Research On Image Encryption Scheme Based On Wide-parameter-range Memristive Chaotic Systems

Thanks to the escalating mobile communication technology and computer network technology,vivid and visual digital images are gradually replacing words as the most popular,universal and convenient information carrier.Images play a significant role in the fields of political,economic,military,cultural and social life.However,the security of image is also becoming more and more prominent,so the research on image encryption is very critical.Among the numerous image encryption schemes,chaotic image encryption is an important branch.The reason is that the ergodicity,initial value sensitivity and long-term unpredictability of chaotic systems make the resulting sequences sufficiently meet the security requirements of big data volume information encryption.It has been found that memristor-based chaotic systems possess not only the excellent properties of ordinary chaotic systems,but also richer dynamical behaviors.As a result,the search for memristive chaotic systems suitable for cryptography has become a popular topic.This thesis focuses on both the chaotic system used to generate the key stream and the specific encryption algorithm to design a new memristive chaotic system with a more secure image encryption technology solution.The main work of the thesis includes the following.Firstly,to address the problem of small parameter space and unstable chaotic states of chaotic systems commonly used in image encryption,two wide parameter range memristive chaotic systems with different properties are designed and their typical dynamical behaviours are analysed respectively.The first chaotic system is characterized by an increasing maximum Lyapunov exponent with increasing parameters and hyperchaotic in some intervals.The second chaotic system has an ultra-wide parameter range of over 10~6 and can generate three different chaotic attractors.Then,the sequences generated by the two new memristive chaotic systems are tested by NIST randomness tests to verify the practicality of chaotic random sequences.Secondly,an image encryption scheme for multiple image morphing is proposed in association with the proposed memristive chaotic system with increasing Lyapunov exponential curve.In this scheme,the generation of the keystream is related to the plain image so that changes in the pixels of the plain image affect each encryption step.The values of the pixels are also changed by operations based on orthogonal Latin cubes and bit-level cyclic shifts.The advantage of this approach is that it is not limited by the size or type of plain image,and is highly universal and resistant to various attacks.Finally,an image encryption method based on chaotic-Brownian-motion permutation is designed by applying the proposed memristive chaotic system with an ultra-wide parameter range.The algorithm implements external key secrecy by the lightweight Grain-128a algorithm and updates the initial values of the chaotic system together with the plaintext information.The Brownian motion matrix obtained from the chaotic cipher stream as a direction control parameter and the multiplicative diffusion on the polynomial finite field GF(2~8)are also used in the encryption process to further improve the robustness of the encryption algorithm.Through simulation and experimentation,the cryptography process accomplished by this method has better encryption results and higher security.