Enhancing Image Encryption with the 2D Cubic Map: A Study of Pseudo-Random Key Stream Generation
Tingting Dai, Dandan Han, Qian Zhang · 2025
With the growing demand for information security, image encryption technology has become a crucial tool for protecting data privacy. Traditional Cubic map, due to its simple structure, ease of implementation, and strong chaotic properties, has been widely used in image encryption. However, Cubic map has some limitations, especially within certain ranges of control parameters, where periodic windows can easily occur. This results in a decline in the quality of pseudorandom number generation, thereby compromising the security of the encryption system. To address this issue, this paper proposes an improved version of the 2D Cubic map. By introducing cross-coupling terms, the 2D Cubic map significantly enhances the system's nonlinear characteristics and chaotic behavior, expanding its pseudorandomness and increasing the complexity of the key stream. Compared to the traditional Cubic map, the 2D Cubic map is more effective in avoiding periodic windows, thus improving the quality of the pseudorandom key stream. To validate the effectiveness of the 2D Cubic map in practical applications, it is applied to image encryption in this study. Experimental results show that the 2D Cubic map outperforms the traditional Cubic map in image encryption, generating more complex and secure key streams, which effectively enhance the encryption system's resistance to attacks and overall security.