Research On Improvement Of Dynamic Characteristics Of Digital Chaotic Map And Its Application In Image Encryption

Chaotic map is widely used in many different science fields due to its complex dynamical characteristics,such as high sensitivity to initial conditions,randomness,non-periodicity,long-term unpredictability,high complexity,etc.However,in practical applications,chaotic maps implemented on computers or other limited-precision devices will suffer dynamic degradation.Such a map is no longer regarded as chaotic map in a strict mathematical sense,because its various dynamic properties have been degraded,and it is no longer suitable for cryptographic design.This type of maps is generally called digital chaotic maps.To this end,this paper proposes two models to improve the dynamical characteristic of digital chaotic map,and based an improved digital chaotic map,a new image encryption algorithm is designed.First,this paper presents an improved model of digital chaotic maps based on hybrid control of perturbation and nonlinear feedback.The mutual perturbation between system parameters and state variables,coupled with nonlinear function feedback control,is used to improve the dynamic performance of digital chaotic map with limited precision.The simulation experiment results really prove that the improved map has better dynamical characteristic.From the perspective of whether the phase space structure changes,the improved model destroys the phase space structure of the original map,and prefers to design a new random source.Secondly,this paper proposes an improved model of digital chaotic map based on parameter perturbation.A fixed parameter perturbation model is originally proposed.Within the numerical range that meets the two constraints proposed by the model,a constant is randomly selected as the perturbation parameter,and parameters and state variables of the map are perturbed by two parameters when repetitive state variable occurs.However,for the improved model with fixed parameters,when the same repeated state variable appears for the second time,due to the same perturbation parameters,its orbit will jump to the same orbit which is jumped by the repeated state variable appeared for the first time,and then period problem would still occur.In order to solve this problem,introduce the current iteration steps to make the parameter vary,which further improves the dynamic performance of the digital chaotic map.The phase space structure before and after the improvement maintains the similarity.Finally,design a new chaotic image encryption algorithm.Use the chaotic sequence generated by any chaotic maps to randomly select some pixels in the plain image,obtaining the average value by a special computing method.And then use the average value and the average value of all pixels to affect the entire encryption algorithm,strengthening the correlation between the plaintext image and the entire encryption algorithm.The experimental results show that this algorithm has high security and is more competitive than other image encryption algorithms.