Entanglement Dynamics Of Discrete Quantum Random Walk And Its Application In Image Encryption

Computer technology's continuous development,information and network are involved in all aspects of our lives.It is becoming more and more important to ensure the security of information.Traditional cryptographic algorithms are mostly based on the complexity of mathematical computation,and can not achieve unconditional security,the information carrier of quantum cryptosystem is quantum state,and the key is transmitted between legitimate users through quantum channels.The security of quantum cryptosystems is guaranteed by quantum mechanics principles,which has nothing to do with the computational power of attackers.Quantum random walk has been used as an effective tool to solve various problems,such as distinguishing different elements,triangle search,data clustering and so on.Quantum random walk(QRW)has the dual advantages of high nonlinearity and parallel computing.Therefore,it is very meaningful to study the QRW model and apply it to image encryption.This paper mainly includes three parts.The first part is to study the online one-dimensional single-particle discrete random walks(QRWs)model and carry out entanglement dynamics analysis.The second part is the simulation experiment of constructing Pseudorandom Number Generators(PRNGs)based on QRWs and performing safety analysis.The third part is to apply the PRNG to grayscale image and color image encryption.The details are as follows:(1)An online one-dimensional single-particle discrete QRWs model is constructed.We study that a pedestrian's motion is alternately controlled by two initially independent coins.We observed a complex inter-coin correlation in quantum walks.Specifically,we study the correlation between two coins by locating the pedestrians,and analyze the classical correlation between the two coins from the aspects of classical mutual information,quantum mutual information and measurement-induced interference.Correlation and quantum correlation.(2)An online one-dimensional single-particle discrete QRWs pseudo-random number generator is constructed.And the performance analysis of the pseudo-random generator,such as statistical complexity measurement,recursive analysis,randomness test,experimental results show that the sequence generated by this PRNG has very good random characteristics.(3)Using the PRNG in(2)as the key generator,a gray image encryption scheme based on the QRWs model in(1)is proposed and simulated.It analyzes from the aspects of correlation,information entropy,key space,sensitivity,and attack test.In addition,compared with the existing image encryption scheme,the results show that the proposed grayscale image encryption scheme has better security.(4)Extending the grayscale image encryption scheme of(3)into color image encryption.Experiments show that the color image encryption scheme based on discrete QRWs is superior to the existing image encryption scheme in terms of correlation,information entropy and sensitivity.