Discrete Sliding Mode Control for Chaos Synchronization and Its Application to an Improved El-Gamal Cryptosystem

Abstract

This paper is concerned with the design of an improved El-Gamal cryptosystem based on chaos synchronization. The El-Gamal cryptosystem is an asymmetric encryption algorithm that must use the public and private keys, respectively, in the encryption and decryption processes. However, in our design, the public key does not have to appear in the public channel. Therefore, this proposed improved El-Gamal cryptosystem becomes a symmetric-like encryption algorithm. First, a discrete sliding mode controller is proposed to ensure the synchronization of master and slave chaotic systems; next, a novel improved El-Gamal cryptosystem is presented. In the traditional El-Gamal cryptosystem, the public key is static and needs to be open which provides an opportunity to attack. However, in this improved design, due to the chaos synchronization, the public key becomes dynamic and does not appear in public channels. As a result, drawbacks of long cipher text and time-consuming calculation in the traditional El-Gamal cryptosystem are all removed. Finally, several performance tests and comparisons have shown the efficiency and security of the proposed algorithm.