operator * method

@override EDPoint operator *(BigInt other)

Multiply an Edwards curve point by a scalar.

This method multiplies an Edwards curve point by a scalar value using an efficient multiplication algorithm. The scalar value is provided as a BigInt, and the result is returned as a new Edwards curve point.

Parameters:

• other: The scalar value to multiply the point by.

Returns:

• A new Edwards curve point resulting from the multiplication.

Implementation

@override
EDPoint operator *(BigInt other) {
  final BigInt x2 = _coords[0];
  final BigInt t2 = _coords[3];
  final BigInt y2 = _coords[1];
  final BigInt z2 = _coords[2];
  if (other == BigInt.zero) {
    return EDPoint.infinity(curve: curve);
  }

  if (order != null) {
    other %= (order! * BigInt.two);
  }
  _maybePrecompute();

  if (_precompute.isNotEmpty) {
    return _mulPrecompute(other);
  }

  BigInt x3 = BigInt.zero;
  BigInt y3 = BigInt.one;
  BigInt z3 = BigInt.one;
  BigInt t3 = BigInt.one;

  final nf = BigintUtils.computeNAF(other).reversed.toList();
  for (final BigInt i in nf) {
    final List<BigInt> resultCoords =
        _double(x3, y3, z3, t3, curve.p, curve.a);
    x3 = resultCoords[0];
    y3 = resultCoords[1];
    z3 = resultCoords[2];
    t3 = resultCoords[3];

    if (i < BigInt.zero) {
      final List<BigInt> doubleCoords =
          _add(x3, y3, z3, t3, -x2, y2, z2, -t2, curve.p, curve.a);
      x3 = doubleCoords[0];
      y3 = doubleCoords[1];
      z3 = doubleCoords[2];
      t3 = doubleCoords[3];
    } else if (i > BigInt.zero) {
      final List<BigInt> doubleCoords =
          _add(x3, y3, z3, t3, x2, y2, z2, t2, curve.p, curve.a);
      x3 = doubleCoords[0];
      y3 = doubleCoords[1];
      z3 = doubleCoords[2];
      t3 = doubleCoords[3];
    }
  }

  return EDPoint._(curve, [x3, y3, z3, t3], order: order);
}