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<p>To tackle the issues of limited dimensions in chaotic systems, rigid rules of Cellular Automata (CA), and precision loss in floating-point operations within existing color image encryption algorithms, a novel encryption scheme that integrates 3D Lorenz memristive time-delayed hyperchaotic system (LM-THS) and reversible second-order cellular automaton (RSCA) is proposed, i.e., CIE-TR. Firstly, using classical Lorenz system, memristor nonlinear components and time-delay feedback mechanism are employed to construct LM-THS, with double positive Lyapunov exponents, enhancing the randomness and unpredictability of the keystream. Secondly, RSCA, which features a dynamic rule pool and second-order evolution architecture, is designed to overcome the irreversibility and poor adaptability of traditional CA. Moreover, integer operations are adopted to avoid precision loss. The encryption process integrates stages of pixel-level scrambling, bit-level scrambling, and RSCA evolution, thereby achieving an integrated scrambling-diffusion (ISD). The innovations are: (1) LM-THS is constructed with rich dynamic chaotic behavior. (2) RSCA is equipped with a dynamic rule pool showing good reversible property. (3) ISD is built by composite operations of both bit-level and pixel-level. Experiments prove that CIE-TR has a large key space, an close of information entropy, NPCR and UACI to ideal values. Moreover, CIE-TR can effectively resist statistical, differential, cropping, and noise attacks.</p>

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Color image encryption scheme using time-delayed memristive hyperchaotic system and reversible second-order cellular automaton

  • 期刊论文

  • 发表日期：

    2026年4月3日

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  • Gang Hu,
  • Yuling Luo,
  • Guodong Ye

摘要

To tackle the issues of limited dimensions in chaotic systems, rigid rules of Cellular Automata (CA), and precision loss in floating-point operations within existing color image encryption algorithms, a novel encryption scheme that integrates 3D Lorenz memristive time-delayed hyperchaotic system (LM-THS) and reversible second-order cellular automaton (RSCA) is proposed, i.e., CIE-TR. Firstly, using classical Lorenz system, memristor nonlinear components and time-delay feedback mechanism are employed to construct LM-THS, with double positive Lyapunov exponents, enhancing the randomness and unpredictability of the keystream. Secondly, RSCA, which features a dynamic rule pool and second-order evolution architecture, is designed to overcome the irreversibility and poor adaptability of traditional CA. Moreover, integer operations are adopted to avoid precision loss. The encryption process integrates stages of pixel-level scrambling, bit-level scrambling, and RSCA evolution, thereby achieving an integrated scrambling-diffusion (ISD). The innovations are: (1) LM-THS is constructed with rich dynamic chaotic behavior. (2) RSCA is equipped with a dynamic rule pool showing good reversible property. (3) ISD is built by composite operations of both bit-level and pixel-level. Experiments prove that CIE-TR has a large key space, an close of information entropy, NPCR and UACI to ideal values. Moreover, CIE-TR can effectively resist statistical, differential, cropping, and noise attacks.