Secret information stored in a tamperfree device is revealed during the decryption or signature generation processes due to fault-based attack. In this paper, based on the coding approach, we propose a new fault-resistant system which enables any fault existing in modular multiplication and exponentiation computations to be detected with a very high probability. The proposed method can be used to implement all crypto-schemes whose basic operations are modular multiplications for resisting both memory and computational fault-based attacks with a very low computational overhead.