A Novel 4D Hyperchaotic System Assisted Josephus Permutation for Secure Substitution-Box Generation

Hyperchaotic systems found to exhibit better dynamics and behaviors compared to chaotic systems due to great possibility of simultaneous exponential expansion of their system’s states in several directions. This feature makes hyperchaotic systems more suitable for the application of cryptographic algorithms design. This paper has multi-fold contributions which begin with the design of a novel four-dimensional dynamical system. The proposed system holds the characteristics of hyperchaotic nature, fractional KY dimension, dissipativeness, equilibrium point, complex phase attractors, etc. The new hyperchaotic system is utilized to assist the conventional Josephus permutation scheme to procure permutations with better randomness. Based on the dynamics of proposed hyperchaotic system and improved chaotic Josephus permutation scheme, a novel cryptographic substitution-box construction method is proposed. Hyperchaos-assisted Josephus permutation is applied to evolve the strength of S-box so that an optimized configuration is attained. The performance appraisal of proposed S-box is effected using standard parameters. The recital comparative analysis with number of existing S-boxes establishes the consistent performance and security of proposed S-box.