Enhanced chaotic maps for sustainable cryptographic security: A comparative study - Mellah, Nasr-Eddine; Ladaci, Samir; Baptista, Murilo S.; Grebogi, Celso (Nonlinear Analysis: Modelling and Control, 2026)
We propose a comparative study of chaotification techniques that enhance the complexity of one-dimensional maps for sustainable cryptographic applications. Specifically, we examine the use of modulo operation, remainder operation, and k-deep-zoom (k-DZ) transformation applied to the sine map. Each technique’s effectiveness is analyzed using bifurcation diagrams, Lyapunov exponents, and correlation results. Additionally, the statistical performance of the techniques is assessed using the NIST SP 800-22 battery of tests, and the computational efficiency is evaluated in terms of the number of operations. The study aims to identify the best chaotification method for generating robust pseudorandom bit generators (PRBGs) suitable for secure encryption and sustainable cryptography.
Keywords: chaotification; cryptography; Lyapunov exponents; NIST tests; complexity enhancement