A Research Of Algebraic Attacks Method On Advanced Encryption Standard

Blockcipher can provide more secure algorithm in data transfer. The most typical technology is AES,Rijndael algorithm.Block cipher analyzing can prove algorithm security in theory and in practice,the threat of algebraic attacks to common cryptosystems has drawn a lot of attention.Algebraic attacks are attacks in which a cryptosystem is broken(for example the key,the plaintext)by solving a system of multivariate equations over a finite field(e.g.GF(2))that describes the whole cryptosystem.The thesis introduces design detail of Rijndael and study general methods known for solving overdefined system of algebraic equation such as relinearization algorithm,XL algorithm and XL improved algorithm over GF(k)(k＞2),GF(2)and GF(2~n).Then XSL algorithm on XSL cipher and algorithm complexity are researched.By define BES cipher the author introduce XSL algorithm over GF(2~8).The measure of algebraic vulnerability and relation between the scale of S box and the resistance against the Algebraic attack were discussed.At last Grobner basis theories are introduced including Buchbeger algorithm,Buchbeger improved algorithm based on Buchbeger criterion. By combining with an extremely sparse overdefined multivariate quadratic system over GF(2)as which Rijndael encryption can be described,a new method of Grobner Basis Attack against block cipher is proposed.By conversion algorithm FGLM,converting degree reverse lexicographic order into lexicographic order,elabrately designed order and solution set judgment,the complexity of Grobner basis attacks can be efficiently reduced.The Grobner basis attack can recover the full cipher key requiring only a minimal number of plaintext/ciphertext pairs. The complexity of Grobner basis attack is analyzed.By F4 algorithm the thesis clarify a relation between the XL algorithm and Grobner basis algorithm.The XL algorithm is also a Grobner basis algorithm that can be represented as a redundant version of a Grobner basis algorithm F4 under the assumption in XL.