Rijndael Algorithm Analysis

The study of cryptanalysis of Rijndael in this paper contains three parts. Firstly, cryptographic properties of a class of S boxes are studied which are compositions of power functions with invertible affine transformations. An algorithm is given to calculate the algebra expressions of this class of S boxes. Applying this algorithm over GF(28) the algebraic expression of Rijndael S box is obtained. Moreover, given randomly an affine transformation matrix, the corresponding algebraic expression can be calculated immediately, which facilitates constructing S boxes resistible against interpolation attacks. Secondly, Two improvements of Square attack are given in this paper, which decrease separately the workload in different degree. Thirdly, by a new method a new system of multivariate quadratic equations over GF(28) is used to describe completely Rijndael. the cryptanalysis of Rijndael can be written as a problem of solving the system of multivariate quadratic equations. This system is simpler than Murphy and Robshavv's, and the complexity is only 2~106.8 while applying XSL technique.