Constructing Keyed Strong S-Boxes with High Nonlinearity Based on a 2D-Hyperchaotic Map and Elliptic Curve

To remedy the weaknesses that exist in some S-Boxes, such as low nonlinearity, fixed point, reverse fixed point, and short iteration period rings, first, a nondegenerate 2D-Hyperchaotic Map (2D-HCM) is constructed and its dynamical behavior is analyzed. The randomness test results indicate that the sum of the two sequences generated by the 2D-HCM exhibits good randomness. Second, an initial S-Box is constructed based on the generalized multiplicative inverse of the x-coordinate of each point on an elliptic curve over GF([Formula: see text]). Then, a strong S-Box is constructed by permuting the Boolean function values of the initial S-Box using the index sequence generated by 2D-HCM and eliminating its weaknesses. Subsequently, the number of the constructed strong S-Boxes and the complexity of the proposed algorithm are analyzed. Finally, the optimal equation is established by analyzing the performance of 5000 strong S-Boxes with different parameters. The performance analysis results indicate that the proposed algorithm can construct S-Boxes with high nonlinearity in batches.