Analysis And Design Of Hash Functions Based On Chaotic Maps

As the popularity of computer and network technology growing quickly, information security has become a widespread hot topic in the field of academic research and industry in recent years. Because previous studies showed that chaos and cryptology are linked closely and similar in the structure, research of secure communications, information encryption and message authentication technology based on chaos theory has become one of the international advanced projects in the cross field of nonlinear science and information science. Chaos is a complex dynamic behavior, which has the properties of hash function such as one-way, randomness, high sensitivity to initial conditions and system parameters and so on. Since 2005, the study of collision problems of hash function has made a great breakthrough. Wang Xiaoyun et al found some unknown flaws in the respect of collision resistance of the widely applied hash functions, such as MD5, SHA-1. Therefore, with its good features, chaos has gained an increasing attention of scholars as a new way to construct hash function.The main contents of this paper are summarized as follows:(1) on the basis of mastering the properties and analysis methods of hash function, studying the hash functions based on chaotic dynamics; (2) security analysis, such as collision analysis on hash function based on chaotic map proposed before; (3) proposing a dedicated keyed hash algorithm based on chaotic map; (4) In addition, learning to realize algorithm simulation by using C language on the platform of VC6.0 and Matlab.This paper has completed the following research work:First, the paper makes collision analysis on the improved and original keyed hash functions based on chaotic map proposed by Xiao Di. Specifically, it presents the chaotic system, description, properties, performance analysis of the original algorithm, weak key analysis and forgery attacks on the original algorithm proposed by Guo Wei, and Xiao's improved algorithm towards Guo's analysis. The paper theoretically analyzes collision problems of the two schemes and gives experiment results of collision by using numerical simulation. One can use the flaw of the hash functions to find a forgery message if he knows the secret key.Second, the paper proposed a dedicated keyed hash algorithm based on the modified coupled chaotic map lattice. The algorithm uses modified one-dimensional coupled chaotic map system, whose characteristics is that both the key and message are parameters of the chaotic map system, the expansion key and the nonlinear transformation are used. Therefore the system has enough confusion and diffusion rate between the message and the key through multiple iterations, also has a uniform and random distribution of hash value. The efficiency of algorithm is evaluated through computer simulation; also the security analysis is finished, including statistical analysis and attacks analysis. The algorithm provides strong collision resistance and high performance efficiency and could be applied in MAC.At last, the conclusion gives a summary of this paper and illustrates the meaning and application outlook of the research.