Cryptographic system based on double parameters fractal sorting vector and new spatiotemporal chaotic system

Abstract

Information security and image encryption have rapidly developed in recent years. This study presents an iterative method for vectors with fractal characteristics. Based on the idea of combining fractal and algebraic theories, the double parameters fractal sorting vector (DPFSV) was originally proposed, which incorporates features such as complexity, self-similarity, and iteration. Based on the practical application requirements, the DPFSV has a good regulatory vector length and increases the diversity of information location change laws. Hence, this study uses the DPFSV to control iterative node relationships in spatiotemporal chaotic systems. The new spatiotemporal chaotic system proposed based on DPFSV exhibits better dynamics than that of the coupled map lattice (CML) system, verified by comparing their Kolmogorov–Sinai entropy, bifurcation diagram, information entropy, and mutual information. Therefore, DPFSV–CML is more suitable in cryptography than CML. Combining the DPFSV and spatiotemporal chaotic system, this study constructs a new cryptographic system to implement permutation–diffusion synchronous encryption. This new encryption method has a good encryption effect and is resistant to various attacks. The security of this proposed cryptographic system is verified through various security analyses and simulated attack validations.