A novel 3D hyperchaotic map coupled with discrete tangent memristor: Dynamic analysis, DSP implementation, and image encryption application

Abstract

This study employs discrete memristors, derived from tangent functions, to generate a novel three-dimensional discrete hyperchaotic map. Initially, an analysis is conducted of the fixed-point attributes of the chaotic map. Subsequently, the dynamic behavior of the chaotic map is investigated, revealing phenomena such as hyperchaos, offset, state transitions, and the coexistence of attractors. The complexity and randomness of the chaotic sequence are evaluated, and the attractor trajectory is displayed on an oscilloscope via the DSP platform, thereby demonstrating the physical feasibility of the chaotic map. Consequently, an encryption algorithm for color images, incorporating selective diffusion processes, is developed. Lastly, a security analysis of the encryption algorithm is performed, affirming its robust security and resilience against various attack strategies.