Research On Constructing One-Way Hash Function Using Hyper-Chaos

Since the 1980s, more and more attentions have been given to constructing a cipher system with digital chaotic system. There are inextricably links between chaos theory and simple cryptography, and chaotic dynamics shows some features that are desirable for the cipher system. Therefore, chaotic dynamics is used to construct encryption algorithm and to encrypt plain-text. Generally speaking, there are two kinds of chaotic cipher: one is the analog chaotic secure communications; the other is the digital chaotic ciphers realized in computers. This dissertation will focuse on digital chaotic ciphers, and constructing Hash Function with hyper-chaotic.The methods of constructing Hash function using chaos are reviewed in this paper, the advantages and disadvantages of existing algorithms are pointed out. On this basis, we will construct two Hash functions using hyper chaotic Chen system and infinite dimensions hyper chaotic system, key stream iterative is also used for confusion the message, the cipher block chaining mode is used to generate the 128bit Hash value for plain-text with arbitrary length. Theoretical analysis and simulation results indicate that the proposed algorithm can obtain good performance, such as value compression function, irreversibility, initial value sensitivity, forgery resistance and collision resistance. Compared with some existing methods, the proposed scheme possesses better collision resistance performance.Theoretically, there are infinite dimensions in a delayed differencial equation, therefore, the largest Lyapunov function can't describe the full characterisitcs of the system. This paper studies the method of calculating of multiple Lyapunov exponents of the delayed differencial equation, the results showed that the delayed hyper chaotic system had the multiple positive Lyapunov exponents and had more complex dynamics.