A New 1D Chaotic Map and <inline-formula> <tex-math notation="LaTeX">$\beta$ </tex-math></inline-formula>-Hill Climbing for Generating Substitution-Boxes

Abstract

One-dimensional (1-D) chaotic maps have been considered as prominent pseudo-random source for the design of different cryptographic primitives. They have the advantages of simplicity, easy to implement, and low computation. This paper proposes a new 1-D discrete-chaotic map which holds better dynamical behavior, lyapunov exponent, bifurcation, and larger chaotic range compared with the chaotic logistic map. We propose a method to construct cryptographically efficient substitution-boxes (S-boxes) using an improved chaotic map and β-hill climbing search technique. S-boxes are used in block ciphers as nonlinear components to bring strong confusion and security. Constructing optimal S-boxes has been a prominent topic of interest for security experts. To begin, the anticipated method generates initial S-box using the improved chaotic map. Then, β-hill climbing search is applied to obtain notable configuration of S-box that optimally satisfies the fitness function. The simulation results are compared with some recent S-boxes approaches to demonstrate that the proposed approach is more proficient in generating strong nonlinear component of block encryption systems.

Keywords

• β-hill climbing
• block ciphers
• improved chaotic map
• substitution-box