Image Encryption Based On Discrete Fractional Order Chaotic System

With the rapid development of Internet technology and the popularity of mobile phones,the security of image information has gradually become the focus of people’s attention.Chaotic system has the characteristics of initial value sensitivity,ergodicity and complex dynamic behavior,which is widely used to improve the security of image encryption algorithm.Discrete fractional-order chaotic system not only has the advantages of discrete integer order chaotic system and continuous fractional-order chaotic system,but also has a wider range of chaotic behavior parameters and more complex dynamic behavior,which is more suitable for image encryption.This dissertations studies the dynamic behavior of several discrete fractional-order chaotic systems and their applications in image encryption,and obtains the following results:A novel three-dimensional discrete fractional-order(FO)Hopfield neural networks(FODHNN)in the left Caputo discrete delta’s sense is proposed.The chaotic behavior of the neural network is studied by numerical methods such as phase diagram,bifurcation diagram and Lyapunov exponent.Based on the stability theorem of discrete fractional-order linear system,a control law is designed to realize the synchronization of this kind of neural network system.Then,an image encryption algorithm based on the chaotic neural network is proposed,and various security analyses are performed.The indicators are compared with the encryption algorithm based on the integer order chaotic system.The results show that the image encryption algorithm based on this kind of discrete chaotic neural network has higher security performance.A novel color image encryption algorithm based on DNA and discrete fractional-order chaotic system is proposed.A new type of discrete fractional Hopfield neural network model was established as a pseudo-random number generator for encryption algorithm.The chaotic dynamic behavior of the neural network is analyzed by phase diagram,bifurcation diagram and 0-1 test.The initial value of the neural network is calculated by the five-digit key entered by the user and the hash value of the plain image obtained by the SHA-2 function,which ensures the algorithm has a large key space and improves the sensitivity of the plain image.A new 3D projection scrambling method is proposed,which can scramble the pixels in the three color channels of the color image.Experimental results and security analysis show that the algorithm has good security performance and can resist many typical attacks.A novel discrete fractional Henon map model is established.The dynamic behavior of the system is analyzed by means of phase diagrams,bifurcation diagrams,and 0-1 test.Based on the system,a double-color image encryption algorithm is designed.A rubik’s cube variation method is proposed to encrypt two images simultaneously in one encryption process.By distributing the image information evenly in two cipher images,the algorithm can better resist the shearing attack.In addition to fractional order and discrete distance,system parameters are introduced as the key of the algorithm,which greatly expands the key space.To further improve the security performance,the Cat transform based on discrete fractional Logistic map is used to scramble the pixel positions in each signal channel.Simulation experiments and security analysis prove that the encryption algorithm has good performance and can meet the encryption requirements in most cases.