The N-level (N ≥ 4) logistic cascade homogenized mapping for image encryption

This paper proposed a chaotic system of N -level logistic cascaded homogenization mapping ( N -LLCHM). The cascade structure of multiple one-dimensional logistic mappings results in an exponential increase in the number of fixed points in the mapping, which greatly increases the initial error divergence of the system during the iteration process, and ultimately increases the complexity of the system to generate time series. In the experiment, the homogenization adjustment function of the mapping is derived according to the maximum entropy theorem. The homogenization adjustment function and the N -level logistic cascade structure are cascaded again to construct a complete dynamics system. The analyses of indicators such as information entropy, Lyapunov exponent, spectral entropy and NIST SP800-22 randomness test reveal that the mapping generates a chaotic time series with good aperiodic and uniform distribution characteristics under the condition that N is greater than or equal to 4. Then, N -LLCHM is used as the core of pseudo-random number generator, and the color image encryption algorithm is constructed by using three steps of pixel bidirectional cross-coding, position scrambling and pixel diffusion as the main system. According to the evaluation of histogram, correlation, information entropy and anti-differential attack test, it is verified that this algorithm has better encryption effect and higher security than the present image encryption algorithms.