A mixed coupled map lattice based on enhanced Chebyshev maps for chaotic image encryption

Abstract

This study proposes an enhanced Chebyshev map (ECM) and an enhanced sin-type Chebyshev map (ESCM) with simplified structure and near-surjective parameter space. The ECM and ESCM form the foundation for an improved mixed coupled map lattice (IMCML) system. Through systematic theoretical analysis and numerical validation, the IMCML system exhibits significantly expanded parameter domains, demonstrating a 78% wider chaotic regime than conventional MCML. Furthermore, it shows enhanced chaotic characteristics compared to non-enhanced MCML and standard CML systems, including a 400% increase in maximum Lyapunov exponent and complete elimination of period and weak chaos phenomena. Building upon these advancements, we propose a novel image encryption scheme that implements efficient diffusion-confusion mechanisms through pseudo-random matrices generated by IMCML, incorporating dynamic pixel substitution and adaptive block rotation operations. Comprehensive cryptanalysis demonstrates the scheme’s superior resistance to differential attacks (NPCR = 99.6%), statistical attacks (information entropy 7.9988), and chosen-plaintext attacks, while maintaining real-time processing capability (average encryption time < 130 ms for 512 × 512 images). These results substantiate the system’s potential for secure real-time communication applications.