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Просмотр файла: BaseCurve.php
<?php
namespace Elliptic\Curve;
use Elliptic\Utils;
use \Exception;
use BN\BN;
abstract class BaseCurve
{
public $type;
public $p;
public $red;
public $zero;
public $one;
public $two;
public $n;
public $g;
protected $_wnafT1;
protected $_wnafT2;
protected $_wnafT3;
protected $_wnafT4;
public $redN;
public $_maxwellTrick;
function __construct($type, $conf)
{
$this->type = $type;
$this->p = new BN($conf["p"], 16);
//Use Montgomery, when there is no fast reduction for the prime
$this->red = isset($conf["prime"]) ? BN::red($conf["prime"]) : BN::mont($this->p);
//Useful for many curves
$this->zero = (new BN(0))->toRed($this->red);
$this->one = (new BN(1))->toRed($this->red);
$this->two = (new BN(2))->toRed($this->red);
//Curve configuration, optional
$this->n = isset($conf["n"]) ? new BN($conf["n"], 16) : null;
$this->g = isset($conf["g"]) ? $this->pointFromJSON($conf["g"], isset($conf["gRed"]) ? $conf["gRed"] : null) : null;
//Temporary arrays
$this->_wnafT1 = array(0,0,0,0);
$this->_wnafT2 = array(0,0,0,0);
$this->_wnafT3 = array(0,0,0,0);
$this->_wnafT4 = array(0,0,0,0);
//Generalized Greg Maxwell's trick
$adjustCount = $this->n != null ? $this->p->div($this->n) : null;
if( $adjustCount == null || $adjustCount->cmpn(100) > 0 )
{
$this->redN = null;
$this->_maxwellTrick = false;
}
else
{
$this->redN = $this->n->toRed($this->red);
$this->_maxwellTrick = true;
}
}
abstract public function point($x, $z);
abstract public function validate($point);
public function _fixedNafMul($p, $k)
{
assert(isset($p->precomputed));
$doubles = $p->_getDoubles();
$naf = Utils::getNAF($k, 1);
$I = (1 << ($doubles["step"] + 1)) - ($doubles["step"] % 2 == 0 ? 2 : 1);
$I = $I / 3;
//Translate to more windowed form
$repr = array();
for($j = 0; $j < count($naf); $j += $doubles["step"])
{
$nafW = 0;
for($k = $j + $doubles["step"] - 1; $k >= $j; $k--)
$nafW = ($nafW << 1) + (isset($naf[$k]) ? $naf[$k] : 0);
array_push($repr, $nafW);
}
$a = $this->jpoint(null, null, null);
$b = $this->jpoint(null, null, null);
for($i = $I; $i > 0; $i--)
{
for($j = 0; $j < count($repr); $j++)
{
$nafW = $repr[$j];
if ($nafW == $i) {
$b = $b->mixedAdd($doubles["points"][$j]);
} else if($nafW == -$i) {
$b = $b->mixedAdd($doubles["points"][$j]->neg());
}
}
$a = $a->add($b);
}
return $a->toP();
}
public function _wnafMul($p, $k)
{
$w = 4;
//Precompute window
$nafPoints = $p->_getNAFPoints($w);
$w = $nafPoints["wnd"];
$wnd = $nafPoints["points"];
//Get NAF form
$naf = Utils::getNAF($k, $w);
//Add `this`*(N+1) for every w-NAF index
$acc = $this->jpoint(null, null, null);
for($i = count($naf) - 1; $i >= 0; $i--)
{
//Count zeros
for($k = 0; $i >= 0 && $naf[$i] == 0; $i--)
$k++;
if($i >= 0)
$k++;
$acc = $acc->dblp($k);
if($i < 0)
break;
$z = $naf[$i];
assert($z != 0);
if( $p->type == "affine" )
{
//J +- P
if( $z > 0 )
$acc = $acc->mixedAdd($wnd[($z - 1) >> 1]);
else
$acc = $acc->mixedAdd($wnd[(-$z - 1) >> 1]->neg());
}
else
{
//J +- J
if( $z > 0 )
$acc = $acc->add($wnd[($z - 1) >> 1]);
else
$acc = $acc->add($wnd[(-$z - 1) >> 1]->neg());
}
}
return $p->type == "affine" ? $acc->toP() : $acc;
}
public function _wnafMulAdd($defW, $points, $coeffs, $len, $jacobianResult = false)
{
$wndWidth = &$this->_wnafT1;
$wnd = &$this->_wnafT2;
$naf = &$this->_wnafT3;
//Fill all arrays
$max = 0;
for($i = 0; $i < $len; $i++)
{
$p = $points[$i];
$nafPoints = $p->_getNAFPoints($defW);
$wndWidth[$i] = $nafPoints["wnd"];
$wnd[$i] = $nafPoints["points"];
}
//Comb all window NAFs
for($i = $len - 1; $i >= 1; $i -= 2)
{
$a = $i - 1;
$b = $i;
if( $wndWidth[$a] != 1 || $wndWidth[$b] != 1 )
{
$naf[$a] = Utils::getNAF($coeffs[$a], $wndWidth[$a]);
$naf[$b] = Utils::getNAF($coeffs[$b], $wndWidth[$b]);
$max = max(count($naf[$a]), $max);
$max = max(count($naf[$b]), $max);
continue;
}
$comb = array(
$points[$a], /* 1 */
null, /* 3 */
null, /* 5 */
$points[$b] /* 7 */
);
//Try to avoid Projective points, if possible
if( $points[$a]->y->cmp($points[$b]->y) == 0 )
{
$comb[1] = $points[$a]->add($points[$b]);
$comb[2] = $points[$a]->toJ()->mixedAdd($points[$b]->neg());
}
elseif( $points[$a]->y->cmp($points[$b]->y->redNeg()) == 0 )
{
$comb[1] = $points[$a]->toJ()->mixedAdd($points[$b]);
$comb[2] = $points[$a]->add($points[$b]->neg());
}
else
{
$comb[1] = $points[$a]->toJ()->mixedAdd($points[$b]);
$comb[2] = $points[$a]->toJ()->mixedAdd($points[$b]->neg());
}
$index = array(
-3, /* -1 -1 */
-1, /* -1 0 */
-5, /* -1 1 */
-7, /* 0 -1 */
0, /* 0 0 */
7, /* 0 1 */
5, /* 1 -1 */
1, /* 1 0 */
3 /* 1 1 */
);
$jsf = Utils::getJSF($coeffs[$a], $coeffs[$b]);
$max = max(count($jsf[0]), $max);
if ($max > 0) {
$naf[$a] = array_fill(0, $max, 0);
$naf[$b] = array_fill(0, $max, 0);
} else {
$naf[$a] = [];
$naf[$b] = [];
}
for($j = 0; $j < $max; $j++)
{
$ja = isset($jsf[0][$j]) ? $jsf[0][$j] : 0;
$jb = isset($jsf[1][$j]) ? $jsf[1][$j] : 0;
$naf[$a][$j] = $index[($ja + 1) * 3 + ($jb + 1)];
$naf[$b][$j] = 0;
$wnd[$a] = $comb;
}
}
$acc = $this->jpoint(null, null, null);
$tmp = &$this->_wnafT4;
for($i = $max; $i >= 0; $i--)
{
$k = 0;
while($i >= 0)
{
$zero = true;
for($j = 0; $j < $len; $j++)
{
$tmp[$j] = isset($naf[$j][$i]) ? $naf[$j][$i] : 0;
if( $tmp[$j] != 0 )
$zero = false;
}
if( !$zero )
break;
$k++;
$i--;
}
if( $i >=0 )
$k++;
$acc = $acc->dblp($k);
if( $i < 0 )
break;
for($j = 0; $j < $len; $j++)
{
$z = $tmp[$j];
$p = null;
if( $z == 0 )
continue;
elseif( $z > 0 )
$p = $wnd[$j][($z - 1) >> 1];
elseif( $z < 0 )
$p = $wnd[$j][(-$z - 1) >> 1]->neg();
if( $p->type == "affine" )
$acc = $acc->mixedAdd($p);
else
$acc = $acc->add($p);
}
}
//Zeroify references
for($i = 0; $i < $len; $i++)
$wnd[$i] = null;
if( $jacobianResult )
return $acc;
else
return $acc->toP();
}
public function decodePoint($bytes, $enc = false)
{
$bytes = Utils::toArray($bytes, $enc);
$len = $this->p->byteLength();
$count = count($bytes);
//uncompressed, hybrid-odd, hybrid-even
if(($bytes[0] == 0x04 || $bytes[0] == 0x06 || $bytes[0] == 0x07) && ($count - 1) == (2 * $len) )
{
if( $bytes[0] == 0x06 )
assert($bytes[$count - 1] % 2 == 0);
elseif( $bytes[0] == 0x07 )
assert($bytes[$count - 1] % 2 == 1);
return $this->point(array_slice($bytes, 1, $len), array_slice($bytes, 1 + $len, $len));
}
if( ($bytes[0] == 0x02 || $bytes[0] == 0x03) && ($count - 1) == $len )
return $this->pointFromX(array_slice($bytes, 1, $len), $bytes[0] == 0x03);
throw new Exception("Unknown point format");
}
}
?>
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