New 2D inserting-log-logistic-sine chaotic map with applications in highly robust image encryption algorithm

Abstract

Chaos-based image encryption methods are highly effective, but existing chaotic systems often suffer from insufficient chaotic performance and low unpredictability. Additionally, Gaussian noise, a common interference in wireless transmission, can significantly degrade signal recovery, making the need for a robust diffusion algorithm critical. To address these issues, this study introduces a novel two-dimensional inserted logistic-logarithmic-sine chaotic map (2D-ILLSCM) which features a uniform output distribution and high Lyapunov exponent values. The proposed chaotic map has also been simulated on a field-programmable gate array. What’s more, the paper proposes a highly robust bit-level encryption diffusion algorithm based on the fast Fourier transform computational network (BLEDA-FFTCN) and an adjacent scrambling algorithm based on 2D-ILLSCM (ASA-ILLSCM). This encryption algorithm addresses the issue of traditional bit-level encryption methods losing resistance to Gaussian noise after multiple diffusion and scrambling stages. Four common encryption structures were used to validate the robustness of this scheme, and the experimental results confirmed its effectiveness and security. Extensive experiments and comparisons demonstrate that the algorithm based on BLEDA-FFTCN and ASA-ILLSCM outperforms many state-of-the-art encryption methods in various aspects, particularly in terms of resistance to Gaussian noise.