Cryptographic Hash Function Design Based On Probability Distribution Of Information Source

The rapid development of multimedia technology, communication technology and transmission technology has brought great convenience; meanwhile, information security has become a problem which cannot be ignored. Due to the special character, the security issues of wireless network have been highlighted. As an important tool in the field of information security, cryptographic hash function is mainly used in file validation, digital signature and authentication protocol etc. The design of a secure cryptographic hash function should abide by three principles, which are anti-preimage attack, anti-second preimage attack and anti-collision attack. Nowadays, proposed cryptographic hash functions mainly are MD series and SHA series, at the same time, attacks against cryptographic hash functions are also of great concern, one typical attack of which is birthday attack. Birthday attack depends on the length of the message digest, which is the length of hash value. Such attack proposes a necessary security condition that the length of the message digest should be long enough. The traditional design of cryptographic hash function assumed that the information to be sent are equally probable events which means the amount of source information is smallest from the perspective of information theory. Actually, from the sight of the sender, the probability distribution of the source information or the amount of source information can be obtained through long-term statistics. Moreover, the probability distribution of source information may be very regular in some cases. The unequally probable distribution of source information is taken into account to design the cryptographic hash function in this dissertation. Compared with traditional cryptographic hash function, the probability of successful attack of the optimized hash function is greatly reduced. In other words, the length of the message digest may be shorter with the same attack probability.The specific research works of this dissertation are as follows.Through analyzing and discussing the mapping problem of cryptographic hash function after considering the probability distribution of source information, the relationship among information probability, mapping relation and probability of successful attack is obtained. In this dissertation, the probability of successful attack was optimized, and then a heuristic algorithm of cryptographic hash function based on probability distribution of source information was proposed. The heuristic algorithm is been simulated and estimated through simulation results. Through multiple iterations, optimized algorithm has found a sub-optimal mapping relation to achieve the convergence of the probability of successful attack. Compared with the traditional algorithm, the sub-optimal algorithm has made the probability of successful attack reduced with the same parameters, which improves the safety performance of the communication process.Secondly, the definitions of the degree of balance and the balance analysis of the birthday attack are introduced, as well as the conclusions of the balance of MD (Merkle-Damgard) transform which is commonly used. The conclusions of previous studies have shown that the balance size of a traditional cryptographic hash function with good security performance is close to1. Moreover, the concept of balance into the proposed hash function is introduced and its balance formula is exported. Through the balance simulation and comparison between traditional ideal cryptographic hash function and optimized hash function, it has verified in this dissertation that a good cryptographic hash function no longer possesses the character that the degree of balance is close to1when the probability of source information is unequally probable. The perfect balance definition and conclusions as well as the corresponding theoretic proofs will be the next research focus.