Cryptanalysis on an Elgamal-like cryptosystem for encrypting large messages

Abstract: This paper considers both the security issues and fundamental properties of a recently pro-posed ElGamal-like cryptosystem for encrypting large messages. This ElGamal-like cryptosystem may be useful for communicating large messages since it reduces both computation and bandwidth requirement. However, the result of this paper shows that security level of this modified ElGamal-like cryptosystem is different from that of the original ElGamal cryptosystem. Furthermore, fundamental weakness exists in this modified system, say successful decryption can not be guaranteed. Finally, we propose an enhance-ment on the security of the ElGamal-like cryptosystem. Key–Words: Carmichael’s lambda function, Discrete logarithm, ElGamal cryptosystem, Primitive root. 1