## 4 The SEME-TDHM Algorithm
### Encryption Process
### Discussion

The SEME-TDHM encryption algorithm proposed in this paper effectively achieves image encryption and decryption. Experimental results show that the information entropy of the encrypted images remains stable around 7.999, which is better than the commonly achieved 7.99 in similar studies, indicating a higher degree of randomness. The histogram distribution of the encrypted images is uniform, with correlation coefficients remaining within three decimal places, demonstrating extremely low correlation. The UACI value of the SEME-TDHM algorithm deviates by only 0.0073 from the ideal value, while other similar studies typically show a deviation of 0.01 or more. The NPCR value deviates by only 0.0012 from the ideal value, also outperforming other studies where the deviation is usually greater than 0.01. Furthermore, the SEME-TDHM algorithm demonstrates strong resistance to Gaussian noise at \(1\times 10^{-6}\) and Pepper and Salt noise at 0.01, further confirming its exceptional anti-interference capability. ## 6 Conclusions

This paper introduces a novel 2D hyperchaotic map based on the memristor model. Through the comprehensive analysis of the properties of the hyperchaotic system, it is proved that the system has a wide range of parameter selection and complex chaotic behavior, which is suitable for image encryption. The constructed universal structure is briefly analyzed, proving its universality and good chaotic behavior, and laying the foundation for further studies of similar systems. In addition, this paper proposes the SEME-TDHM algorithm, which uses the SHA-512 hash function and preprocessed image data for key generation. The transition from single-channel to multi-channel encryption and the introduction of chaotic indexing and positioning diffusion matrices significantly \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Image Size** & & **Ours** & **Ref. [6]** & **Ref. [26]** & **Ref. [10]** \\ \hline \multirow{2}{*}{256 \(\times\) 256} & Encryption & 0.512101 & 2.2234 & 0.459837 & 0.699598 \\  & Decryption & 0.621802 & 2.2703 & 0.212294 & 0.599330 \\ \hline \multirow{2}{*}{512 \(\times\) 512} & Encryption & 1.412310 & 9.0016 & 1.769703 & 2.491453 \\  & Decryption & 2.401233 & 9.1095 & 0.83973 & 2.864108 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Time test of encryption and decryption (in seconds). Figure 15: Data loss analysis. enhance security and diffusion properties. The results show that the key space of the SEME-TDHM algorithm is sufficient, and the key sensitivity ensures that the encrypted image contains minimal statistical information, effectively resisting statistical attacks. The NPCR and UACI calculation results of the SEME-TDHM algorithm are close to the ideal values, indicating strong resistance to differential attacks. Additionally, the information entropy of the ciphertext images is very close to 8, reflecting high randomness and ideal encryption results. Although the SEME-TDHM algorithm demonstrates strong security, its practical application may face challenges related to computational efficiency and resource consumption. Future research could aim to optimize the SEME-TDHM algorithm, ensuring that it enhances encryption effectiveness while reducing computational complexity, especially when processing large-scale images. Although the SEME-TDHM algorithm is designed for color images, its core principles and structure can be adapted to secure other data types, such as video, audio, and multimedia content. By extending the SEME-TDHM algorithm to support diverse media formats, it could offer effective security solutions across a variety of applications. Conceptualization, Y.Y. ; Data curation, Y.Y. ; Funding acquisition, X.X. ; Investigation, X.X. ; Methodology, Y.Y. ; Resources, X.X. ; Software, Y.Y. ; Supervision, Z.J. ; Visualization, Z.J. ; Writing--original draft, Y.Y. ; Writing--review and editing, X.X. All authors have read and agreed to the published version of the manuscript.