The Study Of Several Problems On Algebraic Attacks

Crypt analytics is always an important offset of Cryptology. There is no cipher in absolute safety, but be immune to all known attacks. A new attack—algebraic att-acks is studied in this paper. In chapter 1, both the signification and the new advance in Crypt analytics are mainly introduced, which include the applied background and the studying status in algebraic attacks and so on. In chapter 2, the development of an overdefined system of multivariate algebraic equations are researched, the basic idea of XL algorithm and its several editions are introduced. In chapter 3, the algebraic a-ttacks on public key cryptosystems, block ciphers and stream ciphers are investigated, some new production are summarized and analyzed, two improved algorithms on st-ream cipher without memory and a general algebraic attacks on cipher which the no-nlinear combiner unknown is put forwarded. In chapter 4, the character, index and design criteria of Boolean functions are studied. According to the new requirement of Boolean functions on algebraic attacks, an additional criterion is added. In chapter 5, we continue the study on Boolean functions, the main content is ①study the Shannon effect on several cryptographic complexity criteria; ②study the upper bound on the probability that a random balanced Boolean functions has a low degree multiple; ③construct two different mapping to describe the multiply of Boolean function, and give a upper bound of minimal algebraic degree of annihilators for a random Boolean functions; ④analyze the algorithm on deciding the (non-) existence of low degree annihilators and summarize the contribution and shortage of it.