Analysis Of The Periodicity Of Digital Chaotic Systems And Application Research Of Resistance Methods

Chaos theory is an important branch of nonlinear science,which has some desirable characteristics,such as intrinsic randomness,positive Lyapunov exponent,sensitivity to initial values and boundedness,etc.These characteristics of chaos are closely related to the basic concepts of confusion and diffusion in cryptography,which makes chaotic systems widely used in chaotic secure communication.However,when a chaotic system is implemented in a hardware device with finite calculation precision,its dynamic characteristics will be degraded to varying degrees due to the different calculation precision of the hardware device.The dynamic degradation of digital chaos will threaten the security of chaotic secure communication.Therefore,we conduct an in-depth analysis of the periodicity of digital chaotic systems to search the resistance method of dynamical degradation of digital chaos.These related studies can promote the application of chaos in engineering practice,and its specific work is as follows:First of all,to effectively analyze the degree of degradation of digital chaotic maps,we designed a periodic orbit search algorithm that is based on a tree structure.This algorithm can calculate the maximal transient length,fixed points and periodic limit cycles of digital chaotic maps in finite-precision domains quickly and accurately.Furthermore,in order to test the versatility and effectiveness of our proposed algorithm,the periodic distribution and security of several typical digital chaotic maps are analyzed in detail.Numerical simulation results show that digital chaotic maps have hidden safety hazards.Secondly,when chaotic systems are applied to chaotic cryptography,chaotic real-valued sequences generally need to be converted into binary sequences for the sake of encrypting data.However,some chaotic binary sequences that seem to be random as a whole may exhibit the phenomenon of weakening randomness in a local range.To this end,we proposed a general algorithm with the purpose of detecting the periodicities of chaotic binary sequences.This algorithm can accurately locate the local periodic phenomenon contained in the chaotic binary sequence,thereby evaluating the randomness of the chaotic binary sequence from a new perspective.Thirdly,according to the special law presented by the state-mapping graph of the digital chaos,that is,no matter what the initial value of the digital chaotic system is,its chaotic trajectories will eventually converge to a finite number of fixed points and periodic cycles after several iterative operations.This is also the fundamental cause of the dynamical degradation of digital chaos.In view of this,an effective method based on stochastic jumps of chaotic orbits is proposed to counteract the performance degradation of digital chaos.The corresponding numerical simulation results show that this method can effectively improve the cycle length,complexity and randomness of discrete chaotic sequences.Finally,the improved digital chaotic map is used to construct a pseudo-random sequence generator with good performance,and a chaotic cipher algorithm based on ciphertext feedback is proposed.This algorithm has the advantages of simple structure,high security and low hardware consumption.Furthermore,aiming at the security problems existing in home webcams,we designed a video security transmission system based on the embedded hardware platform to ensure the secure transmission of H.264 video streams in wide-area network environments.The design of this system also provides a feasible scheme for the application of chaos theory in practical engineering.