In this paper, an improved multi‐dimensional hyperchaotic system derived from the logistic map and the ICMIC based on closed‐loop coupling (LICC hyperchaotic system) is proposed and it is used in the design of selective image encryption. The performance analysis shows that the LICC hyperchaotic system with a strong coupling degree has parameters whose value can be set more flexibly and can generate a wider and more uniform distribution of chaotic sequences. Then selective image encryption is proposed. Firstly, an adaptive pseudo‐random sequence generator based on hash function is designed to ensure the difference of sequences used in different encryption steps. Second, a novel bit‐level scrambling is designed to increase the encryption speed. Finally, an efficient rule to select image blocks with weak security is proposed and the second step of the encryption is performed at the selected blocks of the image to ensure security. The encryption performance and security analysis show that the proposed encryption algorithm based on an improved hyperchaotic system is secure enough to resist several types of attacks.

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The application of a memristor in chaotic circuits is increasingly becoming a popular research topic. The influence of a memristor on the dynamics of chaotic systems is worthy of further exploration. In this paper, a multi-dimensional closed-loop coupling model based on a Logistic map and Sine map (CLS) is proposed. The new chaotic model is constructed by cascade operation in which the output of the Logistic map is used as the input of the Sine map. Additionally, the one-dimensional map is extended to any dimension through the coupling modulation. In order to further increase the complexity and stability of CLS, the discrete memristor model is introduced to construct a discrete memristor-based coupling model with a Logistic map and a Sine map (MCLS). By analyzing the Lyapunov exponents, bifurcation diagram, complexity, and the 0–1 test result, the comparison result between CLS and MCLS is obtained. The dynamics performance analysis shows that the Lyapunov exponents and bifurcation diagrams present symmetrical distribution with variations of some parameters. The MCLS has parameters whose values can be set in a wider range and can generate more complex and more stable chaotic sequences. It proves that the proposed discrete memristor-based closed-loop coupling model can produce any higher dimension hyperchaotic system and the discrete memristor model can effectively improve the performance of discrete chaotic map and make this hyperchaotic system more stable.