Design And Implementation Of Image Encryption Algorithm Based On Tri-valued Memristor Hyperchaotic System

Chaos is a pseudorandom phenomenon generated in nonlinear systems,and its rich dynamic characteristics have important research value.Chaos theory has been widely used in the fields of physics,cryptography,communication science and economics.Among them,the research of image encryption algorithm based on chaotic systems belongs to the interdisciplinary research of chaos theory and cryptography,and has become a current research hotspot.Memristor is a circuit element with nonlinear characteristics,which can be used to construct chaotic circuits.The chaotic system constructed based on the memristor is conducive to generating special chaotic signals and exhibits complex dynamic characteristics,such as hyper-chaotic characteristics,hidden attractors and coexisting attractors.Applying this special chaotic signal to the design of an image encryption algorithm can reflect certain advantages and help improve the security performance of the algorithm.Therefore,the study of hyper-chaotic systems based on tri-valued memristors is of great significance in expanding system dynamics and improving information security.The research content of this thesis includes the following:(1)The mathematical model and circuit characteristics of the tri-valued memristor are analyzed,and the influence of the input signal on the multiple pinch-off points of the memristor is studied.The circuit characteristics of the model are verified by building an equivalent circuit.(2)The tri-valued memristor model is introduced into the Lü system to construct a new memristive hyper-chaotic system,and the dynamic characteristics of the system are analyzed.Analysis shows that the system has no equilibrium point,so it has the characteristics of hidden attractors.In further research,the initial sensitivity and coexistence attractor characteristics of the system are analyzed,and compared with binary-valued memristor-based chaotic system,the results show that the new system has more rich dynamic characteristics,such as hyper-chaos and coexistence attractor.In addition,an equivalent circuit is built to realize the system,which verifies the effectiveness of the system.Finally,a pseudorandom number generator(PRNG)is designed based on the system,and pseudorandom numbers with high randomness were generated.(3)Based on the tri-valued memristor hyper-chaotic system,a new image encryption algorithm is proposed.The encryption process is based on the structure of permutation-diffusion,and the transmission of secret keys is realized through chaotic synchronization technology.First,the initial values containing the plain image information is obtained by the secure hash algorithm(SHA-512).Second,the chaotic sequence is used to generate the permutation sequence with the structure of the Hash table,and the pixel bit-level permutation is combined to achieve the double permutation operation.Third,the elements in the chaotic sequence are sorted through the Hilbert curve,and the diffusion operation is completed by combining the cipher image feedback mechanism.Finally,the effectiveness and safety of the algorithm are analyzed.(4)Based on the embedded linux system and software programming technology,the hyper-chaotic image encryption software is implemented on the platform terminal,and the user interface is designed to realize human-computer interaction.The software can read local image files for encryption and decryption operations,and can transfer files over the network.