Cryptanalysis of an ElGamal-Like Cryptosystem for Enciphering Large Messages

In 2002, Hwang et al. propose an asymmetric cryptosystem in which a large message is broken into smaller plaintexts which are then encrypted efficiently. They claim that based on the assumption of the intractability of the discrete logarithm problem, their cryptosystem is secure in the sense that even knowing some pairs of plaintext-ciphertext does not allow an intruder to acquire other plaintexts easily. This paper disproves this claim. Key-Words: Asymmetric cryptosystem, ElGamal cryptosystem, Cryptanalysis, Discrete logarithm, Order of element.