Construction of a New 2D Hyperchaotic Map with Application in Efficient Pseudo-Random Number Generator Design and Color Image Encryption

This paper proposes a new two-dimensional discrete hyperchaotic system and utilizes it to design a pseudo-random number generator (PRNG) and an efficient color image encryption algorithm. This hyperchaotic system has very complex dynamic properties and can generate highly random chaotic sequences. The complex hyperchaotic characteristics of the system are confirmed via bifurcation diagram, chaotic attractor, Lyapunov exponents, correlation analysis, approximate entropy and permutation entropy. Compared with some traditional discrete chaotic systems, the new chaotic system has a larger range of chaotic parameters and more complex hyperchaotic characteristics, making it more suitable for application in information encryption. The proposed PRNG can generate highly random bit sequences that can fully pass all NIST testing items. The proposed color image encryption algorithm achieves cross-channel permutation and diffusion of pixels in parallel. These strategies not only greatly improve the encryption speed of color images, but also enhance the security level of cipher images. The simulation experiments and security analysis results show that the algorithm has strong robustness against differential attacks, statistical attacks and interference attacks, and has good application potential in real-time secure communication applications of color images.