A novel approach to constructing a parameter-controlled multi-scroll conservative hyperchaotic system: applications in image encryption

Abstract This paper proposes, for the first time, a novel parameter-controllable four-dimensional multi-scroll conservative hyperchaotic system, constructed using nonlinear feedback based on modulus operations. The system exhibits rich dynamic characteristics, with a simplified mathematical model, and is more suitable for hardware implementation compared to traditional multi-scroll chaotic systems. This feature is highly significant for hardware-centric applications where both security and computational speed are of paramount importance. The size, number and spatial distribution of the scrolls in phase space can be precisely controlled through the parameters n and T. Through theoretical analysis and numerical simulations, we investigate the system's behavior at equilibrium points, energy, phase-space volume, Lyapunov exponents, bifurcation characteristics, and sequence complexity. Moreover, the system demonstrates rich coexisting behaviors not only dependent on initial conditions but also under the influence of control parameters. In addition, it exhibits hyperchaotic characteristics over a wide parameter range (a and b), which significantly enhances the security and unpredictability of the system. Based on the proposed multi-scroll conservative hyperchaotic system, a novel color image encryption algorithm is devised. The innovative plane reorganization and scrambling algorithms facilitate more effective mixing of the color planes. In conjunction with a bidirectional encryption diffusion algorithm, the changes to any pixel in any plane are propagated across all three color planes. The scrambling algorithm, derived from the controlled multi-scroll conservative chaotic system, processes row and column scrambling in parallel, thereby streamlining the scrambling procedure. Experimental results and subsequent analysis demonstrate that the proposed color image encryption algorithm exhibits robust security and is well-suited for communication scenarios with real-time processing requirements.