Constructing keyed strong S-Box with higher nonlinearity based on 2D hyper chaotic map and algebraic operation.

As the only nonlinear component, S-Box plays an important role in cryptography. To overcome the problems in some 1D chaotic maps such as poor randomness and lacking ergodicity, we constructed a 2D exponential quadratic chaotic map (2D-EQCM), and analyzed its dynamic behavior through phase diagram, Lyapunov exponent, Kolmogorov entropy, correlation dimension and randomness testing. The results demonstrated that the 2D-EQCM with ergodicity and better randomness can be served as pseudo-random number generator (PRNG). Furthermore, to generate a large number of S-Boxes with higher nonlinearity, we designed a keyed strong S-Box construction algorithm using the 2D-EQCM and algebraic operation based on seed S-Boxes. Experimental results verified the effectiveness of the proposed keyed strong S-Box construction algorithm.