Image encryption scheme based on thorp shuffle and pseudo dequeue

To enhance the security level of image data transmission, this paper proposes a four-dimensional hyperchaotic image encryption scheme based on the combination of Thorp shuffle and pseudo dequeue. First, the nonlinear term of the classic four-dimensional Chen chaotic system is improved to construct an improved four-dimensional hyperchaotic system. Phase diagrams, Lyapunov exponents, and equilibrium points are used to analyze its dynamic characteristics. The system has rich dynamic behaviors, and its maximum Lyapunov exponent reaches 11.3. Second, the SHA-256 algorithm is used in combination with plain image information to generate an initial chaotic key. On the basis of this key, a pseudorandom sequence is generated by the chaotic system and used for scrambling and diffusion operations. An image encryption algorithm combined with chaotic sequences is subsequently designed, which includes index scrambling, a double-ended Thorp shuffle, and a diffusion step based on a multiplane bit operation. Finally, the performance of this algorithm is evaluated through experiments such as statistical analysis, differential attack analysis, and noise attack analysis. The information entropy of the cipher image can reach 7.9994, with the number of pixel change rates and the unified average change intensity being close to the ideal value, and the percentage of floating frequency can reach 63%. The results show that the algorithm proposed in this paper has high encryption efficiency and security and performs excellently in terms of anti-attack performance. © The Author(s) 2025.