Construction of High Quality Key-dependent S-boxes.dvi

High quality key-dependent S-boxes can break the preconditions of many cryptanalysis technologies, but it is difficult to construct them efficiently. Here, we proposed a method for fast constructing good key-dependent S-boxes, which are generated by means of a key-dependent affine transformation on a good base S-box. We proved their security by classifying the evaluative criteria of S-boxes into three categories: affine static, conditional affine static and affine dynamic criteria. We found that algebraic degree of an S-box may be decreased through an affine transformation and proved the condition for keeping it invariant under an affine transformation. In order to efficiently get affine key-dependent S-boxes, we presented three fast constructing algorithms for obtaining key-dependent nonsingular Boolean matrix, matrix multiplication of an Sbox, and eliminating fixed points, respectively. The theoretical analysis and statistical results show that the key-dependent S-boxes generated by this method have good cryptographic properties.