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 (extension_loaded('gmp') && USE_EXT == 'GMP') {
if (CurveFp::cmp($p1->curve, $p2->curve) == 0) {
if (gmp_cmp(gmp_Utils::gmp_mod2(gmp_sub($p1->x, $p2->x), $p1->curve->getPrime()), '0') === 0) {
if (gmp_cmp(gmp_Utils::gmp_mod2(gmp_add($p1->y, $p2->y), $p1->curve->getPrime()), '0') === 0) {
return self::$infinity;
} else {
if (gmp_cmp(gmp_Utils::gmp_mod2(gmp_sub($p1->y, $p2->y), $p1->curve->getPrime()), '0') === 0) {
return self::double($p1);
}
}
}
$p = $p1->curve->getPrime();
// $l = gmp_strval(gmp_mul(gmp_sub($p2->y, $p1->y), NumberTheory::inverse_mod(gmp_sub($p2->x, $p1->x), $p)));
$l = gmp_strval(gmp_mul(gmp_sub($p2->y, $p1->y), gmp_strval(gmp_invert(gmp_sub($p2->x, $p1->x), $p))));
$x3 = gmp_strval(gmp_Utils::gmp_mod2(gmp_sub(gmp_sub(gmp_pow($l, 2), $p1->x), $p2->x), $p));
$y3 = gmp_strval(gmp_Utils::gmp_mod2(gmp_sub(gmp_mul($l, gmp_sub($p1->x, $x3)), $p1->y), $p));
$p3 = new Point($p1->curve, $x3, $y3);
return $p3;
} else {
throw new ErrorException("The Elliptic Curves do not match.");
}
} else {
throw new ErrorException("Please install GMP");
}
}
public static function add($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 (extension_loaded('gmp') && USE_EXT == 'GMP') {
if (CurveFp::cmp($p1->curve, $p2->curve) == 0) {
if (gmp_Utils::gmp_mod2(gmp_cmp($p1->x, $p2->x), $p1->curve->getPrime()) == 0) {
if (gmp_Utils::gmp_mod2(gmp_add($p1->y, $p2->y), $p1->curve->getPrime()) == 0) {
return self::$infinity;
} else {
return self::double($p1);
}
}
$p = $p1->curve->getPrime();
$l = gmp_strval(gmp_mul(gmp_sub($p2->y, $p1->y), NumberTheory::inverse_mod(gmp_sub($p2->x, $p1->x), $p)));
$x3 = gmp_strval(gmp_Utils::gmp_mod2(gmp_sub(gmp_sub(gmp_pow($l, 2), $p1->x), $p2->x), $p));
$y3 = gmp_strval(gmp_Utils::gmp_mod2(gmp_sub(gmp_mul($l, gmp_sub($p1->x, $x3)), $p1->y), $p));
$p3 = new Point($p1->curve, $x3, $y3);
return $p3;
} else {
throw new ErrorException("The Elliptic Curves do not match.");
}
} elseif (extension_loaded('bcmath') && USE_EXT == 'BCMATH') {
if (CurveFp::cmp($p1->curve, $p2->curve) == 0) {
if (bcmod(bccomp($p1->x, $p2->x), $p1->curve->getPrime()) == 0) {
if (bcmod(bcadd($p1->y, $p2->y), $p1->curve->getPrime()) == 0) {
return self::$infinity;
} else {
return self::double($p1);
}
}
$p = $p1->curve->getPrime();
$l = bcmod(bcmul(bcsub($p2->y, $p1->y), NumberTheory::inverse_mod(bcsub($p2->x, $p1->x), $p)), $p);
$x3 = bcmod(bcsub(bcsub(bcpow($l, 2), $p1->x), $p2->x), $p);
$step0 = bcsub($p1->x, $x3);
$step1 = bcmul($l, $step0);
$step2 = bcsub($step1, $p1->y);
$step3 = bcmod($step2, $p);
$y3 = bcmod(bcsub(bcmul($l, bcsub($p1->x, $x3)), $p1->y), $p);
if (bccomp(0, $y3) == 1) {
$y3 = bcadd($p, $y3);
}
$p3 = new Point($p1->curve, $x3, $y3);
return $p3;
} else {
throw new ErrorException("The Elliptic Curves do not match.");
}
} else {
throw new ErrorException("Please install BCMATH or GMP");
}
}