An improved digital logistic map and its application in image encryption

Abstract

Chaos maps are widely used in image encryption systems due to their intrinsic advantages such as extreme sensitivity to initial values., ergodicity and pseudo-randomness. 1D Logistic map has attracted the attention of researchers due to its simple structure and easy implementation, but also because of this, the map is easy to be affected by finite precision, resulting in dynamic degradation, at low precision, the sequence generated by this map not only enters a period quickly, but also has a shorter period. Thus, taking 1D Logistic map as an example, we proposed a method to suppress the dynamic degradation of digital chaotic systems by using parameter variables and state variables to influence each other, and using sine function as feedback function to destroy the state space. The simulation results show that the improved logistic mapping with the proposed method has better randomness and higher complexity than the original logistic mapping. To prove the practicability and applicability of the improved chaotic map, we design a new image encryption algorithm, which is suitable for both color image and grayscale image. The numerical results indicate that the proposed algorithm has high encryption efficiency, good resistance to various attacks and certain competitiveness with other encryption algorithms.