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 .