Security Research Of Hash Functions Based On Chaotic System

As the high development of Internet, the pace and rhythm of social informatization are both accelerated. As an unbodied resource, Information has become an important force in promoting economy and society. For information security, there are more and higher requiments for the theory and the technology of information security. In the same time, as the key technology of information security, cryptology is payed more and more close attention to again. At present, it has been found that more and more cryptosystems have security flaws. For example, in the International Cryptology Conference in2005, Professor Wang Xiaoyun and her workmates showed their research results of MD5, SHA-1and others, which are all the standard of secure hash function algorithms, and the results indicated that some hash function algorithms are not able to resist against collision attack, which were considered to be very secure in the past. No matter for cryptology their own development needs or for concern about the traditional cipher security vulnerabilities exposed frequently, at present people are more and more urgently hope to look for cryptosystems with new design. As a complex dynamic behavior, chaos is used to design new cryptosystem with its mixing property and its random-like behavior. As a new kind of cryptosystem, chaotic cryptosystem not only has been attracting a lot of researcher to research it, but also has been attracting broad attention of people concerned about information security.In this paper, we research the security analysis of hash functions based on chaotic systems, which mainly includes three different kinds of hash function algorithm based on chaotic systems. Our result indicates that some hash functions based on chaotic systems have construction flaws, which can lead to local collision attack, second-preimage attack, forgery attack and so on. Furthermore, in design of hash function algorithms based on chaotic systems, designers usually use parameters of chaotic maps as keys of hash function algorithms, and it maybe leads to that there exist weak keys for most of chaotic maps are not one-to-one mapping.In this paper, our main work as follows:(1) We introduce the base knowledge of the cryptographic hash function, including the basic concepts of the cryptographic hash function, the discussion of the security of the cryptographic hash function in detail, the basic knowledge of two common construction, which is used to design cryptographic hash functions, some evaluative criterias about cryptographic hash function, the application of hash function in the information security and current situation, achievements and bottlenecks of the research of the hash functions based on chaotic systems.(2) We give a security analysis of a parallel keyed hash function based on chaotic neural network. And the results of security analysis indicate that the original hash function is not able to resist against collision attack and forgery attack and it has weak keys. We propose an improved hash function algorithm to remove those design deficiencies and security flaws in original hash function algorithm. And the improved algorithm is more secure and keeps the parallel merit of the original hash function by security analysis.(3) We take a security analysis of a keyed hash function based on a chaotic map. And the results of security analysis indicate that the original hash function is not able to resist against collision attack and second-preimage attack, it has three kinds of weak keys, whose amount is more than half of keys, and the IV defect in the original hash function is too serious to be useful in practice. At last, we give the reason why this algorithm is not secure and propose some suggestions to inprove the original hash function.(4) We take a security analysis of a parallel hash function construction based on coupled map lattices. And our results of security analysis show that for the periodic boundary in the coupled map lattices, the original algorithm has a construction flaw, which can lead to that when some plaintext and corresponding hash value are both known, we can require the cyclic shift of hash value in specific lattic with the cyclic shift of plaintext.