Study On Several Key Problems In Rijndael

The Rijndael algorithm was chosen by NIST (National Institute of Standard and Technology) as advanced encryption standard(AES) on October2,2010, and it has become the international standard in commerce field. The cryptanalysis and optimization study of Rijndael are becoming more and more important. At present, solving the insecurity problem of Rijndael and seeking efficient attack methods for specific cryptanalysis technology are interesting topics of cryptology.An investigation of the Rijndael algorithm is taken in this thesis. We have focused on developing the basic principle of Rijndael, on developing the algebraic property of the Rijndael S-box, on the new S-box construction scheme, on the related-key attacks against the reduced variants of Rijndael, on the equation systems of the Rijndael algorithm, and on the algebraic cryptanalysis problem based on Grobner basis. The key contributions are as follows:1. The new S-box scheme is proposed. Aiming at the weaknesses in algebraic complexity, avalanche effect, affine transformation period and iterative period, the new S-box scheme is proposed to solve the problem that the performance of the Rijndael S-box is bad. The new S-box has almost the best properties in balance criteria, differential uniformity, Resistance of algebraic attacks, avalanche effect, Nonlinearity, algebraic complexity, affine transformation period and iterative period.2. The improved related-key attacks against the reduced variants of Rijndael-128/192are proposed. Two attacks against7-round Rijndael-128/192are proposed to improve the known cryptanalysis by changing the order of round transformation, using the alternative representation of the round keys, exploiting the relationship of keys, and designing the key difference pattern properly.3. The improved related-key attacks against the reduced variants of Rijndael-128/256are proposed. Two attacks against7-round Rijndael-128/256are proposed to improve the known cryptanalysis by using the implementation flexibility and the key relevance. Furthermore, an attack against8-round Rijndael-128/256is proposed to improve the known cryptanalysis. And an attack against9-round Rijndael-128/256is presented too.4. The approach to generating the equation system of the Rijndael S-box is proposed. Based on the construction principle of the Rijndael S-box and the component expression method, a new approach to generating the multivariate quadratic equation system over GF(2) is proposed, and the generation process is given explicitly.5. The three equation systems of the Rijndael algorithm are studied. Based on the basic principle of Rijndael, the equation systems over GF(2) and GF(28) are presented, and the equation system of Rijndael as an embedding in BES is also presented. The investigation of the three equation systems lay a solid foundation for the algebraic attack against Rijndael.6. The construction method of Rijndael-192/192zero-dimensional Grobner basis is proposed. Based on the Grobner basis theory, the method to improve algebraic attack against Rijndael is explored. A construction method of Rijndael-192/192zero-dimensional Grobner basis is proposed through choosing suitable term order and variable order, and the necessary theorical proves are given.