add method

Point add(Point other)

Point addition: P+Q, complete, exception

Implementation

Point add(Point other) {
  final (BigInt X1, BigInt Y1, BigInt Z1) = (px, py, pz);

  final (BigInt X2, BigInt Y2, BigInt Z2) = (other.px, other.py, other.pz);

  final a = Curve.secp256k1.a;
  final b = Curve.secp256k1.b;
  var X3 = BigInt.zero, Y3 = BigInt.zero, Z3 = BigInt.zero;
  final b3 = Utilities.mod(b * BigInt.from(3));
  // step 1
  var t0 = Utilities.mod(X1 * X2),
      t1 = Utilities.mod(Y1 * Y2),
      t2 = Utilities.mod(Z1 * Z2),
      t3 = Utilities.mod(X1 + Y1),
      t4 = Utilities.mod(X2 + Y2); // step 5

  t3 = Utilities.mod(t3 * t4);
  t4 = Utilities.mod(t0 + t1);
  t3 = Utilities.mod(t3 - t4);
  t4 = Utilities.mod(X1 + Z1);
  // step 10
  var t5 = Utilities.mod(X2 + Z2);
  t4 = Utilities.mod(t4 * t5);
  t5 = Utilities.mod(t0 + t2);
  t4 = Utilities.mod(t4 - t5);
  t5 = Utilities.mod(Y1 + Z1);
  // step 15
  X3 = Utilities.mod(Y2 + Z2);
  t5 = Utilities.mod(t5 * X3);
  X3 = Utilities.mod(t1 + t2);
  t5 = Utilities.mod(t5 - X3);
  Z3 = Utilities.mod(a * t4);
  // step 20
  X3 = Utilities.mod(b3 * t2);
  Z3 = Utilities.mod(X3 + Z3);
  X3 = Utilities.mod(t1 - Z3);
  Z3 = Utilities.mod(t1 + Z3);
  Y3 = Utilities.mod(X3 * Z3);
  // step 25
  t1 = Utilities.mod(t0 + t0);
  t1 = Utilities.mod(t1 + t0);
  t2 = Utilities.mod(a * t2);
  t4 = Utilities.mod(b3 * t4);
  t1 = Utilities.mod(t1 + t2);
  // step 30
  t2 = Utilities.mod(t0 - t2);
  t2 = Utilities.mod(a * t2);
  t4 = Utilities.mod(t4 + t2);
  t0 = Utilities.mod(t1 * t4);
  Y3 = Utilities.mod(Y3 + t0);
  // step 35
  t0 = Utilities.mod(t5 * t4);
  X3 = Utilities.mod(t3 * X3);
  X3 = Utilities.mod(X3 - t0);
  t0 = Utilities.mod(t3 * t1);
  Z3 = Utilities.mod(t5 * Z3);
  // step 40
  Z3 = Utilities.mod(Z3 + t0);
  return Point(X3, Y3, Z3);
}