def sign(privkey, nonce, message):
    known_bits = 6
    kbi = int(2 ** known_bits)
    kp = nonce % kbi  # k nonce % kbi

    z = message
    nonceG = nonce * G

    rx = nonceG.x()
    ry = nonceG.y()
    rx = int(rx)
    s = (z + rx * privkey) * modinv(nonce, n) % n

    return rx, s, z , kp

# Example usage
private = 0x12345678901234567890  # Example private key
public_key_point = private * G
public_key = (int(public_key_point.x()), int(public_key_point.y()))  # Get x, y coordinates
print('public_key (x, y):', public_key)
for i in range(1, 5):
    nonce = random.randrange(2 ** 256 - 1)
    message = random.randrange(2 ** 256 - 1)
    r, s, z ,kp = sign(private, nonce, message)
    print("k =", nonce)
    print("kp =", kp)
    print("r =", r)
    print("s =", s)
    print("z =", z)

    print()