Research On Improvement Of Algorithm Of Fractional Differential Equation And DNA Image Encryption

In the background of the big data era,the digital media information is transmitted through the network in large numbers,As the high-speed transmission of data information,the problem of data security have also attracted increasing attention.Compared with traditional text information,the digital image is more colorful and more vivid than traditional text information,so digital image has become one of the most common and important information carriers in today's society.If you want to transmit image information safely in a relatively open network platform environment,a complete and efficient image encryption system is inevitably needed to escort.The chaotic design based cryptosystem just satisfies this requirement.The fundamental reason why the chaotic system is used to design the cryptographic algorithm is its own unique sensitivity to initial conditions and control parameters,pseudo-randomness and ergodicity.From an application perspective,the dynamic system of fractional order model is very important for the practical application.How to design the efficient and accurate numerical analysis algorithm of fractional differential equation is widely concerned by scholars both at home and abroad.Based on variational iteration and DNA sequence operations,this paper designs an improved numerical algorithm for fractional differential equations and a new double-color image encryption algorithm,and analyzes the performance of the proposed algorithm.The main work and findings are as follows:1.An improved numerical algorithm for the fractional differential equations is proposed based on the variational iteration method.Using the improved numerical scheme,we investigate a new fractional-order hyperchaotic system,and find that hyperchaos does exist in the new fractional-order four-dimensional system with order less than 4.The lowest order we find to yield hyperchaos is 3.46 in this new fractional-order system.The existence of two positive Lyapunov exponents further verifies our results.Numerical results show that the proposed method has a faster speed and more accurate comparing with the traditional predictor-corrector algorithm.Finally,based on the stability theory of fractional order systems,a nonlinear controller is constructed by using pole configuration technology,which makes different fractional order hyperchaotic systems achieve synchronization.2.We propose a double color images encryption scheme based on Deoxyribonucleic Acid(DNA)sequence,chaotic system and block permutation.Mean Square Error(MSE)of the double images,LSS and 2D-LASM chaotic systems are firstly employed to generate the key streams.Then,divide the plain-images into equal blocks and scramble the blocks using the key streams.Next,encode the permuted images into the DNA matrices according to the DNA encoding rules and a DNA XOR operation is carried out on the DNA matrices.Finally,decode the encrypted the DNA matrices via the DNA decoding rules,and a pixel-level diffusion is further adopted to strengthen the security and sensitivity of the cryptosystem,and the resulting cipher-images are obtained.The experimental results show that the presented encryption algorithm has the advantages of large key space and high security.