y property

@override BigInt get y

Get the y-coordinate of this point in projective elliptic curve coordinates.

If the point's z-coordinate is already one, this returns the y-coordinate directly. Otherwise, it computes the normalized y-coordinate.

Returns: The y-coordinate of the point in the elliptic curve coordinates.

Note:

• The value is computed modulo the prime field 'p' of the curve.
• This property is used for coordinate transformation and point retrieval.

Implementation

@override
BigInt get y {
  final yCoordinate = _coords[1];
  final zCoordinate = _coords[2];
  final primeField = curve.p;

  // Check if the z-coordinate is already one.
  if (zCoordinate == BigInt.one) {
    return yCoordinate;
  }

  // Calculate the modular inverse of z-coordinate.
  final zInverse = BigintUtils.inverseMod(zCoordinate, primeField);

  // Compute the normalized y-coordinate using the formula.
  final normalizedY =
      (yCoordinate * zInverse * zInverse * zInverse) % primeField;

  return normalizedY;
}