#############################################################
# Problem 0: Find base point
def GetCurveParameters():
    # Certicom secp256-k1
    # Hints: https://en.bitcoin.it/wiki/Secp256k1
    _p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
    _a = 0x0000000000000000000000000000000000000000000000000000000000000000
    _b = 0x0000000000000000000000000000000000000000000000000000000000000007
    _Gx = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
    _Gy = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
    _Gz = 0x0000000000000000000000000000000000000000000000000000000000000001
    _n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
    _h = 0x01
    return _p, _a, _b, _Gx, _Gy, _Gz, _n, _h


#############################################################
# Problem 1: Evaluate 4G
def compute4G(G, callback_get_INFINITY):
    """Compute 4G"""

    """ Your code here """
    result = callback_get_INFINITY()
    return result


#############################################################
# Problem 2: Evaluate 5G
def compute5G(G, callback_get_INFINITY):
    """Compute 5G"""

    """ Your code here """
    result = callback_get_INFINITY()
    return result


#############################################################
# Problem 3: Evaluate dG
# Problem 4: Double-and-Add algorithm
def double_and_add(n, point, callback_get_INFINITY):
    """Calculate n * point using the Double-and-Add algorithm."""

    """ Your code here """
    result = callback_get_INFINITY()
    num_doubles = 0
    num_additions = 0

    return result, num_doubles, num_additions


#############################################################
# Problem 5: Optimized Double-and-Add algorithm
def optimized_double_and_add(n, point, callback_get_INFINITY):
    """Optimized Double-and-Add algorithm that simplifies sequences of consecutive 1's."""

    """ Your code here """
    result = callback_get_INFINITY()
    num_doubles = 0
    num_additions = 0

    return result, num_doubles, num_additions


#############################################################
# Problem 6: Sign a Bitcoin transaction with a random k and private key d
def sign_transaction(private_key, hashID, callback_getG, callback_get_n, callback_randint):
    """Sign a bitcoin transaction using the private key."""

    """ Your code here """
    G = callback_getG()
    n = callback_get_n()
    signature = callback_randint()

    return signature


##############################################################
# Step 7: Verify the digital signature with the public key Q
def verify_signature(public_key, hashID, signature, callback_getG, callback_get_n, callback_get_INFINITY):
    """Verify the digital signature."""

    """ Your code here """
    G = callback_getG()
    n = callback_get_n()
    infinity_point = callback_get_INFINITY()
    is_valid_signature = TRUE if callback_get_n() > 0 else FALSE

    return is_valid_signature