Analysis And Application Of Chaotic Systems In Digital Domain

With the fast development of the internet and the advent of 5G era,more and more people are keen on social media to post various photos to record their life and work.Therefore,people can get all kinds of information more easily,among which,the security of multimedia data(image,audio,video,etc.)has aroused people's wide attention,especially the image security.The large amount of image data and the strong correlation between adjacent pixels make the traditional text encryption algorithm unable to meet the needs of image security.In order to solve this problem,a large number of image privacy protection schemes based on digital chaotic system have been proposed since 1980 s.There is a natural connection between chaos system and traditional cryptography.The dynamic properties of chaotic system correspond to the security characteristics of cryptography system.The study on dynamics of digital chaotic system is the guarantee for the wide application of secure communication system.However,most of the chaotic cipher designers have not seriously consider to the phenomenon that the related dynamic properties of chaotic systems will degrade to different degrees under the finite precision digital device.One task of this dissertation is to emphasize this issue and to give some initial investigations.In this dissertation,the dynamic properties of digital chaotic systems are studied by using state-mapping networks.The related studies of digital chaotic systems mainly include two-dimensional Baker map,coupled-chaotic system(involving Logistic map,Sine map and Tent map).Meanwhile,a classical image privacy protection algorithm based on chaotic system is analyzed and improved.The main work of this dissertation is structured as follows.1.The dynamic properties of Baker map in digital computer are studied,and the relationship between the corresponding nodes of state-mapping network(SMN)of onedimensional chaotic map is extended to two-dimensional.The basic properties of statemapping network(SMN)of two-dimensional continuous Baker map in fixed point domain and the high-dimensional extension of Baker map are studied.At the same time,we found that the state-mapping network(SMN)of two-dimensional discrete Baker map is a circle structure,and the phenomenon is analyzed.2.The analysis object is extended to the coupled-chaotic system(CCS),the degradation process of SMN in digital domain is analyzed by the relation between SMN and operation precision.The bifurcation characteristics of the coupled Logistic-Sine system(CLS)are analyzed in detail the definition of the CCS is introduced in detail.Furthermore,the properties of the state-mapping network of the CCS with different precision in same quantization strategies are studied,as well as the properties of the different quantization strategies with the same precision.3.An image encryption algorithm based on DNA coding and coupled-chaotic system(MPPS)is analyzed and improved.Based on the characteristics of DNA coding,a chosen-plaintext attack is carried out to crack the algorithm,and an algorithm to obtain the equivalent key of MPPS is designed.In addition,we improve the algorithm to adapt the practicability of the algorithm.