Batch generating keyed strong S-Boxes with high nonlinearity using 2D hyper chaotic map

Abstract

Cryptanalysis result of the S-Box construction in AES revealed that, (1) the number of irreducible polynomials can be extend to 30, (2) if we ignore the existence of fixed point(s) and reverse fixed point(s) in an S-Box, the affine transformation constant c can select from [01, FF], and (3) the S-Box in AES is fixed, which causes potential security risks to the AES algorithm. Based on the above analysis, first we constructed a non-degenerate 2D enhanced quadratic map (2D-EQM) with ergodicity and randomness, and then used it to generate affine transformation matrices and affine transformation constants which were applied to seed S-Boxes to generate a batch of keyed strong S-Boxes with high nonlinearity. Furthermore, we counted that of all the generated 4.0913 × 1022 S-Boxes, about 5.4414 × 1020 of them can still keep the nonlinearity of 112. Finally, we used six criteria to evaluate the performance of constructed S-Boxes. Security and statistical analysis demonstrated the effectiveness and practicability of the proposed S-Box batch generating algorithm.