public static function add($p1, $p2)
{
if (self::cmp($p2, self::INFINITY) == 0 && $p1 instanceof Point) {
return $p1;
}
if (self::cmp($p1, self::INFINITY) == 0 && $p2 instanceof Point) {
return $p2;
}
if (self::cmp($p1, self::INFINITY) == 0 && self::cmp($p2, self::INFINITY) == 0) {
return self::INFINITY;
}
if (Curve::cmp($p1->curve, $p2->curve) == 0) {
if (gmp_cmp($p1->x, $p2->x) == 0) {
if (gmp_mod(gmp_add($p1->y, $p2->y), $p1->curve->prime) == 0) {
return self::INFINITY;
} else {
return self::double($p1);
}
}
$p = $p1->curve->prime;
$l = gmp_mul(gmp_sub($p2->y, $p1->y), gmp_invert(gmp_sub($p2->x, $p1->x), $p));
$x3 = gmp_mod(gmp_sub(gmp_sub(gmp_pow($l, 2), $p1->x), $p2->x), $p);
$y3 = gmp_mod(gmp_sub(gmp_mul($l, gmp_sub($p1->x, $x3)), $p1->y), $p);
return new Point($p1->curve, $x3, $y3);
} else {
throw new ErrorException('Elliptic curves do not match');
}
}
