An Efficient and Secure Cryptosystem for Encrypting Long Messages

Traditionally, due to efficiency considerations, when encrypting long messages using an asymmtric cryptosystem, one needs to use a symmetric cryptosystem in addition. To eliminate this requirement, Hwang, Chang, and Hwang introduced an asymmetric cryptosystem for encrypting long messages. However, they did not give any formal proof of the security of this cryptosystem. In this paper, we propose an improved asymmetric cryptosystem for encrypting long messages, which is both efficient and secure. In the aspect of efficiency, our cryptosystem is about twice as fast as the Hwang-Chang-Hwang cryptosystem. In the aspect of security, besides providing an informal analysis, we rigorously show that computing any part of the plaintext message encrypted using our cryptosystem is as hard as breaking the ElGamal cryptosystem, even if all other parts of the message are already known to the adversary.