verify function

bool verify(PublicKey pub, List<int> hash, Signature sig)

verify verifies the signature in r, s of hash using the public key, pub. Its return value records whether the signature is valid.

Implementation

bool verify(PublicKey pub, List<int> hash, Signature sig) {
  // See [NSA] 3.4.2
  var curve = pub.curve;
  var byteLen = (curve.bitSize + 7) ~/ 8;

  if (sig.R.sign <= 0 || sig.S.sign <= 0) {
    return false;
  }

  if (sig.R >= curve.n || sig.S >= curve.n) {
    return false;
  }

  var e = bitsToInt(hash, curve.n.bitLength);
  var w = sig.S.modInverse(curve.n);

  var u1 = e * w;
  u1 = u1 % curve.n;
  var u2 = sig.R * w;
  u2 = u2 % curve.n;

  // Check if implements S1*g + S2*p
  var hexU1 = u1.toRadixString(16).padLeft(byteLen * 2, '0');
  var hexU2 = u2.toRadixString(16).padLeft(byteLen * 2, '0');
  var p1 = curve.scalarBaseMul(List<int>.generate(hexU1.length ~/ 2,
      (i) => int.parse(hexU1.substring(i * 2, i * 2 + 2), radix: 16)));
  var p2 = curve.scalarMul(
      pub,
      List<int>.generate(hexU2.length ~/ 2,
          (i) => int.parse(hexU2.substring(i * 2, i * 2 + 2), radix: 16)));
  var p = curve.add(p1, p2);

  if (p.X.sign == 0 && p.Y.sign == 0) {
    return false;
  }

  p.X = p.X % curve.n;
  return p.X == sig.R;
}