Research On Hash Function Analysis Method Of SHA Series Based On ARX

The research on the SHA family is an important branch of the symmetric cryptography.In recent years, the collision search attacks on the Hash function is a series of expansionaround the methods which proposed by Wang Xiaoyun et al., namely the local collisionsand multi-block collisions, message modification techniques and automatic searchtechniques. The collision attacks on SHA-0to SHA-2mostly follow this idea. This articlecarries on the detailed analysis on the Wang Xiaoyun‘s method to find better results. At thesame time, the recent studies showed that for the SHA Hash functions the collision searchattack has reached the limit, and researchers started to study methods combined withother attacks, so this paper also researches and analyze the boomerang attack on SHA-512.The main work of this paper is: a detailed analysis on Wang Xiaoyun‘s methods onattack SHA-1, and some supplement and improvement is also be proposed, including theintroduction of the weighted algorithm that combine the number of conditions and disturbancevectors, and the specific characteristic of the MSB‘s condition number is also be pointed out.Six disturbance vectors of the full round SHA-1with the best complexity was found by theprogram that applies the ideas mentioned above, and it means that there are more choices canbe used to find differential path with lower complexity. By this work, we can summarize acomplete method to attack the hash functions based on LFSR. Then by combining with the38round semi-free-start differential path mentioned by Maria Eichlseder, a research on thediffusion of messages‘difference is conducted, and the rules of calculating Wi‘s differenceare summarized. By it, this paper gives more message differential characteristics meetingrequirements. Finally I analyze the boomerang attack on SHA-512, summarize an overall wayof boomerang attack on Hash functions, analyze the two sources which conditions influencetime complexity come from: the conditions of intermediate states and the expansion ofinformation messages. Two rules of setting differences in intermediate states are summarized,which can be applied to concrete the method to search differential paths automatically ormanually.This paper gives a lot of specific analysis, and we can see there are a lot of problems thatneed further research in the future study, for example, how to realize a specific algorithm tosearch confirming message pairs; how to implement message modification technology; thefurther research on the boomerang attack on other SHA algorithms is valuable.