Cryptosystems with discretized chaotic maps

Many kinds of chaotic cryptosystems have been proposed so far. Chaotic systems dissipate information due to orbital instability with positive Lyapunov exponents and ergodicity. If these properties are appropriately utilized, chaotic cryptosystems are supposed to realize high security. However, most of the existing secure communication techniques using chaos do not have enough security. For example, secure communication protocols based on chaos synchronization require robustness which gives useful information to attackers. The cryptosystems based on direct applications of chaotic maps have been weak against linear and differential cryptoanalysis. In this paper, a new kind of chaotic cryptosystem which overcomes these difficulties to some extents is proposed. The cryptosystem is based on a discretization of the skew tent map. We also show some of the desirable properties of the proposed cryptosystem using dynamical characteristics. These properties regarding ciphertext randomness may be closely related to the cryptological security. Our new cryptosystem shall be one step to connect the theory of commonly used cryptosystems and dynamical system theory.