Research On Image Encryption Algorithm Based On Chaotic Sequence

As a major branch of nonlinear dynamics,chaos reveals the unity of certainty,randomness,and unpredictability that widely exist in nature and society.The study of chaotic system dynamics helps us to understand its nature more deeply and then to control and apply it.Especially,the high sensitivity of chaotic sequences to initial values and good pseudo-randomness provide new ideas for digital image encryption.The construction of chaotic systems and chaotic image encryption are independent and closely related research topics,which are also the current hot issues in the field of chaos research,with relatively important theoretical significance and practical application value.In this paper,from the perspective of nonlinear dynamics,the mechanism and dynamics of three types of chaotic systems are explored,and their applications in digital image encryption are further investigated.The main research contents are as follows:1.To investigate the changes of neuronal firing patterns affected by electromagnetic fields,a new five-dimensional non-autonomous HR neuron model is established by introducing magnetic flux variables and electric field variables on a three-dimensional Hindmarsh-Rose（HR）neuron model.Firstly,the equilibrium point distribution of the model is analyzed based on Matcont software,and it is found that subcritical Hopf bifurcation and coexisting discharge patterns exist in the model.Secondly,simulations are performed by one-parameter bifurcation,peak-to-peak interval（ISI）bifurcation and maximum Lyapunov exponent.The experimental results show that the model exhibits a period-adding bifurcation structure with chaos and mixed mode discharge.The superior dynamic characteristics and rich discharge behavior make the model more suitable for image encryption applications.Finally,a grayscale image encryption scheme is designed by combining the compressive sensing theory,which is mainly composed of five parts:sparse,compressive calculation,forward diffusion,rank scrambling and backward diffusion.The security analysis results show that the designed encryption scheme not only has excellent compressive performance and high security,but also has fast processing speed.That is to say the algorithm can effectively reduce the cost of data transmission,improve the encryption efficiency,and has the potential to be applied in the field of real time encryption.It is worth mentioning that the influence of different dimensional compression methods on the encryption and reconstruction effects is analyzed for the first time.The research results in this chapter not only provide some ideas to improve the neuron model,reveal the influence of electromagnetic field on biological nervous system and explore the pathogenic mechanism of some neurological diseases,but also provide theoretical guidance and experimental basis for the practical application of digital image encryption.2.Compared with integer order chaotic systems,fractional order chaotic systems can reflect natural phenomena more accurately and are more suitable for chaotic cryptosystems.In order to explore the application of fractional order chaotic systems in cryptography,a novel fractional order hyperchaotic system is constructed and implemented on DSP platform.More progressively,based on Adomian decomposition method,the dynamic behavior is studied by phase diagram,bifurcation diagram,Lyapunov exponent spectrum and spectral entropy（SE）complexity.It is found that each parameter and order have a large range of intervals that can keep the system in a hyperchaotic state.Therefore,the hyperchaotic sequences generated by the constructed fractional order hyperchaotic system are sufficiently random and well suited for applications in secure communications.In addition,a new color image encryption scheme is designed based on the fractional order hyperchaotic system and DNA coding.Firstly,the pixel positions of the plaintext image are scrambled using the improved Arnold algorithm,then the second dislocation is performed based on the column cyclic shift method,and finally pixel values are changed by DNA sequence operations.The security analysis results indicate that the designed encryption algorithm can not only encrypt images effectively,but also has high security and can resist various common attacks.3.Compared with the conventional multi-scroll attractor,the multi-wing butterfly chaotic attractor is easier to design and implement through analog circuitry and thus has greater potential for applications.In this chapter,a new four-wing chaotic system is designed and its dynamic behaviors are analyzed in terms of phase diagram,bifurcation diagram,Lyapunov exponent spectrum,and C₀ structural complexity.It is revealed that each parameter has a large chaotic interval and the generated sequences have sufficient randomness to be applied to image encryption.Then,the circuit model of the constructed four-wing chaotic system is built with basic operational amplifiers and other devices,and the accuracy of the circuit implementation is verified using Multisim software.Finally,a color image compression encryption scheme is designed based on the theory of compressive sensing and DNA dynamic coding.The algorithm is mainly composed of five parts:sparse,compressive calculation,3D projection scrambling,DNA diffusion and plaintext association confusion.The security analysis results suggest that the designed encryption scheme not only has excellent compression performance and high security,but also has no limitation on the size of the test image.