Research On The Application Of Discrete Chaotic Systems In Image Encryption

With the advantages of initial value sensitivity,unpredictability and fast iteration,chaotic maps meet the current requirements in the field of image encryption.How to design more secure and faster image encryption algorithms has become a hot research topic in recent years.In order to avoid the degradation problem of randomness of chaotic sequences and to improve the efficiency of image encryption algorithms,it is necessary to design more complex chaotic maps.In this paper,the hyperchaotic maps are designed,the corresponding image encryption algorithms are designed,and the performance of the encryption algorithms is analyzed.(1)A two-dimensional Cosine Logistic ICMIC hyperchaotic Map(2D-CLIM)is proposed based on the ICMIC map and Logistic map,and an image encryption algorithm based on hyperchaotic map is designed.The plaintext image is subjected t o dynamic Josephus permutation and DNA diffusion in the frequency domain to finally form the ciphertext image.The simulation results and performance analysis show that the image information is effectively hidden and the algorithm is resistant to known/chosen plaintext attacks.The designed chaotic map has a small chaotic range,low complexity,and the encryption process is lossy,which limits its applicability.(2)A new two-dimensional Logistic Cosine Cascade hyperchaotic Map(2D-LCCM)and a three-dimensional Logistic Cosine Cascade hyperchaotic Map(3D-LCCM)are designed,it is found that the chaotic range is larger and the complexity is better.An DNA image encryption algorithm based on a double chaotic maps is designed,which overcomes the limitation of lossy encryption.Finally,after performance analysis,it is shown that the algorithm has good effects on image encryption,reflected in terms of efficiency and anti-interference performance.(3)To further improve the efficiency and security of the algorithm,a new four-dimensional discrete Hopfield neural network system is constructed based on the neuron structure framework.The map has high complexity,large parameter range,and good pseudo-randomness.Based on the four-dimensional discrete hyper-chaotic system,a Chaotic Magic Random Scramble(CMRS)and Pixel-dependent bit-plane Chaotic random Diffusion(PbCrD)are designed.The algorithm can not only resist known plaintext attacks,but also adopt multiple diffusion rules related to pixels to improve the flexibility and security of the algorithm.The hyperchaotic maps are used and the corresponding encryption algorithm is designed for testing and comparative analysis.The results show that the proposed image encryption scheme based on a hyperchaotic maps gradually improves encryption efficiency and security.At the same time,the algorithms have a good security and strong robustness,which can meet most encryption needs.