goldrat/vendor/simplito/elliptic-php/lib/Curve/EdwardsCurve/Point.php
2025-10-09 17:41:57 +00:00

324 lines
9.9 KiB
PHP

<?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); }
}