Cross-channel color image encryption scheme based on a novel 3D hyperchaotic map, Peano curve and compressed sensing

Abstract Chaotic maps serve as a cornerstone in image encryption, with chaos theory acting as a fundamental driving force in cryptographic algorithm development. However, current chaotic mapping and image encryption methods often exhibit limitations such as low sensitivity to initial conditions, insufficient disorder capability, and suboptimal dynamic performance. To address these constraints, this study proposes a comprehensive encryption framework comprising three key innovations. First, we develop an enhanced 3D hyperchaotic map that successfully passes the NIST randomness tests, exhibiting favorable Lyapunov exponents, distinct bifurcation behavior, and rich dynamic characteristics. Second, we introduce an improved Peano curve algorithm for the scrambling phase, achieving 3D cross-channel scrambling by jointly permuting the R, G, and B planes of color images. Third, a novel bit-based diffusion algorithm is proposed, which utilizes chaotic sequences to select, invert, and cyclically shift binary bits of target pixels, thereby realizing robust image diffusion. Furthermore, we incorporate a block compressive sensing (BCS) algorithm to enhance both transmission efficiency and security. This integration allows for image preprocessing to improve encryption efficiency. The proposed scheme achieves three-level protection at the pixel, channel, and spatial levels. Experimental results demonstrate that at a compression ratio of 0.5, the PSNR exceeds 30 dB, and the scheme exhibits high security with strong resistance to differential and brute-force attacks. Notably, the NPCR and UACI values reach 99.60% and 33.46%, respectively, with an average encryption time of approximately 2.6 seconds.