366642be",
|
||||
"b318e0ec3354028add669827f9d4b2870aaa971d2f7e5ed1d0b297483d83efd0"
|
||||
),
|
||||
array(
|
||||
"fa50c0f61d22e5f07e3acebb1aa07b128d0012209a28b9776d76a8793180eef9",
|
||||
"6b84c6922397eba9b72cd2872281a68a5e683293a57a213b38cd8d7d3f4f2811"
|
||||
),
|
||||
array(
|
||||
"da1d61d0ca721a11b1a5bf6b7d88e8421a288ab5d5bba5220e53d32b5f067ec2",
|
||||
"8157f55a7c99306c79c0766161c91e2966a73899d279b48a655fba0f1ad836f1"
|
||||
),
|
||||
array(
|
||||
"a8e282ff0c9706907215ff98e8fd416615311de0446f1e062a73b0610d064e13",
|
||||
"7f97355b8db81c09abfb7f3c5b2515888b679a3e50dd6bd6cef7c73111f4cc0c"
|
||||
),
|
||||
array(
|
||||
"174a53b9c9a285872d39e56e6913cab15d59b1fa512508c022f382de8319497c",
|
||||
"ccc9dc37abfc9c1657b4155f2c47f9e6646b3a1d8cb9854383da13ac079afa73"
|
||||
),
|
||||
array(
|
||||
"959396981943785c3d3e57edf5018cdbe039e730e4918b3d884fdff09475b7ba",
|
||||
"2e7e552888c331dd8ba0386a4b9cd6849c653f64c8709385e9b8abf87524f2fd"
|
||||
),
|
||||
array(
|
||||
"d2a63a50ae401e56d645a1153b109a8fcca0a43d561fba2dbb51340c9d82b151",
|
||||
"e82d86fb6443fcb7565aee58b2948220a70f750af484ca52d4142174dcf89405"
|
||||
),
|
||||
array(
|
||||
"64587e2335471eb890ee7896d7cfdc866bacbdbd3839317b3436f9b45617e073",
|
||||
"d99fcdd5bf6902e2ae96dd6447c299a185b90a39133aeab358299e5e9faf6589"
|
||||
),
|
||||
array(
|
||||
"8481bde0e4e4d885b3a546d3e549de042f0aa6cea250e7fd358d6c86dd45e458",
|
||||
"38ee7b8cba5404dd84a25bf39cecb2ca900a79c42b262e556d64b1b59779057e"
|
||||
),
|
||||
array(
|
||||
"13464a57a78102aa62b6979ae817f4637ffcfed3c4b1ce30bcd6303f6caf666b",
|
||||
"69be159004614580ef7e433453ccb0ca48f300a81d0942e13f495a907f6ecc27"
|
||||
),
|
||||
array(
|
||||
"bc4a9df5b713fe2e9aef430bcc1dc97a0cd9ccede2f28588cada3a0d2d83f366",
|
||||
"d3a81ca6e785c06383937adf4b798caa6e8a9fbfa547b16d758d666581f33c1"
|
||||
),
|
||||
array(
|
||||
"8c28a97bf8298bc0d23d8c749452a32e694b65e30a9472a3954ab30fe5324caa",
|
||||
"40a30463a3305193378fedf31f7cc0eb7ae784f0451cb9459e71dc73cbef9482"
|
||||
),
|
||||
array(
|
||||
"8ea9666139527a8c1dd94ce4f071fd23c8b350c5a4bb33748c4ba111faccae0",
|
||||
"620efabbc8ee2782e24e7c0cfb95c5d735b783be9cf0f8e955af34a30e62b945"
|
||||
),
|
||||
array(
|
||||
"dd3625faef5ba06074669716bbd3788d89bdde815959968092f76cc4eb9a9787",
|
||||
"7a188fa3520e30d461da2501045731ca941461982883395937f68d00c644a573"
|
||||
),
|
||||
array(
|
||||
"f710d79d9eb962297e4f6232b40e8f7feb2bc63814614d692c12de752408221e",
|
||||
"ea98e67232d3b3295d3b535532115ccac8612c721851617526ae47a9c77bfc82"
|
||||
)
|
||||
)
|
||||
),
|
||||
"naf" => array(
|
||||
"wnd" => 7,
|
||||
"points" => array(
|
||||
array(
|
||||
"f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9",
|
||||
"388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672"
|
||||
),
|
||||
array(
|
||||
"2f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4",
|
||||
"d8ac222636e5e3d6d4dba9dda6c9c426f788271bab0d6840dca87d3aa6ac62d6"
|
||||
),
|
||||
array(
|
||||
"5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bc",
|
||||
"6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264da"
|
||||
),
|
||||
array(
|
||||
"acd484e2f0c7f65309ad178a9f559abde09796974c57e714c35f110dfc27ccbe",
|
||||
"cc338921b0a7d9fd64380971763b61e9add888a4375f8e0f05cc262ac64f9c37"
|
||||
),
|
||||
array(
|
||||
"774ae7f858a9411e5ef4246b70c65aac5649980be5c17891bbec17895da008cb",
|
||||
"d984a032eb6b5e190243dd56d7b7b365372db1e2dff9d6a8301d74c9c953c61b"
|
||||
),
|
||||
array(
|
||||
"f28773c2d975288bc7d1d205c3748651b075fbc6610e58cddeeddf8f19405aa8",
|
||||
"ab0902e8d880a89758212eb65cdaf473a1a06da521fa91f29b5cb52db03ed81"
|
||||
),
|
||||
array(
|
||||
"d7924d4f7d43ea965a465ae3095ff41131e5946f3c85f79e44adbcf8e27e080e",
|
||||
"581e2872a86c72a683842ec228cc6defea40af2bd896d3a5c504dc9ff6a26b58"
|
||||
),
|
||||
array(
|
||||
"defdea4cdb677750a420fee807eacf21eb9898ae79b9768766e4faa04a2d4a34",
|
||||
"4211ab0694635168e997b0ead2a93daeced1f4a04a95c0f6cfb199f69e56eb77"
|
||||
),
|
||||
array(
|
||||
"2b4ea0a797a443d293ef5cff444f4979f06acfebd7e86d277475656138385b6c",
|
||||
"85e89bc037945d93b343083b5a1c86131a01f60c50269763b570c854e5c09b7a"
|
||||
),
|
||||
array(
|
||||
"352bbf4a4cdd12564f93fa332ce333301d9ad40271f8107181340aef25be59d5",
|
||||
"321eb4075348f534d59c18259dda3e1f4a1b3b2e71b1039c67bd3d8bcf81998c"
|
||||
),
|
||||
array(
|
||||
"2fa2104d6b38d11b0230010559879124e42ab8dfeff5ff29dc9cdadd4ecacc3f",
|
||||
"2de1068295dd865b64569335bd5dd80181d70ecfc882648423ba76b532b7d67"
|
||||
),
|
||||
array(
|
||||
"9248279b09b4d68dab21a9b066edda83263c3d84e09572e269ca0cd7f5453714",
|
||||
"73016f7bf234aade5d1aa71bdea2b1ff3fc0de2a887912ffe54a32ce97cb3402"
|
||||
),
|
||||
array(
|
||||
"daed4f2be3a8bf278e70132fb0beb7522f570e144bf615c07e996d443dee8729",
|
||||
"a69dce4a7d6c98e8d4a1aca87ef8d7003f83c230f3afa726ab40e52290be1c55"
|
||||
),
|
||||
array(
|
||||
"c44d12c7065d812e8acf28d7cbb19f9011ecd9e9fdf281b0e6a3b5e87d22e7db",
|
||||
"2119a460ce326cdc76c45926c982fdac0e106e861edf61c5a039063f0e0e6482"
|
||||
),
|
||||
array(
|
||||
"6a245bf6dc698504c89a20cfded60853152b695336c28063b61c65cbd269e6b4",
|
||||
"e022cf42c2bd4a708b3f5126f16a24ad8b33ba48d0423b6efd5e6348100d8a82"
|
||||
),
|
||||
array(
|
||||
"1697ffa6fd9de627c077e3d2fe541084ce13300b0bec1146f95ae57f0d0bd6a5",
|
||||
"b9c398f186806f5d27561506e4557433a2cf15009e498ae7adee9d63d01b2396"
|
||||
),
|
||||
array(
|
||||
"605bdb019981718b986d0f07e834cb0d9deb8360ffb7f61df982345ef27a7479",
|
||||
"2972d2de4f8d20681a78d93ec96fe23c26bfae84fb14db43b01e1e9056b8c49"
|
||||
),
|
||||
array(
|
||||
"62d14dab4150bf497402fdc45a215e10dcb01c354959b10cfe31c7e9d87ff33d",
|
||||
"80fc06bd8cc5b01098088a1950eed0db01aa132967ab472235f5642483b25eaf"
|
||||
),
|
||||
array(
|
||||
"80c60ad0040f27dade5b4b06c408e56b2c50e9f56b9b8b425e555c2f86308b6f",
|
||||
"1c38303f1cc5c30f26e66bad7fe72f70a65eed4cbe7024eb1aa01f56430bd57a"
|
||||
),
|
||||
array(
|
||||
"7a9375ad6167ad54aa74c6348cc54d344cc5dc9487d847049d5eabb0fa03c8fb",
|
||||
"d0e3fa9eca8726909559e0d79269046bdc59ea10c70ce2b02d499ec224dc7f7"
|
||||
),
|
||||
array(
|
||||
"d528ecd9b696b54c907a9ed045447a79bb408ec39b68df504bb51f459bc3ffc9",
|
||||
"eecf41253136e5f99966f21881fd656ebc4345405c520dbc063465b521409933"
|
||||
),
|
||||
array(
|
||||
"49370a4b5f43412ea25f514e8ecdad05266115e4a7ecb1387231808f8b45963",
|
||||
"758f3f41afd6ed428b3081b0512fd62a54c3f3afbb5b6764b653052a12949c9a"
|
||||
),
|
||||
array(
|
||||
"77f230936ee88cbbd73df930d64702ef881d811e0e1498e2f1c13eb1fc345d74",
|
||||
"958ef42a7886b6400a08266e9ba1b37896c95330d97077cbbe8eb3c7671c60d6"
|
||||
),
|
||||
array(
|
||||
"f2dac991cc4ce4b9ea44887e5c7c0bce58c80074ab9d4dbaeb28531b7739f530",
|
||||
"e0dedc9b3b2f8dad4da1f32dec2531df9eb5fbeb0598e4fd1a117dba703a3c37"
|
||||
),
|
||||
array(
|
||||
"463b3d9f662621fb1b4be8fbbe2520125a216cdfc9dae3debcba4850c690d45b",
|
||||
"5ed430d78c296c3543114306dd8622d7c622e27c970a1de31cb377b01af7307e"
|
||||
),
|
||||
array(
|
||||
"f16f804244e46e2a09232d4aff3b59976b98fac14328a2d1a32496b49998f247",
|
||||
"cedabd9b82203f7e13d206fcdf4e33d92a6c53c26e5cce26d6579962c4e31df6"
|
||||
),
|
||||
array(
|
||||
"caf754272dc84563b0352b7a14311af55d245315ace27c65369e15f7151d41d1",
|
||||
"cb474660ef35f5f2a41b643fa5e460575f4fa9b7962232a5c32f908318a04476"
|
||||
),
|
||||
array(
|
||||
"2600ca4b282cb986f85d0f1709979d8b44a09c07cb86d7c124497bc86f082120",
|
||||
"4119b88753c15bd6a693b03fcddbb45d5ac6be74ab5f0ef44b0be9475a7e4b40"
|
||||
),
|
||||
array(
|
||||
"7635ca72d7e8432c338ec53cd12220bc01c48685e24f7dc8c602a7746998e435",
|
||||
"91b649609489d613d1d5e590f78e6d74ecfc061d57048bad9e76f302c5b9c61"
|
||||
),
|
||||
array(
|
||||
"754e3239f325570cdbbf4a87deee8a66b7f2b33479d468fbc1a50743bf56cc18",
|
||||
"673fb86e5bda30fb3cd0ed304ea49a023ee33d0197a695d0c5d98093c536683"
|
||||
),
|
||||
array(
|
||||
"e3e6bd1071a1e96aff57859c82d570f0330800661d1c952f9fe2694691d9b9e8",
|
||||
"59c9e0bba394e76f40c0aa58379a3cb6a5a2283993e90c4167002af4920e37f5"
|
||||
),
|
||||
array(
|
||||
"186b483d056a033826ae73d88f732985c4ccb1f32ba35f4b4cc47fdcf04aa6eb",
|
||||
"3b952d32c67cf77e2e17446e204180ab21fb8090895138b4a4a797f86e80888b"
|
||||
),
|
||||
array(
|
||||
"df9d70a6b9876ce544c98561f4be4f725442e6d2b737d9c91a8321724ce0963f",
|
||||
"55eb2dafd84d6ccd5f862b785dc39d4ab157222720ef9da217b8c45cf2ba2417"
|
||||
),
|
||||
array(
|
||||
"5edd5cc23c51e87a497ca815d5dce0f8ab52554f849ed8995de64c5f34ce7143",
|
||||
"efae9c8dbc14130661e8cec030c89ad0c13c66c0d17a2905cdc706ab7399a868"
|
||||
),
|
||||
array(
|
||||
"290798c2b6476830da12fe02287e9e777aa3fba1c355b17a722d362f84614fba",
|
||||
"e38da76dcd440621988d00bcf79af25d5b29c094db2a23146d003afd41943e7a"
|
||||
),
|
||||
array(
|
||||
"af3c423a95d9f5b3054754efa150ac39cd29552fe360257362dfdecef4053b45",
|
||||
"f98a3fd831eb2b749a93b0e6f35cfb40c8cd5aa667a15581bc2feded498fd9c6"
|
||||
),
|
||||
array(
|
||||
"766dbb24d134e745cccaa28c99bf274906bb66b26dcf98df8d2fed50d884249a",
|
||||
"744b1152eacbe5e38dcc887980da38b897584a65fa06cedd2c924f97cbac5996"
|
||||
),
|
||||
array(
|
||||
"59dbf46f8c94759ba21277c33784f41645f7b44f6c596a58ce92e666191abe3e",
|
||||
"c534ad44175fbc300f4ea6ce648309a042ce739a7919798cd85e216c4a307f6e"
|
||||
),
|
||||
array(
|
||||
"f13ada95103c4537305e691e74e9a4a8dd647e711a95e73cb62dc6018cfd87b8",
|
||||
"e13817b44ee14de663bf4bc808341f326949e21a6a75c2570778419bdaf5733d"
|
||||
),
|
||||
array(
|
||||
"7754b4fa0e8aced06d4167a2c59cca4cda1869c06ebadfb6488550015a88522c",
|
||||
"30e93e864e669d82224b967c3020b8fa8d1e4e350b6cbcc537a48b57841163a2"
|
||||
),
|
||||
array(
|
||||
"948dcadf5990e048aa3874d46abef9d701858f95de8041d2a6828c99e2262519",
|
||||
"e491a42537f6e597d5d28a3224b1bc25df9154efbd2ef1d2cbba2cae5347d57e"
|
||||
),
|
||||
array(
|
||||
"7962414450c76c1689c7b48f8202ec37fb224cf5ac0bfa1570328a8a3d7c77ab",
|
||||
"100b610ec4ffb4760d5c1fc133ef6f6b12507a051f04ac5760afa5b29db83437"
|
||||
),
|
||||
array(
|
||||
"3514087834964b54b15b160644d915485a16977225b8847bb0dd085137ec47ca",
|
||||
"ef0afbb2056205448e1652c48e8127fc6039e77c15c2378b7e7d15a0de293311"
|
||||
),
|
||||
array(
|
||||
"d3cc30ad6b483e4bc79ce2c9dd8bc54993e947eb8df787b442943d3f7b527eaf",
|
||||
"8b378a22d827278d89c5e9be8f9508ae3c2ad46290358630afb34db04eede0a4"
|
||||
),
|
||||
array(
|
||||
"1624d84780732860ce1c78fcbfefe08b2b29823db913f6493975ba0ff4847610",
|
||||
"68651cf9b6da903e0914448c6cd9d4ca896878f5282be4c8cc06e2a404078575"
|
||||
),
|
||||
array(
|
||||
"733ce80da955a8a26902c95633e62a985192474b5af207da6df7b4fd5fc61cd4",
|
||||
"f5435a2bd2badf7d485a4d8b8db9fcce3e1ef8e0201e4578c54673bc1dc5ea1d"
|
||||
),
|
||||
array(
|
||||
"15d9441254945064cf1a1c33bbd3b49f8966c5092171e699ef258dfab81c045c",
|
||||
"d56eb30b69463e7234f5137b73b84177434800bacebfc685fc37bbe9efe4070d"
|
||||
),
|
||||
array(
|
||||
"a1d0fcf2ec9de675b612136e5ce70d271c21417c9d2b8aaaac138599d0717940",
|
||||
"edd77f50bcb5a3cab2e90737309667f2641462a54070f3d519212d39c197a629"
|
||||
),
|
||||
array(
|
||||
"e22fbe15c0af8ccc5780c0735f84dbe9a790badee8245c06c7ca37331cb36980",
|
||||
"a855babad5cd60c88b430a69f53a1a7a38289154964799be43d06d77d31da06"
|
||||
),
|
||||
array(
|
||||
"311091dd9860e8e20ee13473c1155f5f69635e394704eaa74009452246cfa9b3",
|
||||
"66db656f87d1f04fffd1f04788c06830871ec5a64feee685bd80f0b1286d8374"
|
||||
),
|
||||
array(
|
||||
"34c1fd04d301be89b31c0442d3e6ac24883928b45a9340781867d4232ec2dbdf",
|
||||
"9414685e97b1b5954bd46f730174136d57f1ceeb487443dc5321857ba73abee"
|
||||
),
|
||||
array(
|
||||
"f219ea5d6b54701c1c14de5b557eb42a8d13f3abbcd08affcc2a5e6b049b8d63",
|
||||
"4cb95957e83d40b0f73af4544cccf6b1f4b08d3c07b27fb8d8c2962a400766d1"
|
||||
),
|
||||
array(
|
||||
"d7b8740f74a8fbaab1f683db8f45de26543a5490bca627087236912469a0b448",
|
||||
"fa77968128d9c92ee1010f337ad4717eff15db5ed3c049b3411e0315eaa4593b"
|
||||
),
|
||||
array(
|
||||
"32d31c222f8f6f0ef86f7c98d3a3335ead5bcd32abdd94289fe4d3091aa824bf",
|
||||
"5f3032f5892156e39ccd3d7915b9e1da2e6dac9e6f26e961118d14b8462e1661"
|
||||
),
|
||||
array(
|
||||
"7461f371914ab32671045a155d9831ea8793d77cd59592c4340f86cbc18347b5",
|
||||
"8ec0ba238b96bec0cbdddcae0aa442542eee1ff50c986ea6b39847b3cc092ff6"
|
||||
),
|
||||
array(
|
||||
"ee079adb1df1860074356a25aa38206a6d716b2c3e67453d287698bad7b2b2d6",
|
||||
"8dc2412aafe3be5c4c5f37e0ecc5f9f6a446989af04c4e25ebaac479ec1c8c1e"
|
||||
),
|
||||
array(
|
||||
"16ec93e447ec83f0467b18302ee620f7e65de331874c9dc72bfd8616ba9da6b5",
|
||||
"5e4631150e62fb40d0e8c2a7ca5804a39d58186a50e497139626778e25b0674d"
|
||||
),
|
||||
array(
|
||||
"eaa5f980c245f6f038978290afa70b6bd8855897f98b6aa485b96065d537bd99",
|
||||
"f65f5d3e292c2e0819a528391c994624d784869d7e6ea67fb18041024edc07dc"
|
||||
),
|
||||
array(
|
||||
"78c9407544ac132692ee1910a02439958ae04877151342ea96c4b6b35a49f51",
|
||||
"f3e0319169eb9b85d5404795539a5e68fa1fbd583c064d2462b675f194a3ddb4"
|
||||
),
|
||||
array(
|
||||
"494f4be219a1a77016dcd838431aea0001cdc8ae7a6fc688726578d9702857a5",
|
||||
"42242a969283a5f339ba7f075e36ba2af925ce30d767ed6e55f4b031880d562c"
|
||||
),
|
||||
array(
|
||||
"a598a8030da6d86c6bc7f2f5144ea549d28211ea58faa70ebf4c1e665c1fe9b5",
|
||||
"204b5d6f84822c307e4b4a7140737aec23fc63b65b35f86a10026dbd2d864e6b"
|
||||
),
|
||||
array(
|
||||
"c41916365abb2b5d09192f5f2dbeafec208f020f12570a184dbadc3e58595997",
|
||||
"4f14351d0087efa49d245b328984989d5caf9450f34bfc0ed16e96b58fa9913"
|
||||
),
|
||||
array(
|
||||
"841d6063a586fa475a724604da03bc5b92a2e0d2e0a36acfe4c73a5514742881",
|
||||
"73867f59c0659e81904f9a1c7543698e62562d6744c169ce7a36de01a8d6154"
|
||||
),
|
||||
array(
|
||||
"5e95bb399a6971d376026947f89bde2f282b33810928be4ded112ac4d70e20d5",
|
||||
"39f23f366809085beebfc71181313775a99c9aed7d8ba38b161384c746012865"
|
||||
),
|
||||
array(
|
||||
"36e4641a53948fd476c39f8a99fd974e5ec07564b5315d8bf99471bca0ef2f66",
|
||||
"d2424b1b1abe4eb8164227b085c9aa9456ea13493fd563e06fd51cf5694c78fc"
|
||||
),
|
||||
array(
|
||||
"336581ea7bfbbb290c191a2f507a41cf5643842170e914faeab27c2c579f726",
|
||||
"ead12168595fe1be99252129b6e56b3391f7ab1410cd1e0ef3dcdcabd2fda224"
|
||||
),
|
||||
array(
|
||||
"8ab89816dadfd6b6a1f2634fcf00ec8403781025ed6890c4849742706bd43ede",
|
||||
"6fdcef09f2f6d0a044e654aef624136f503d459c3e89845858a47a9129cdd24e"
|
||||
),
|
||||
array(
|
||||
"1e33f1a746c9c5778133344d9299fcaa20b0938e8acff2544bb40284b8c5fb94",
|
||||
"60660257dd11b3aa9c8ed618d24edff2306d320f1d03010e33a7d2057f3b3b6"
|
||||
),
|
||||
array(
|
||||
"85b7c1dcb3cec1b7ee7f30ded79dd20a0ed1f4cc18cbcfcfa410361fd8f08f31",
|
||||
"3d98a9cdd026dd43f39048f25a8847f4fcafad1895d7a633c6fed3c35e999511"
|
||||
),
|
||||
array(
|
||||
"29df9fbd8d9e46509275f4b125d6d45d7fbe9a3b878a7af872a2800661ac5f51",
|
||||
"b4c4fe99c775a606e2d8862179139ffda61dc861c019e55cd2876eb2a27d84b"
|
||||
),
|
||||
array(
|
||||
"a0b1cae06b0a847a3fea6e671aaf8adfdfe58ca2f768105c8082b2e449fce252",
|
||||
"ae434102edde0958ec4b19d917a6a28e6b72da1834aff0e650f049503a296cf2"
|
||||
),
|
||||
array(
|
||||
"4e8ceafb9b3e9a136dc7ff67e840295b499dfb3b2133e4ba113f2e4c0e121e5",
|
||||
"cf2174118c8b6d7a4b48f6d534ce5c79422c086a63460502b827ce62a326683c"
|
||||
),
|
||||
array(
|
||||
"d24a44e047e19b6f5afb81c7ca2f69080a5076689a010919f42725c2b789a33b",
|
||||
"6fb8d5591b466f8fc63db50f1c0f1c69013f996887b8244d2cdec417afea8fa3"
|
||||
),
|
||||
array(
|
||||
"ea01606a7a6c9cdd249fdfcfacb99584001edd28abbab77b5104e98e8e3b35d4",
|
||||
"322af4908c7312b0cfbfe369f7a7b3cdb7d4494bc2823700cfd652188a3ea98d"
|
||||
),
|
||||
array(
|
||||
"af8addbf2b661c8a6c6328655eb96651252007d8c5ea31be4ad196de8ce2131f",
|
||||
"6749e67c029b85f52a034eafd096836b2520818680e26ac8f3dfbcdb71749700"
|
||||
),
|
||||
array(
|
||||
"e3ae1974566ca06cc516d47e0fb165a674a3dabcfca15e722f0e3450f45889",
|
||||
"2aeabe7e4531510116217f07bf4d07300de97e4874f81f533420a72eeb0bd6a4"
|
||||
),
|
||||
array(
|
||||
"591ee355313d99721cf6993ffed1e3e301993ff3ed258802075ea8ced397e246",
|
||||
"b0ea558a113c30bea60fc4775460c7901ff0b053d25ca2bdeee98f1a4be5d196"
|
||||
),
|
||||
array(
|
||||
"11396d55fda54c49f19aa97318d8da61fa8584e47b084945077cf03255b52984",
|
||||
"998c74a8cd45ac01289d5833a7beb4744ff536b01b257be4c5767bea93ea57a4"
|
||||
),
|
||||
array(
|
||||
"3c5d2a1ba39c5a1790000738c9e0c40b8dcdfd5468754b6405540157e017aa7a",
|
||||
"b2284279995a34e2f9d4de7396fc18b80f9b8b9fdd270f6661f79ca4c81bd257"
|
||||
),
|
||||
array(
|
||||
"cc8704b8a60a0defa3a99a7299f2e9c3fbc395afb04ac078425ef8a1793cc030",
|
||||
"bdd46039feed17881d1e0862db347f8cf395b74fc4bcdc4e940b74e3ac1f1b13"
|
||||
),
|
||||
array(
|
||||
"c533e4f7ea8555aacd9777ac5cad29b97dd4defccc53ee7ea204119b2889b197",
|
||||
"6f0a256bc5efdf429a2fb6242f1a43a2d9b925bb4a4b3a26bb8e0f45eb596096"
|
||||
),
|
||||
array(
|
||||
"c14f8f2ccb27d6f109f6d08d03cc96a69ba8c34eec07bbcf566d48e33da6593",
|
||||
"c359d6923bb398f7fd4473e16fe1c28475b740dd098075e6c0e8649113dc3a38"
|
||||
),
|
||||
array(
|
||||
"a6cbc3046bc6a450bac24789fa17115a4c9739ed75f8f21ce441f72e0b90e6ef",
|
||||
"21ae7f4680e889bb130619e2c0f95a360ceb573c70603139862afd617fa9b9f"
|
||||
),
|
||||
array(
|
||||
"347d6d9a02c48927ebfb86c1359b1caf130a3c0267d11ce6344b39f99d43cc38",
|
||||
"60ea7f61a353524d1c987f6ecec92f086d565ab687870cb12689ff1e31c74448"
|
||||
),
|
||||
array(
|
||||
"da6545d2181db8d983f7dcb375ef5866d47c67b1bf31c8cf855ef7437b72656a",
|
||||
"49b96715ab6878a79e78f07ce5680c5d6673051b4935bd897fea824b77dc208a"
|
||||
),
|
||||
array(
|
||||
"c40747cc9d012cb1a13b8148309c6de7ec25d6945d657146b9d5994b8feb1111",
|
||||
"5ca560753be2a12fc6de6caf2cb489565db936156b9514e1bb5e83037e0fa2d4"
|
||||
),
|
||||
array(
|
||||
"4e42c8ec82c99798ccf3a610be870e78338c7f713348bd34c8203ef4037f3502",
|
||||
"7571d74ee5e0fb92a7a8b33a07783341a5492144cc54bcc40a94473693606437"
|
||||
),
|
||||
array(
|
||||
"3775ab7089bc6af823aba2e1af70b236d251cadb0c86743287522a1b3b0dedea",
|
||||
"be52d107bcfa09d8bcb9736a828cfa7fac8db17bf7a76a2c42ad961409018cf7"
|
||||
),
|
||||
array(
|
||||
"cee31cbf7e34ec379d94fb814d3d775ad954595d1314ba8846959e3e82f74e26",
|
||||
"8fd64a14c06b589c26b947ae2bcf6bfa0149ef0be14ed4d80f448a01c43b1c6d"
|
||||
),
|
||||
array(
|
||||
"b4f9eaea09b6917619f6ea6a4eb5464efddb58fd45b1ebefcdc1a01d08b47986",
|
||||
"39e5c9925b5a54b07433a4f18c61726f8bb131c012ca542eb24a8ac07200682a"
|
||||
),
|
||||
array(
|
||||
"d4263dfc3d2df923a0179a48966d30ce84e2515afc3dccc1b77907792ebcc60e",
|
||||
"62dfaf07a0f78feb30e30d6295853ce189e127760ad6cf7fae164e122a208d54"
|
||||
),
|
||||
array(
|
||||
"48457524820fa65a4f8d35eb6930857c0032acc0a4a2de422233eeda897612c4",
|
||||
"25a748ab367979d98733c38a1fa1c2e7dc6cc07db2d60a9ae7a76aaa49bd0f77"
|
||||
),
|
||||
array(
|
||||
"dfeeef1881101f2cb11644f3a2afdfc2045e19919152923f367a1767c11cceda",
|
||||
"ecfb7056cf1de042f9420bab396793c0c390bde74b4bbdff16a83ae09a9a7517"
|
||||
),
|
||||
array(
|
||||
"6d7ef6b17543f8373c573f44e1f389835d89bcbc6062ced36c82df83b8fae859",
|
||||
"cd450ec335438986dfefa10c57fea9bcc521a0959b2d80bbf74b190dca712d10"
|
||||
),
|
||||
array(
|
||||
"e75605d59102a5a2684500d3b991f2e3f3c88b93225547035af25af66e04541f",
|
||||
"f5c54754a8f71ee540b9b48728473e314f729ac5308b06938360990e2bfad125"
|
||||
),
|
||||
array(
|
||||
"eb98660f4c4dfaa06a2be453d5020bc99a0c2e60abe388457dd43fefb1ed620c",
|
||||
"6cb9a8876d9cb8520609af3add26cd20a0a7cd8a9411131ce85f44100099223e"
|
||||
),
|
||||
array(
|
||||
"13e87b027d8514d35939f2e6892b19922154596941888336dc3563e3b8dba942",
|
||||
"fef5a3c68059a6dec5d624114bf1e91aac2b9da568d6abeb2570d55646b8adf1"
|
||||
),
|
||||
array(
|
||||
"ee163026e9fd6fe017c38f06a5be6fc125424b371ce2708e7bf4491691e5764a",
|
||||
"1acb250f255dd61c43d94ccc670d0f58f49ae3fa15b96623e5430da0ad6c62b2"
|
||||
),
|
||||
array(
|
||||
"b268f5ef9ad51e4d78de3a750c2dc89b1e626d43505867999932e5db33af3d80",
|
||||
"5f310d4b3c99b9ebb19f77d41c1dee018cf0d34fd4191614003e945a1216e423"
|
||||
),
|
||||
array(
|
||||
"ff07f3118a9df035e9fad85eb6c7bfe42b02f01ca99ceea3bf7ffdba93c4750d",
|
||||
"438136d603e858a3a5c440c38eccbaddc1d2942114e2eddd4740d098ced1f0d8"
|
||||
),
|
||||
array(
|
||||
"8d8b9855c7c052a34146fd20ffb658bea4b9f69e0d825ebec16e8c3ce2b526a1",
|
||||
"cdb559eedc2d79f926baf44fb84ea4d44bcf50fee51d7ceb30e2e7f463036758"
|
||||
),
|
||||
array(
|
||||
"52db0b5384dfbf05bfa9d472d7ae26dfe4b851ceca91b1eba54263180da32b63",
|
||||
"c3b997d050ee5d423ebaf66a6db9f57b3180c902875679de924b69d84a7b375"
|
||||
),
|
||||
array(
|
||||
"e62f9490d3d51da6395efd24e80919cc7d0f29c3f3fa48c6fff543becbd43352",
|
||||
"6d89ad7ba4876b0b22c2ca280c682862f342c8591f1daf5170e07bfd9ccafa7d"
|
||||
),
|
||||
array(
|
||||
"7f30ea2476b399b4957509c88f77d0191afa2ff5cb7b14fd6d8e7d65aaab1193",
|
||||
"ca5ef7d4b231c94c3b15389a5f6311e9daff7bb67b103e9880ef4bff637acaec"
|
||||
),
|
||||
array(
|
||||
"5098ff1e1d9f14fb46a210fada6c903fef0fb7b4a1dd1d9ac60a0361800b7a00",
|
||||
"9731141d81fc8f8084d37c6e7542006b3ee1b40d60dfe5362a5b132fd17ddc0"
|
||||
),
|
||||
array(
|
||||
"32b78c7de9ee512a72895be6b9cbefa6e2f3c4ccce445c96b9f2c81e2778ad58",
|
||||
"ee1849f513df71e32efc3896ee28260c73bb80547ae2275ba497237794c8753c"
|
||||
),
|
||||
array(
|
||||
"e2cb74fddc8e9fbcd076eef2a7c72b0ce37d50f08269dfc074b581550547a4f7",
|
||||
"d3aa2ed71c9dd2247a62df062736eb0baddea9e36122d2be8641abcb005cc4a4"
|
||||
),
|
||||
array(
|
||||
"8438447566d4d7bedadc299496ab357426009a35f235cb141be0d99cd10ae3a8",
|
||||
"c4e1020916980a4da5d01ac5e6ad330734ef0d7906631c4f2390426b2edd791f"
|
||||
),
|
||||
array(
|
||||
"4162d488b89402039b584c6fc6c308870587d9c46f660b878ab65c82c711d67e",
|
||||
"67163e903236289f776f22c25fb8a3afc1732f2b84b4e95dbda47ae5a0852649"
|
||||
),
|
||||
array(
|
||||
"3fad3fa84caf0f34f0f89bfd2dcf54fc175d767aec3e50684f3ba4a4bf5f683d",
|
||||
"cd1bc7cb6cc407bb2f0ca647c718a730cf71872e7d0d2a53fa20efcdfe61826"
|
||||
),
|
||||
array(
|
||||
"674f2600a3007a00568c1a7ce05d0816c1fb84bf1370798f1c69532faeb1a86b",
|
||||
"299d21f9413f33b3edf43b257004580b70db57da0b182259e09eecc69e0d38a5"
|
||||
),
|
||||
array(
|
||||
"d32f4da54ade74abb81b815ad1fb3b263d82d6c692714bcff87d29bd5ee9f08f",
|
||||
"f9429e738b8e53b968e99016c059707782e14f4535359d582fc416910b3eea87"
|
||||
),
|
||||
array(
|
||||
"30e4e670435385556e593657135845d36fbb6931f72b08cb1ed954f1e3ce3ff6",
|
||||
"462f9bce619898638499350113bbc9b10a878d35da70740dc695a559eb88db7b"
|
||||
),
|
||||
array(
|
||||
"be2062003c51cc3004682904330e4dee7f3dcd10b01e580bf1971b04d4cad297",
|
||||
"62188bc49d61e5428573d48a74e1c655b1c61090905682a0d5558ed72dccb9bc"
|
||||
),
|
||||
array(
|
||||
"93144423ace3451ed29e0fb9ac2af211cb6e84a601df5993c419859fff5df04a",
|
||||
"7c10dfb164c3425f5c71a3f9d7992038f1065224f72bb9d1d902a6d13037b47c"
|
||||
),
|
||||
array(
|
||||
"b015f8044f5fcbdcf21ca26d6c34fb8197829205c7b7d2a7cb66418c157b112c",
|
||||
"ab8c1e086d04e813744a655b2df8d5f83b3cdc6faa3088c1d3aea1454e3a1d5f"
|
||||
),
|
||||
array(
|
||||
"d5e9e1da649d97d89e4868117a465a3a4f8a18de57a140d36b3f2af341a21b52",
|
||||
"4cb04437f391ed73111a13cc1d4dd0db1693465c2240480d8955e8592f27447a"
|
||||
),
|
||||
array(
|
||||
"d3ae41047dd7ca065dbf8ed77b992439983005cd72e16d6f996a5316d36966bb",
|
||||
"bd1aeb21ad22ebb22a10f0303417c6d964f8cdd7df0aca614b10dc14d125ac46"
|
||||
),
|
||||
array(
|
||||
"463e2763d885f958fc66cdd22800f0a487197d0a82e377b49f80af87c897b065",
|
||||
"bfefacdb0e5d0fd7df3a311a94de062b26b80c61fbc97508b79992671ef7ca7f"
|
||||
),
|
||||
array(
|
||||
"7985fdfd127c0567c6f53ec1bb63ec3158e597c40bfe747c83cddfc910641917",
|
||||
"603c12daf3d9862ef2b25fe1de289aed24ed291e0ec6708703a5bd567f32ed03"
|
||||
),
|
||||
array(
|
||||
"74a1ad6b5f76e39db2dd249410eac7f99e74c59cb83d2d0ed5ff1543da7703e9",
|
||||
"cc6157ef18c9c63cd6193d83631bbea0093e0968942e8c33d5737fd790e0db08"
|
||||
),
|
||||
array(
|
||||
"30682a50703375f602d416664ba19b7fc9bab42c72747463a71d0896b22f6da3",
|
||||
"553e04f6b018b4fa6c8f39e7f311d3176290d0e0f19ca73f17714d9977a22ff8"
|
||||
),
|
||||
array(
|
||||
"9e2158f0d7c0d5f26c3791efefa79597654e7a2b2464f52b1ee6c1347769ef57",
|
||||
"712fcdd1b9053f09003a3481fa7762e9ffd7c8ef35a38509e2fbf2629008373"
|
||||
),
|
||||
array(
|
||||
"176e26989a43c9cfeba4029c202538c28172e566e3c4fce7322857f3be327d66",
|
||||
"ed8cc9d04b29eb877d270b4878dc43c19aefd31f4eee09ee7b47834c1fa4b1c3"
|
||||
),
|
||||
array(
|
||||
"75d46efea3771e6e68abb89a13ad747ecf1892393dfc4f1b7004788c50374da8",
|
||||
"9852390a99507679fd0b86fd2b39a868d7efc22151346e1a3ca4726586a6bed8"
|
||||
),
|
||||
array(
|
||||
"809a20c67d64900ffb698c4c825f6d5f2310fb0451c869345b7319f645605721",
|
||||
"9e994980d9917e22b76b061927fa04143d096ccc54963e6a5ebfa5f3f8e286c1"
|
||||
),
|
||||
array(
|
||||
"1b38903a43f7f114ed4500b4eac7083fdefece1cf29c63528d563446f972c180",
|
||||
"4036edc931a60ae889353f77fd53de4a2708b26b6f5da72ad3394119daf408f9"
|
||||
)
|
||||
)
|
||||
)
|
||||
);
|
||||
|
||||
Curves::defineCurve("secp256k1", array(
|
||||
"type" => "short",
|
||||
"prime" => "k256",
|
||||
"p" => "ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f",
|
||||
"a" => "0",
|
||||
"b" => "7",
|
||||
"n" => "ffffffff ffffffff ffffffff fffffffe baaedce6 af48a03b bfd25e8c d0364141",
|
||||
"h" => "1",
|
||||
"hash" => array(
|
||||
"outSize" => 256,
|
||||
"hmacStrength" => 192,
|
||||
"algo" => "sha256"
|
||||
),
|
||||
|
||||
// Precomputed endomorphism
|
||||
"beta" => "7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee",
|
||||
"lambda" => "5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72",
|
||||
"basis" => array(
|
||||
array(
|
||||
"a" => "3086d221a7d46bcde86c90e49284eb15",
|
||||
"b" => "-e4437ed6010e88286f547fa90abfe4c3"
|
||||
),
|
||||
array(
|
||||
"a" => "114ca50f7a8e2f3f657c1108d9d44cfd8",
|
||||
"b" => "3086d221a7d46bcde86c90e49284eb15"
|
||||
)
|
||||
),
|
||||
|
||||
"gRed" => false,
|
||||
"g" => array(
|
||||
"79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798",
|
||||
"483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8",
|
||||
$pre
|
||||
)
|
||||
));
|
||||
|
||||
?>
|
||||
+278
@@ -0,0 +1,278 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic;
|
||||
|
||||
use Elliptic\Curve\PresetCurve;
|
||||
use Elliptic\EC\KeyPair;
|
||||
use Elliptic\EC\Signature;
|
||||
use BN\BN;
|
||||
|
||||
class EC
|
||||
{
|
||||
public $curve;
|
||||
public $n;
|
||||
public $nh;
|
||||
public $g;
|
||||
public $hash;
|
||||
|
||||
function __construct($options)
|
||||
{
|
||||
if( is_string($options) )
|
||||
{
|
||||
$options = Curves::getCurve($options);
|
||||
}
|
||||
|
||||
if( $options instanceof PresetCurve )
|
||||
$options = array("curve" => $options);
|
||||
|
||||
$this->curve = $options["curve"]->curve;
|
||||
$this->n = $this->curve->n;
|
||||
$this->nh = $this->n->ushrn(1);
|
||||
|
||||
//Point on curve
|
||||
$this->g = $options["curve"]->g;
|
||||
$this->g->precompute($options["curve"]->n->bitLength() + 1);
|
||||
|
||||
//Hash for function for DRBG
|
||||
if( isset($options["hash"]) )
|
||||
$this->hash = $options["hash"];
|
||||
else
|
||||
$this->hash = $options["curve"]->hash;
|
||||
}
|
||||
|
||||
public function keyPair(#[\SensitiveParameter]
|
||||
$options) {
|
||||
return new KeyPair($this, $options);
|
||||
}
|
||||
|
||||
public function keyFromPrivate(#[\SensitiveParameter]
|
||||
$priv, $enc = false) {
|
||||
return KeyPair::fromPrivate($this, $priv, $enc);
|
||||
}
|
||||
|
||||
public function keyFromPublic($pub, $enc = false) {
|
||||
return KeyPair::fromPublic($this, $pub, $enc);
|
||||
}
|
||||
|
||||
public function genKeyPair($options = null)
|
||||
{
|
||||
// Instantiate HmacDRBG
|
||||
$drbg = new HmacDRBG(array(
|
||||
"hash" => $this->hash,
|
||||
"pers" => isset($options["pers"]) ? $options["pers"] : "",
|
||||
"entropy" => isset($options["entropy"]) ? $options["entropy"] : Utils::randBytes($this->hash["hmacStrength"]),
|
||||
"nonce" => $this->n->toArray()
|
||||
));
|
||||
|
||||
$bytes = $this->n->byteLength();
|
||||
$ns2 = $this->n->sub(new BN(2));
|
||||
while(true)
|
||||
{
|
||||
$priv = new BN($drbg->generate($bytes));
|
||||
if( $priv->cmp($ns2) > 0 )
|
||||
continue;
|
||||
|
||||
$priv->iaddn(1);
|
||||
return $this->keyFromPrivate($priv);
|
||||
}
|
||||
}
|
||||
|
||||
private function _truncateToN($msg, $truncOnly = false)
|
||||
{
|
||||
$delta = intval(($msg->byteLength() * 8) - $this->n->bitLength());
|
||||
if( $delta > 0 ) {
|
||||
$msg = $msg->ushrn($delta);
|
||||
}
|
||||
if( $truncOnly || $msg->cmp($this->n) < 0 )
|
||||
return $msg;
|
||||
|
||||
return $msg->sub($this->n);
|
||||
}
|
||||
|
||||
public function sign($msg, #[\SensitiveParameter]
|
||||
$key, $enc = null, $options = null)
|
||||
{
|
||||
if( !is_string($enc) )
|
||||
{
|
||||
$options = $enc;
|
||||
$enc = null;
|
||||
}
|
||||
|
||||
$key = $this->keyFromPrivate($key, $enc);
|
||||
$msg = $this->_truncateToN(new BN($msg, 16));
|
||||
|
||||
// Zero-extend key to provide enough entropy
|
||||
$bytes = $this->n->byteLength();
|
||||
$bkey = $key->getPrivate()->toArray("be", $bytes);
|
||||
|
||||
// Zero-extend nonce to have the same byte size as N
|
||||
$nonce = $msg->toArray("be", $bytes);
|
||||
|
||||
$kFunc = null;
|
||||
if( isset($options["k"]) )
|
||||
$kFunc = $options["k"];
|
||||
else
|
||||
{
|
||||
// Instatiate HmacDRBG
|
||||
$drbg = new HmacDRBG(array(
|
||||
"hash" => $this->hash,
|
||||
"entropy" => $bkey,
|
||||
"nonce" => $nonce,
|
||||
"pers" => isset($options["pers"]) ? $options["pers"] : "",
|
||||
"persEnc" => isset($options["persEnc"]) ? $options["persEnc"] : false
|
||||
));
|
||||
|
||||
$kFunc = function($iter) use ($drbg, $bytes) {
|
||||
return new BN($drbg->generate($bytes));
|
||||
};
|
||||
}
|
||||
|
||||
// Number of bytes to generate
|
||||
$ns1 = $this->n->sub(new BN(1));
|
||||
|
||||
$canonical = isset($options["canonical"]) ? $options["canonical"] : false;
|
||||
for($iter = 0; true; $iter++)
|
||||
{
|
||||
$k = $kFunc($iter);
|
||||
$k = $this->_truncateToN($k, true);
|
||||
|
||||
if( $k->cmpn(1) <= 0 || $k->cmp($ns1) >= 0 )
|
||||
continue;
|
||||
|
||||
// Fix the bit-length of the random nonce,
|
||||
// so that it doesn't leak via timing.
|
||||
// This does not change that ks = k mod k
|
||||
$ks = $k->add($this->n);
|
||||
$kt = $ks->add($this->n);
|
||||
if ($ks->bitLength() === $this->n->bitLength()) {
|
||||
$kp = $this->g->mul($kt);
|
||||
} else {
|
||||
$kp = $this->g->mul($ks);
|
||||
}
|
||||
|
||||
if( $kp->isInfinity() )
|
||||
continue;
|
||||
|
||||
$kpX = $kp->getX();
|
||||
$r = $kpX->umod($this->n);
|
||||
if( $r->isZero() )
|
||||
continue;
|
||||
|
||||
$s = $k->invm($this->n)->mul($r->mul($key->getPrivate())->iadd($msg));
|
||||
$s = $s->umod($this->n);
|
||||
if( $s->isZero() )
|
||||
continue;
|
||||
|
||||
$recoveryParam = ($kp->getY()->isOdd() ? 1 : 0) | ($kpX->cmp($r) !== 0 ? 2 : 0);
|
||||
|
||||
// Use complement of `s`, if it is > `n / 2`
|
||||
if( $canonical && $s->cmp($this->nh) > 0 )
|
||||
{
|
||||
$s = $this->n->sub($s);
|
||||
$recoveryParam ^= 1;
|
||||
}
|
||||
|
||||
return new Signature(array(
|
||||
"r" => $r,
|
||||
"s" => $s,
|
||||
"recoveryParam" => $recoveryParam
|
||||
));
|
||||
}
|
||||
}
|
||||
|
||||
public function verify($msg, $signature, $key, $enc = false)
|
||||
{
|
||||
$msg = $this->_truncateToN(new BN($msg, 16));
|
||||
$key = $this->keyFromPublic($key, $enc);
|
||||
$signature = new Signature($signature, "hex");
|
||||
|
||||
// Perform primitive values validation
|
||||
$r = $signature->r;
|
||||
$s = $signature->s;
|
||||
|
||||
if( $r->cmpn(1) < 0 || $r->cmp($this->n) >= 0 )
|
||||
return false;
|
||||
if( $s->cmpn(1) < 0 || $s->cmp($this->n) >= 0 )
|
||||
return false;
|
||||
|
||||
// Validate signature
|
||||
$sinv = $s->invm($this->n);
|
||||
$u1 = $sinv->mul($msg)->umod($this->n);
|
||||
$u2 = $sinv->mul($r)->umod($this->n);
|
||||
|
||||
if( !$this->curve->_maxwellTrick )
|
||||
{
|
||||
$p = $this->g->mulAdd($u1, $key->getPublic(), $u2);
|
||||
if( $p->isInfinity() )
|
||||
return false;
|
||||
|
||||
return $p->getX()->umod($this->n)->cmp($r) === 0;
|
||||
}
|
||||
|
||||
// NOTE: Greg Maxwell's trick, inspired by:
|
||||
// https://git.io/vad3K
|
||||
|
||||
$p = $this->g->jmulAdd($u1, $key->getPublic(), $u2);
|
||||
if( $p->isInfinity() )
|
||||
return false;
|
||||
|
||||
// Compare `p.x` of Jacobian point with `r`,
|
||||
// this will do `p.x == r * p.z^2` instead of multiplying `p.x` by the
|
||||
// inverse of `p.z^2`
|
||||
return $p->eqXToP($r);
|
||||
}
|
||||
|
||||
public function recoverPubKey($msg, $signature, $j, $enc = false)
|
||||
{
|
||||
assert((3 & $j) === $j); //, "The recovery param is more than two bits");
|
||||
$signature = new Signature($signature, $enc);
|
||||
|
||||
$e = new BN($msg, 16);
|
||||
$r = $signature->r;
|
||||
$s = $signature->s;
|
||||
|
||||
// A set LSB signifies that the y-coordinate is odd
|
||||
$isYOdd = ($j & 1) == 1;
|
||||
$isSecondKey = $j >> 1;
|
||||
|
||||
if ($r->cmp($this->curve->p->umod($this->curve->n)) >= 0 && $isSecondKey)
|
||||
throw new \Exception("Unable to find second key candinate");
|
||||
|
||||
// 1.1. Let x = r + jn.
|
||||
if( $isSecondKey )
|
||||
$r = $this->curve->pointFromX($r->add($this->curve->n), $isYOdd);
|
||||
else
|
||||
$r = $this->curve->pointFromX($r, $isYOdd);
|
||||
|
||||
$eNeg = $this->n->sub($e);
|
||||
|
||||
// 1.6.1 Compute Q = r^-1 (sR - eG)
|
||||
// Q = r^-1 (sR + -eG)
|
||||
$rInv = $signature->r->invm($this->n);
|
||||
return $this->g->mulAdd($eNeg, $r, $s)->mul($rInv);
|
||||
}
|
||||
|
||||
public function getKeyRecoveryParam($e, $signature, $Q, $enc = false)
|
||||
{
|
||||
$signature = new Signature($signature, $enc);
|
||||
if( $signature->recoveryParam != null )
|
||||
return $signature->recoveryParam;
|
||||
|
||||
for($i = 0; $i < 4; $i++)
|
||||
{
|
||||
$Qprime = null;
|
||||
try {
|
||||
$Qprime = $this->recoverPubKey($e, $signature, $i);
|
||||
}
|
||||
catch(\Exception $e) {
|
||||
continue;
|
||||
}
|
||||
|
||||
if( $Qprime->eq($Q))
|
||||
return $i;
|
||||
}
|
||||
throw new \Exception("Unable to find valid recovery factor");
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
+144
@@ -0,0 +1,144 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic\EC;
|
||||
|
||||
use BN\BN;
|
||||
|
||||
class KeyPair
|
||||
{
|
||||
public $ec;
|
||||
public $pub;
|
||||
public $priv;
|
||||
|
||||
function __construct($ec, #[\SensitiveParameter]
|
||||
$options)
|
||||
{
|
||||
$this->ec = $ec;
|
||||
|
||||
$this->priv = null;
|
||||
$this->pub = null;
|
||||
|
||||
if( isset($options["priv"]) )
|
||||
$this->_importPrivate($options["priv"], $options["privEnc"]);
|
||||
|
||||
if( isset($options["pub"]) )
|
||||
$this->_importPublic($options["pub"], $options["pubEnc"]);
|
||||
}
|
||||
|
||||
public static function fromPublic($ec, $pub, $enc)
|
||||
{
|
||||
if( $pub instanceof KeyPair )
|
||||
return $pub;
|
||||
|
||||
return new KeyPair($ec, array(
|
||||
"pub" => $pub,
|
||||
"pubEnc" => $enc
|
||||
));
|
||||
}
|
||||
|
||||
public static function fromPrivate($ec, #[\SensitiveParameter]
|
||||
$priv, $enc)
|
||||
{
|
||||
if( $priv instanceof KeyPair )
|
||||
return $priv;
|
||||
|
||||
return new KeyPair($ec, array(
|
||||
"priv" => $priv,
|
||||
"privEnc" => $enc
|
||||
));
|
||||
}
|
||||
|
||||
public function validate()
|
||||
{
|
||||
$pub = $this->getPublic();
|
||||
|
||||
if( $pub->isInfinity() )
|
||||
return array( "result" => false, "reason" => "Invalid public key" );
|
||||
|
||||
if( !$pub->validate() )
|
||||
return array( "result" => false, "reason" => "Public key is not a point" );
|
||||
|
||||
if( !$pub->mul($this->ec->curve->n)->isInfinity() )
|
||||
return array( "result" => false, "reason" => "Public key * N != O" );
|
||||
|
||||
return array( "result" => true, "reason" => null );
|
||||
}
|
||||
|
||||
public function getPublic($compact = false, $enc = "")
|
||||
{
|
||||
//compact is optional argument
|
||||
if( is_string($compact) )
|
||||
{
|
||||
$enc = $compact;
|
||||
$compact = false;
|
||||
}
|
||||
|
||||
if( $this->pub === null )
|
||||
$this->pub = $this->ec->g->mul($this->priv);
|
||||
|
||||
if( !$enc )
|
||||
return $this->pub;
|
||||
|
||||
return $this->pub->encode($enc, $compact);
|
||||
}
|
||||
|
||||
public function getPrivate($enc = false)
|
||||
{
|
||||
if( $enc === "hex" )
|
||||
return $this->priv->toString(16, 2);
|
||||
|
||||
return $this->priv;
|
||||
}
|
||||
|
||||
private function _importPrivate(#[\SensitiveParameter]
|
||||
$key, $enc)
|
||||
{
|
||||
$this->priv = new BN($key, (isset($enc) && $enc) ? $enc : 16);
|
||||
|
||||
// Ensure that the priv won't be bigger than n, otherwise we may fail
|
||||
// in fixed multiplication method
|
||||
$this->priv = $this->priv->umod($this->ec->curve->n);
|
||||
}
|
||||
|
||||
private function _importPublic($key, $enc)
|
||||
{
|
||||
$x = $y = null;
|
||||
if ( is_object($key) ) {
|
||||
$x = $key->x;
|
||||
$y = $key->y;
|
||||
} elseif ( is_array($key) ) {
|
||||
$x = isset($key["x"]) ? $key["x"] : null;
|
||||
$y = isset($key["y"]) ? $key["y"] : null;
|
||||
}
|
||||
|
||||
if( $x != null || $y != null )
|
||||
$this->pub = $this->ec->curve->point($x, $y);
|
||||
else
|
||||
$this->pub = $this->ec->curve->decodePoint($key, $enc);
|
||||
}
|
||||
|
||||
//ECDH
|
||||
public function derive($pub) {
|
||||
return $pub->mul($this->priv)->getX();
|
||||
}
|
||||
|
||||
//ECDSA
|
||||
public function sign($msg, $enc = false, $options = false) {
|
||||
return $this->ec->sign($msg, $this, $enc, $options);
|
||||
}
|
||||
|
||||
public function verify($msg, $signature) {
|
||||
return $this->ec->verify($msg, $signature, $this);
|
||||
}
|
||||
|
||||
public function inspect() {
|
||||
return "<Key priv: " . (isset($this->priv) ? $this->priv->toString(16, 2) : "") .
|
||||
" pub: " . (isset($this->pub) ? $this->pub->inspect() : "") . ">";
|
||||
}
|
||||
|
||||
public function __debugInfo() {
|
||||
return ["priv" => $this->priv, "pub" => $this->pub];
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
+155
@@ -0,0 +1,155 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic\EC;
|
||||
|
||||
use Elliptic\Utils;
|
||||
use BN\BN;
|
||||
|
||||
class Signature
|
||||
{
|
||||
public $r;
|
||||
public $s;
|
||||
public $recoveryParam;
|
||||
|
||||
function __construct($options, $enc = false)
|
||||
{
|
||||
if ($options instanceof Signature) {
|
||||
$this->r = $options->r;
|
||||
$this->s = $options->s;
|
||||
$this->recoveryParam = $options->recoveryParam;
|
||||
return;
|
||||
}
|
||||
|
||||
if (isset($options['r'])) {
|
||||
assert(isset($options["r"]) && isset($options["s"])); //, "Signature without r or s");
|
||||
$this->r = new BN($options["r"], 16);
|
||||
$this->s = new BN($options["s"], 16);
|
||||
|
||||
if( isset($options["recoveryParam"]) )
|
||||
$this->recoveryParam = $options["recoveryParam"];
|
||||
else
|
||||
$this->recoveryParam = null;
|
||||
return;
|
||||
}
|
||||
|
||||
if (!$this->_importDER($options, $enc))
|
||||
throw new \Exception('Unknown signature format');
|
||||
|
||||
}
|
||||
|
||||
private static function getLength($buf, &$pos)
|
||||
{
|
||||
$initial = $buf[$pos++];
|
||||
if( !($initial & 0x80) )
|
||||
return $initial;
|
||||
|
||||
$octetLen = $initial & 0xf;
|
||||
$val = 0;
|
||||
for($i = 0; $i < $octetLen; $i++)
|
||||
{
|
||||
$val = $val << 8;
|
||||
$val = $val | $buf[$pos];
|
||||
$pos++;
|
||||
}
|
||||
return $val;
|
||||
}
|
||||
|
||||
private static function rmPadding(&$buf)
|
||||
{
|
||||
$i = 0;
|
||||
$len = count($buf) - 1;
|
||||
while($i < $len && !$buf[$i] && !($buf[$i+1] & 0x80) )
|
||||
$i++;
|
||||
|
||||
if( $i === 0 )
|
||||
return $buf;
|
||||
|
||||
return array_slice($buf, $i);
|
||||
}
|
||||
|
||||
private function _importDER($data, $enc)
|
||||
{
|
||||
$data = Utils::toArray($data, $enc);
|
||||
$dataLen = count($data);
|
||||
$place = 0;
|
||||
|
||||
if( $data[$place++] !== 0x30)
|
||||
return false;
|
||||
|
||||
$len = self::getLength($data, $place);
|
||||
if( ($len + $place) !== $dataLen )
|
||||
return false;
|
||||
|
||||
if( $data[$place++] !== 0x02 )
|
||||
return false;
|
||||
|
||||
$rlen = self::getLength($data, $place);
|
||||
$r = array_slice($data, $place, $rlen);
|
||||
$place += $rlen;
|
||||
|
||||
if( $data[$place++] !== 0x02 )
|
||||
return false;
|
||||
|
||||
$slen = self::getLength($data, $place);
|
||||
if( $dataLen !== $slen + $place )
|
||||
return false;
|
||||
$s = array_slice($data, $place, $slen);
|
||||
|
||||
if( $r[0] === 0 && ($r[1] & 0x80 ) )
|
||||
$r = array_slice($r, 1);
|
||||
if( $s[0] === 0 && ($s[1] & 0x80 ) )
|
||||
$s = array_slice($s, 1);
|
||||
|
||||
$this->r = new BN($r);
|
||||
$this->s = new BN($s);
|
||||
$this->recoveryParam = null;
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
private static function constructLength(&$arr, $len)
|
||||
{
|
||||
if( $len < 0x80 )
|
||||
{
|
||||
array_push($arr, $len);
|
||||
return;
|
||||
}
|
||||
|
||||
$octets = 1 + (log($len) / M_LN2 >> 3);
|
||||
array_push($arr, $octets | 0x80);
|
||||
while(--$octets)
|
||||
array_push($arr, ($len >> ($octets << 3)) & 0xff);
|
||||
array_push($arr, $len);
|
||||
}
|
||||
|
||||
public function toDER($enc = false)
|
||||
{
|
||||
$r = $this->r->toArray();
|
||||
$s = $this->s->toArray();
|
||||
|
||||
//Pad values
|
||||
if( $r[0] & 0x80 )
|
||||
array_unshift($r, 0);
|
||||
if( $s[0] & 0x80 )
|
||||
array_unshift($s, 0);
|
||||
|
||||
$r = self::rmPadding($r);
|
||||
$s = self::rmPadding($s);
|
||||
|
||||
while(!$s[0] && !($s[1] & 0x80))
|
||||
array_slice($s, 1);
|
||||
|
||||
$arr = array(0x02);
|
||||
self::constructLength($arr, count($r));
|
||||
$arr = array_merge($arr, $r, array(0x02));
|
||||
self::constructLength($arr, count($s));
|
||||
$backHalf = array_merge($arr, $s);
|
||||
$res = array(0x30);
|
||||
self::constructLength($res, count($backHalf));
|
||||
$res = array_merge($res, $backHalf);
|
||||
|
||||
return Utils::encode($res, $enc);
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
+124
@@ -0,0 +1,124 @@
|
||||
<?php
|
||||
namespace Elliptic;
|
||||
|
||||
use Elliptic\EdDSA\KeyPair;
|
||||
use Elliptic\EdDSA\Signature;
|
||||
|
||||
class EdDSA {
|
||||
|
||||
public $curve;
|
||||
public $g;
|
||||
public $pointClass;
|
||||
public $encodingLength;
|
||||
public $hash;
|
||||
|
||||
function __construct($curve) {
|
||||
assert($curve == "ed25519"); //, 'only tested with ed25519 so far');
|
||||
|
||||
$curve = \Elliptic\Curves::getCurve($curve)->curve;
|
||||
$this->curve = $curve;
|
||||
$this->g = $curve->g;
|
||||
$this->g->precompute($curve->n->bitLength() + 1);
|
||||
|
||||
$this->pointClass = get_class($curve->point());
|
||||
$this->encodingLength = intval(ceil($curve->n->bitLength() / 8));
|
||||
// TODO: !!!
|
||||
$this->hash = [ "algo" => "sha512" ];
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {Array|String} message - message bytes
|
||||
* @param {Array|String|KeyPair} secret - secret bytes or a keypair
|
||||
* @returns {Signature} - signature
|
||||
*/
|
||||
public function sign($message, #[\SensitiveParameter]
|
||||
$secret) {
|
||||
$message = Utils::parseBytes($message);
|
||||
$key = $this->keyFromSecret($secret);
|
||||
$r = $this->hashInt($key->messagePrefix(), $message);
|
||||
$R = $this->g->mul($r);
|
||||
$Rencoded = $this->encodePoint($R);
|
||||
$s_ = $this->hashInt($Rencoded, $key->pubBytes(), $message)
|
||||
->mul($key->priv());
|
||||
$S = $r->add($s_)->umod($this->curve->n);
|
||||
return $this->makeSignature([ "R" => $R, "S" => $S, "Rencoded" => $Rencoded ]);
|
||||
}
|
||||
|
||||
/**
|
||||
* @param {Array} message - message bytes
|
||||
* @param {Array|String|Signature} sig - sig bytes
|
||||
* @param {Array|String|Point|KeyPair} pub - public key
|
||||
* @returns {Boolean} - true if public key matches sig of message
|
||||
*/
|
||||
public function verify($message, $sig, $pub) {
|
||||
$message = Utils::parseBytes($message);
|
||||
$sig = $this->makeSignature($sig);
|
||||
$key = $this->keyFromPublic($pub);
|
||||
$h = $this->hashInt($sig->Rencoded(), $key->pubBytes(), $message);
|
||||
$SG = $this->g->mul($sig->S());
|
||||
$RplusAh = $sig->R()->add($key->pub()->mul($h));
|
||||
return $RplusAh->eq($SG);
|
||||
}
|
||||
|
||||
public function hashInt() {
|
||||
$arguments = func_get_args();
|
||||
// TODO: refactor when hash-php is ready
|
||||
$hash = hash_init($this->hash["algo"]);
|
||||
for ($i = 0; $i < count($arguments); $i++)
|
||||
hash_update($hash, Utils::toBin($arguments[$i]));
|
||||
return Utils::intFromLE(hash_final($hash))->umod($this->curve->n);
|
||||
}
|
||||
|
||||
public function keyFromPublic($pub) {
|
||||
return KeyPair::fromPublic($this, $pub);
|
||||
}
|
||||
|
||||
public function keyFromSecret(#[\SensitiveParameter]
|
||||
$secret) {
|
||||
return KeyPair::fromSecret($this, $secret);
|
||||
}
|
||||
|
||||
public function makeSignature($sig) {
|
||||
if ($sig instanceof Signature)
|
||||
return $sig;
|
||||
return new Signature($this, $sig);
|
||||
}
|
||||
|
||||
/**
|
||||
* * https://tools.ietf.org/html/draft-josefsson-eddsa-ed25519-03#section-5.2
|
||||
*
|
||||
* EdDSA defines methods for encoding and decoding points and integers. These are
|
||||
* helper convenience methods, that pass along to utility functions implied
|
||||
* parameters.
|
||||
*
|
||||
*/
|
||||
public function encodePoint($point) {
|
||||
$enc = $point->getY()->toArray('le', $this->encodingLength);
|
||||
$enc[$this->encodingLength - 1] |= $point->getX()->isOdd() ? 0x80 : 0;
|
||||
return $enc;
|
||||
}
|
||||
|
||||
public function decodePoint($bytes) {
|
||||
$bytes = Utils::parseBytes($bytes);
|
||||
|
||||
$lastIx = count($bytes) - 1;
|
||||
$normed = $bytes;
|
||||
$normed[$lastIx] = $bytes[$lastIx] & ~0x80;
|
||||
$xIsOdd = ($bytes[$lastIx] & 0x80) !== 0;
|
||||
|
||||
$y = Utils::intFromLE($normed);
|
||||
return $this->curve->pointFromY($y, $xIsOdd);
|
||||
}
|
||||
|
||||
public function encodeInt($num) {
|
||||
return $num->toArray('le', $this->encodingLength);
|
||||
}
|
||||
|
||||
public function decodeInt($bytes) {
|
||||
return Utils::intFromLE($bytes);
|
||||
}
|
||||
|
||||
public function isPoint($val) {
|
||||
return is_a($val, $this->pointClass);
|
||||
}
|
||||
}
|
||||
+128
@@ -0,0 +1,128 @@
|
||||
<?php
|
||||
namespace Elliptic\EdDSA;
|
||||
|
||||
use Elliptic\Utils;
|
||||
|
||||
class KeyPair {
|
||||
public $eddsa;
|
||||
public $_pubBytes;
|
||||
/**
|
||||
* @param {\Elliptic\EdDSA} eddsa - instance
|
||||
* @param {Object} params - public/private key parameters
|
||||
*
|
||||
* @param {Array<Byte>} [params.secret] - secret seed bytes
|
||||
* @param {Point} [params.pub] - public key point (aka `A` in eddsa terms)
|
||||
* @param {Array<Byte>} [params.pub] - public key point encoded as bytes
|
||||
*
|
||||
*/
|
||||
function __construct($eddsa, #[\SensitiveParameter]
|
||||
$params) {
|
||||
$this->eddsa = $eddsa;
|
||||
$this->_secret = isset($params["secret"]) ? Utils::parseBytes($params["secret"]) : null;
|
||||
if (!isset($params["pub"])) {
|
||||
$this->_pub = null;
|
||||
$this->_pubBytes = null;
|
||||
return;
|
||||
}
|
||||
if ($eddsa->isPoint($params["pub"]))
|
||||
$this->_pub = $params["pub"];
|
||||
else
|
||||
$this->_pubBytes = Utils::parseBytes($params["pub"]);
|
||||
}
|
||||
|
||||
public static function fromPublic($eddsa, $pub) {
|
||||
if ($pub instanceof KeyPair)
|
||||
return $pub;
|
||||
return new KeyPair($eddsa, [ "pub" => $pub ]);
|
||||
}
|
||||
|
||||
public static function fromSecret($eddsa, #[\SensitiveParameter]
|
||||
$secret) {
|
||||
if ($secret instanceof KeyPair)
|
||||
return $secret;
|
||||
return new KeyPair($eddsa, [ "secret" => $secret ]);
|
||||
}
|
||||
|
||||
private $_secret;
|
||||
public function secret() {
|
||||
return $this->_secret;
|
||||
}
|
||||
|
||||
public function pubBytes() {
|
||||
if (!$this->_pubBytes)
|
||||
$this->_pubBytes = $this->eddsa->encodePoint($this->pub());
|
||||
return $this->_pubBytes;
|
||||
}
|
||||
|
||||
private $_pub;
|
||||
public function pub() {
|
||||
if (!$this->_pub) {
|
||||
if ($this->_pubBytes)
|
||||
$this->_pub = $this->eddsa->decodePoint($this->_pubBytes);
|
||||
else
|
||||
$this->_pub = $this->eddsa->g->mul($this->priv());
|
||||
}
|
||||
return $this->_pub;
|
||||
}
|
||||
|
||||
private $_privBytes;
|
||||
public function privBytes() {
|
||||
if (!$this->_privBytes) {
|
||||
$eddsa = $this->eddsa;
|
||||
$hash = $this->hash();
|
||||
$lastIx = $eddsa->encodingLength - 1;
|
||||
|
||||
$a = array_slice($hash, 0, $eddsa->encodingLength);
|
||||
$a[0] &= 248;
|
||||
$a[$lastIx] &= 127;
|
||||
$a[$lastIx] |= 64;
|
||||
$this->_privBytes = $a;
|
||||
}
|
||||
return $this->_privBytes;
|
||||
}
|
||||
|
||||
private $_priv;
|
||||
public function priv() {
|
||||
if (!$this->_priv) {
|
||||
$this->_priv = $this->eddsa->decodeInt($this->privBytes());
|
||||
}
|
||||
return $this->_priv;
|
||||
}
|
||||
|
||||
private $_hash;
|
||||
public function hash() {
|
||||
if (!$this->_hash) {
|
||||
// TODO: !!!
|
||||
$hash = hash_init('sha512');
|
||||
hash_update($hash, Utils::toBin($this->secret()));
|
||||
$this->_hash = Utils::toArray( hash_final($hash), 'hex' );
|
||||
}
|
||||
return $this->_hash;
|
||||
}
|
||||
|
||||
private $_messagePrefix;
|
||||
public function messagePrefix() {
|
||||
if (!$this->_messagePrefix) {
|
||||
$this->_messagePrefix = array_slice($this->hash(), $this->eddsa->encodingLength);
|
||||
}
|
||||
return $this->_messagePrefix;
|
||||
}
|
||||
|
||||
public function sign($message) {
|
||||
assert($this->_secret); //, 'KeyPair can only verify');
|
||||
return $this->eddsa->sign($message, $this);
|
||||
}
|
||||
|
||||
public function verify($message, $sig) {
|
||||
return $this->eddsa->verify($message, $sig, $this);
|
||||
}
|
||||
|
||||
public function getSecret($enc = false) {
|
||||
assert($this->_secret); //, 'KeyPair is public only');
|
||||
return Utils::encode($this->secret(), $enc);
|
||||
}
|
||||
|
||||
public function getPublic($enc = false) {
|
||||
return Utils::encode($this->pubBytes(), $enc);
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,82 @@
|
||||
<?php
|
||||
namespace Elliptic\EdDSA;
|
||||
|
||||
use Elliptic\Utils;
|
||||
use BN\BN;
|
||||
|
||||
class Signature {
|
||||
|
||||
public $eddsa;
|
||||
|
||||
/**
|
||||
* @param {EdDSA} eddsa - eddsa instance
|
||||
* @param {Array<Bytes>|Object} sig -
|
||||
* @param {Array<Bytes>|Point} [sig.R] - R point as Point or bytes
|
||||
* @param {Array<Bytes>|bn} [sig.S] - S scalar as bn or bytes
|
||||
* @param {Array<Bytes>} [sig.Rencoded] - R point encoded
|
||||
* @param {Array<Bytes>} [sig.Sencoded] - S scalar encoded
|
||||
*/
|
||||
function __construct($eddsa, $sig) {
|
||||
$this->eddsa = $eddsa;
|
||||
|
||||
if (is_string($sig))
|
||||
$sig = Utils::parseBytes($sig);
|
||||
|
||||
if (is_array($sig) && !isset($sig["R"])) {
|
||||
$sig = [
|
||||
"R" => array_slice($sig, 0, $eddsa->encodingLength),
|
||||
"S" => array_slice($sig, $eddsa->encodingLength)
|
||||
];
|
||||
}
|
||||
|
||||
assert($sig["R"] && $sig["S"]); //, 'Signature without R or S');
|
||||
|
||||
if ($eddsa->isPoint($sig["R"]))
|
||||
$this->_R = $sig["R"];
|
||||
if ($sig["S"] instanceof BN)
|
||||
$this->_S = $sig["S"];
|
||||
|
||||
$this->_Rencoded = is_array($sig["R"]) ? $sig["R"] : (isset($sig["Rencoded"]) ?$sig["Rencoded"] : null);
|
||||
$this->_Sencoded = is_array($sig["S"]) ? $sig["S"] : (isset($sig["Sencoded"]) ?$sig["Sencoded"] : null);
|
||||
}
|
||||
|
||||
private $_S;
|
||||
public function S() {
|
||||
if (!$this->_S) {
|
||||
$this->_S = $this->eddsa->decodeInt($this->Sencoded());
|
||||
}
|
||||
return $this->_S;
|
||||
}
|
||||
|
||||
private $_R;
|
||||
public function R() {
|
||||
if (!$this->_R) {
|
||||
$this->_R = $this->eddsa->decodePoint($this->Rencoded());
|
||||
}
|
||||
return $this->_R;
|
||||
}
|
||||
|
||||
private $_Rencoded;
|
||||
public function Rencoded() {
|
||||
if (!$this->_Rencoded) {
|
||||
$this->_Rencoded = $this->eddsa->encodePoint($this->R());
|
||||
}
|
||||
return $this->_Rencoded;
|
||||
}
|
||||
|
||||
private $_Sencoded;
|
||||
public function Sencoded() {
|
||||
if (!$this->_Sencoded) {
|
||||
$this->_Sencoded = $this->eddsa->encodeInt($this->S());
|
||||
}
|
||||
return $this->_Sencoded;
|
||||
}
|
||||
|
||||
public function toBytes() {
|
||||
return array_merge($this->Rencoded(), $this->Sencoded());
|
||||
}
|
||||
|
||||
public function toHex() {
|
||||
return strtoupper(Utils::encode($this->toBytes(), 'hex'));
|
||||
}
|
||||
}
|
||||
+135
@@ -0,0 +1,135 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic;
|
||||
|
||||
class HmacDRBG
|
||||
{
|
||||
private $hash;
|
||||
private $predResist;
|
||||
private $outLen;
|
||||
private $minEntropy;
|
||||
private $reseed;
|
||||
private $reseedInterval;
|
||||
private $K;
|
||||
private $V;
|
||||
|
||||
function __construct($options)
|
||||
{
|
||||
Utils::optionAssert($options, "predResist");
|
||||
Utils::optionAssert($options, "hash", null, true);
|
||||
Utils::optionAssert($options["hash"], "outSize", null, true);
|
||||
Utils::optionAssert($options["hash"], "hmacStrength", null, true);
|
||||
Utils::optionAssert($options["hash"], "algo", null, true);
|
||||
Utils::optionAssert($options, "minEntropy");
|
||||
Utils::optionAssert($options, "entropy", null, true);
|
||||
Utils::optionAssert($options, "entropyEnc");
|
||||
Utils::optionAssert($options, "nonce", "");
|
||||
Utils::optionAssert($options, "nonceEnc");
|
||||
Utils::optionAssert($options, "pers", "");
|
||||
Utils::optionAssert($options, "persEnc");
|
||||
|
||||
$this->hash = $options["hash"];
|
||||
$this->predResist = $options["predResist"];
|
||||
|
||||
$this->outLen = $this->hash["outSize"];
|
||||
$this->minEntropy = $options["minEntropy"] ?: $this->hash["hmacStrength"];
|
||||
|
||||
$this->reseed = null;
|
||||
$this->reseedInterval = null;
|
||||
$this->K = null;
|
||||
$this->V = null;
|
||||
|
||||
$entropy = Utils::toBin($options["entropy"], $options["entropyEnc"]);
|
||||
$nonce = Utils::toBin($options["nonce"], $options["nonceEnc"]);
|
||||
$pers = Utils::toBin($options["pers"], $options["persEnc"]);
|
||||
|
||||
if (Utils::$ASSERT_ENABLED) {
|
||||
assert(strlen($entropy) >= ($this->minEntropy / 8));
|
||||
}
|
||||
$this->_init($entropy, $nonce, $pers);
|
||||
}
|
||||
|
||||
private function _init($entropy, $nonce, $pers)
|
||||
{
|
||||
$seed = $entropy . $nonce . $pers;
|
||||
|
||||
$this->K = str_repeat(chr(0x00), $this->outLen / 8);
|
||||
$this->V = str_repeat(chr(0x01), $this->outLen / 8);
|
||||
|
||||
$this->_update($seed);
|
||||
$this->reseed = 1;
|
||||
$this->reseedInterval = 0x1000000000000; // 2^48
|
||||
}
|
||||
|
||||
private function _hmac()
|
||||
{
|
||||
return hash_init($this->hash["algo"], HASH_HMAC, $this->K);
|
||||
}
|
||||
|
||||
private function _update($seed = false)
|
||||
{
|
||||
$kmac = $this->_hmac();
|
||||
hash_update($kmac, $this->V);
|
||||
hash_update($kmac, chr(0x00));
|
||||
|
||||
if( $seed )
|
||||
hash_update($kmac, $seed);
|
||||
$this->K = hash_final($kmac, true);
|
||||
|
||||
$kmac = $this->_hmac();
|
||||
hash_update($kmac, $this->V);
|
||||
$this->V = hash_final($kmac, true);
|
||||
|
||||
if(!$seed)
|
||||
return;
|
||||
|
||||
$kmac = $this->_hmac();
|
||||
hash_update($kmac, $this->V);
|
||||
hash_update($kmac, chr(0x01));
|
||||
hash_update($kmac, $seed);
|
||||
$this->K = hash_final($kmac, true);
|
||||
|
||||
$kmac = $this->_hmac();
|
||||
hash_update($kmac, $this->V);
|
||||
$this->V = hash_final($kmac, true);
|
||||
}
|
||||
|
||||
// TODO: reseed()
|
||||
|
||||
public function generate($len, $enc = null, $add = null, $addEnc = null)
|
||||
{
|
||||
if ($this->reseed > $this->reseedInterval)
|
||||
throw new \Exception("Reseed is required");
|
||||
|
||||
// Optional encoding
|
||||
if( !is_string($enc) )
|
||||
{
|
||||
$addEnc = $enc;
|
||||
$add = $enc;
|
||||
$enc = null;
|
||||
}
|
||||
|
||||
// Optional additional data
|
||||
if( $add != null ) {
|
||||
$add = Utils::toBin($add, $addEnc);
|
||||
$this->_update($add);
|
||||
}
|
||||
|
||||
$temp = "";
|
||||
while( strlen($temp) < $len )
|
||||
{
|
||||
$hmac = $this->_hmac();
|
||||
hash_update($hmac, $this->V);
|
||||
$this->V = hash_final($hmac, true);
|
||||
$temp .= $this->V;
|
||||
}
|
||||
|
||||
$res = substr($temp, 0, $len);
|
||||
$this->_update($add);
|
||||
$this->reseed++;
|
||||
|
||||
return Utils::encode(Utils::toArray($res), $enc);
|
||||
}
|
||||
}
|
||||
|
||||
?>
|
||||
+176
@@ -0,0 +1,176 @@
|
||||
<?php
|
||||
|
||||
namespace Elliptic;
|
||||
|
||||
use \Exception;
|
||||
use BN\BN;
|
||||
|
||||
if (!function_exists("random_int")) {
|
||||
function random_int($a, $b) {
|
||||
return rand($a, $b);
|
||||
}
|
||||
}
|
||||
|
||||
class Utils
|
||||
{
|
||||
public static $ASSERT_ENABLED;
|
||||
|
||||
public static function toArray($msg, $enc = false)
|
||||
{
|
||||
if( is_array($msg) )
|
||||
return array_slice($msg, 0);
|
||||
|
||||
if( !$msg )
|
||||
return array();
|
||||
|
||||
if( !is_string($msg) )
|
||||
throw new Exception("Not implemented");
|
||||
|
||||
if( !$enc )
|
||||
return array_slice(unpack("C*", $msg), 0);
|
||||
|
||||
if( $enc === "hex" )
|
||||
return array_slice(unpack("C*", hex2bin($msg)), 0);
|
||||
|
||||
return $msg;
|
||||
}
|
||||
|
||||
public static function toHex($msg)
|
||||
{
|
||||
if( is_string($msg) )
|
||||
return bin2hex($msg);
|
||||
|
||||
if( !is_array($msg) )
|
||||
throw new Exception("Not implemented");
|
||||
|
||||
$binary = call_user_func_array("pack", array_merge(["C*"], $msg));
|
||||
return bin2hex($binary);
|
||||
}
|
||||
|
||||
public static function toBin($msg, $enc = false)
|
||||
{
|
||||
if( is_array($msg) )
|
||||
return call_user_func_array("pack", array_merge(["C*"], $msg));
|
||||
|
||||
if( $enc === "hex" )
|
||||
return hex2bin($msg);
|
||||
|
||||
return $msg;
|
||||
}
|
||||
|
||||
public static function encode($arr, $enc)
|
||||
{
|
||||
if( $enc === "hex" )
|
||||
return self::toHex($arr);
|
||||
return $arr;
|
||||
}
|
||||
|
||||
// Represent num in a w-NAF form
|
||||
public static function getNAF($num, $w)
|
||||
{
|
||||
$naf = array();
|
||||
$ws = 1 << ($w + 1);
|
||||
$k = clone($num);
|
||||
|
||||
while( $k->cmpn(1) >= 0 )
|
||||
{
|
||||
if( !$k->isOdd() )
|
||||
array_push($naf, 0);
|
||||
else
|
||||
{
|
||||
$mod = $k->andln($ws - 1);
|
||||
$z = $mod;
|
||||
if( $mod > (($ws >> 1) - 1))
|
||||
$z = ($ws >> 1) - $mod;
|
||||
$k->isubn($z);
|
||||
array_push($naf, $z);
|
||||
}
|
||||
|
||||
// Optimization, shift by word if possible
|
||||
$shift = (!$k->isZero() && $k->andln($ws - 1) === 0) ? ($w + 1) : 1;
|
||||
for($i = 1; $i < $shift; $i++)
|
||||
array_push($naf, 0);
|
||||
$k->iushrn($shift);
|
||||
}
|
||||
|
||||
return $naf;
|
||||
}
|
||||
|
||||
// Represent k1, k2 in a Joint Sparse Form
|
||||
public static function getJSF($k1, $k2)
|
||||
{
|
||||
$jsf = array( array(), array() );
|
||||
$k1 = $k1->_clone();
|
||||
$k2 = $k2->_clone();
|
||||
$d1 = 0;
|
||||
$d2 = 0;
|
||||
|
||||
while( $k1->cmpn(-$d1) > 0 || $k2->cmpn(-$d2) > 0 )
|
||||
{
|
||||
// First phase
|
||||
$m14 = ($k1->andln(3) + $d1) & 3;
|
||||
$m24 = ($k2->andln(3) + $d2) & 3;
|
||||
if( $m14 === 3 )
|
||||
$m14 = -1;
|
||||
if( $m24 === 3 )
|
||||
$m24 = -1;
|
||||
|
||||
$u1 = 0;
|
||||
if( ($m14 & 1) !== 0 )
|
||||
{
|
||||
$m8 = ($k1->andln(7) + $d1) & 7;
|
||||
$u1 = ( ($m8 === 3 || $m8 === 5) && $m24 === 2 ) ? -$m14 : $m14;
|
||||
}
|
||||
array_push($jsf[0], $u1);
|
||||
|
||||
$u2 = 0;
|
||||
if( ($m24 & 1) !== 0 )
|
||||
{
|
||||
$m8 = ($k2->andln(7) + $d2) & 7;
|
||||
$u2 = ( ($m8 === 3 || $m8 === 5) && $m14 === 2 ) ? -$m24 : $m24;
|
||||
}
|
||||
array_push($jsf[1], $u2);
|
||||
|
||||
// Second phase
|
||||
if( (2 * $d1) === ($u1 + 1) )
|
||||
$d1 = 1 - $d1;
|
||||
if( (2 * $d2) === ($u2 + 1) )
|
||||
$d2 = 1 - $d2;
|
||||
$k1->iushrn(1);
|
||||
$k2->iushrn(1);
|
||||
}
|
||||
|
||||
return $jsf;
|
||||
}
|
||||
|
||||
public static function intFromLE($bytes) {
|
||||
return new BN($bytes, 'hex', 'le');
|
||||
}
|
||||
|
||||
public static function parseBytes($bytes) {
|
||||
if (is_string($bytes))
|
||||
return self::toArray($bytes, 'hex');
|
||||
return $bytes;
|
||||
}
|
||||
|
||||
public static function randBytes($count)
|
||||
{
|
||||
$res = "";
|
||||
for($i = 0; $i < $count; $i++)
|
||||
$res .= chr(random_int(0, 255));
|
||||
return $res;
|
||||
}
|
||||
|
||||
public static function optionAssert(&$array, $key, $value = false, $required = false)
|
||||
{
|
||||
if( isset($array[$key]) )
|
||||
return;
|
||||
if( $required )
|
||||
throw new Exception("Missing option " . $key);
|
||||
$array[$key] = $value;
|
||||
}
|
||||
}
|
||||
|
||||
Utils::$ASSERT_ENABLED = ini_get("zend.assertions") === "1";
|
||||
|
||||
?>
|
||||
Reference in New Issue
Block a user