Construction And Security Analysis Of Multivariate Chaotic Hash Function

Hash function is an algorithm converts variable length message to a fixed length of digest, which is called hash value. Hash function has a wide range of application in information security, such as data integrity authentication, identity authentication and digital signature. Merkle-Damgard construction is used in the design of classical hash algorithms such as MD family and SHA family. But there are many attack algorithms against MD5 which are very popular. The Merkle-Damgard construction is proved not secure enough. Also, the serial computing mode of the construction is not suitable for large data processing. Now researchers are confronted with the problem how to construct more effective and secure hash functions. Meanwhile, due to the similarities between the performance of chaos theory and the confusion and diffusion requirements of cryptology, chaotic hash functions become popular in information security. In this paper, we propose novel hash functions based on the complexity of chaos theory and the difficulty of solving multivariate polynomial equations. The main work of this paper is shown below:(1)Firstly, we research the developments and current condition of hash functions. Also, we summarize proposed chaotic hash algorithm and multivariate cryptosystems.(2) Secondly, we propose a cross processing hash algorithm based on the difficulty of solving multivariate polynomial equations and the complexity of chaos theory to resist forge attack. The cross processing structure of chaotic maps solves the security problem existed in many parallel hash algorithms caused by contents of a certain block cannot influence process of other blocks. After that, we process messages by multivariate polynomial equations which can improve the performance of the algorithm further. Theoretical analysis and experimental results indicate that the parallel structure compensates the inefficiency of traditional multivariate polynomial cryptosystems, and it can resist forge attack and differential attack. The algorithm satisfies the requirements of hash function.(3)Thirdly, referring to HAIFA construction we propose a novel hash algorithm without secret key to solve security and inefficient problems existed in traditional Merkle-Damgard construction. To increase speed the compress functions of the algorithm process messages with parallel chaotic maps. Also the algorithm could adjust the length of output hash value, by multivariate polynomial equations. Theoretical analysis and experimental results indicate that the algorithm can resist common attacks and satisfies the requirements of hash functions.