Abstract: Disclosed is a method for designing public key cryptosystems against fault-based attacks in which secret information stored in a tamperfree device is revealed during the encryption/decryption or signature generation processes due to fault-based attacks. A new fault-resistant system which enables any fault existing in modular multiplications and exponential computations to be detected with a very high probability based on a coding approach. This method can be used to implement all cryptosystems whose basic operations are modular multiplications for resisting both memory and computational fault-based attacks with a very low computational overhead.