Research Of Hash Functions Based On Chaotic Dynamic Systems

Hash functions are important components in modern cryptography and widely applied in data integrity, message authentication and digital signature, etc. MD5and SHA-1algorithm, which were used as international standards have been successively proved to be not secure, traditional hash functions face the challenge. For this reason, National Institute of Standards and Technology(NIST) announced a public competition in2007to develop a new cryptographic hash algorithm, called SHA-3, for standardization. Many novel algorithms were proposed, and these hash functions supply thinking for design secure hash functions. Due to the sensitivity to initial conditions, ergodicity and pseudo randomness, hash functions based on chaotic systems become a hot spot in the field of information security.In this thesis, we did the following work:According to the analysis of the modern hash functions and chaotic hash functions, a hash function with serial and parallel composition construction is proposed. A finite number of message blocks are processed in parallel and for each parallel branch block messages are compressed in serial implementation. The serial process is wide-pipe construction that aims to resist multicollision attack. The compression function is based on two-dimensional coupled map lattice, which has fast diffusion and confusion rate. The length of hash values is changeable and that enhances the flexibility of the algorithm. We compute the number of operations of the proposed hash function and estimate its efficiency. Considered the trade-off between security and efficiency, the algorithm can serve as a new type of hash function candidates for parallel implementation. A keyed hash function based on a dynamic lookup table is analyzed. The original algorithm exploits the piecewise linear chaotic map that is iterated with the specified secret keys to produce four32-bit initial buffers and then applies the composite functions associated with messages to update dynamic lookup table and buffers state. After all the message blocks are processed in sequence, the final buffer value is the hash value. In this paper, we give the constraint conditions of buffer states such that a collision is produced. The cost of finding collisions is O(2100), much larger than that of birthday attack. But the algorithm does not resist multicollision attack as its inner state bit length does not reach2times that of output hash value.