Research On Encryption Scheme Based On Generalized M-J Set And Complex Lorenz System

With the rapid development of information technology and computers,information security is receiving more and more attention.Information security is not only related to personal privacy,but also to the security and development of the whole country.Chaotic systems have been the focus of research in the field of information security because of their sensitivity to initial values,ergodicity and other characteristics.The block cipher and stream cipher encryption system designed by chaotic system and the secret communication scheme based on chaotic synchronization are the two main resear-ch subjects of chaotic cryptography.Fractal and chaos are both important components of nonlinear theory.And as a typical fractal set,the iterative dynamic system of the generalized M-J(Mandelbrot-Julia)set has excellent chaotic characteristics.This thesis mainly proposes an image encryption scheme based on generalized M-J set and one-time keys,and studies the design and application of complex Lorenz system circuit and anti-synchronization control circuit.With the rapid development of quantum computers,the encryption schemes of low key space face a huge security threat.And the chaotic image encryption scheme takes the initial value of the system as the key,and the key space is often immutable,which provides a way for the cracker to perform exhaustive attacks.To solve the above problems,an image encryption scheme based on one-time keys and generalized M-J set is proposed.The scheme has a large key space(23250)far beyond most existing encryption schemes.and can choose key parameters arbitrarily according to need.In order to weaken the difficulty of key transmission and key management caused by large key space and improve the security of encryption scheme,this scheme uses the true random environmental noise signal and SHA-512 to obtain the one-time parameters of generalized M-J set.In order to achieve efficient encryption,this scheme uses multi-round XOR algorithm to diffuse plaintext images.Various security tests show that the scheme has high security,and can resist differential attack,chosen plaintext attack.known plaintext attack and other attacks.Finally,the randomness of real part and imaginary part sequences of generalized M-J set are tested by NIST randomness testing software.On the other hand,the feasibility of applying generalized M-J sets to image encryption is verified.Due to the existence of complex variables,complex chaotic systems can improve the ability of information transmission and the complexity of information encryption.Therefore,complex sy'stems have important application value in chaotic secure communication.Over the years,people have made a lot of research results on the theoretical and synchronous control of complex chaotic systems.The secret communication scheme using MATLAB numerical simulation has also been mentioned,but the corresponding circuit implementation research work is lacking,while the synchronous circuit Implementation is the core technology for simulating a secure communications solution.In this thesis,the circuit implementation method of the complex Lorenz system is proposed.The anti-synchronization controller and anti-synchronization control circuit of the complex Lorenz system are designed according to the anti-synchronization control theory.On the basis of anti-synchronization circuit,a secure communication scheme is designed by combining chaotic masking technology.By comparing and analyzing the simulation results of MATLAB numerical simulation and Multisim circuit,the correctness of the design of complex Lorenz system circuit and synchronous circuit is proved.The research of complex Lorenz circuit and synchronous circuit has important practical significance for the theory and application of complex chaotic system.