Research On Theory Of Non-degenerate Chaotic System And Applications Of Stream Cipher

The theoretical research and implementation of chaotic stream cipher are in line with the national key strategic requirement of "Focus on research and development of new cryptography".Using nonlinear driving sources or iterations to directly and rapidly generate nonlinear sequences is widely concerned and favored in the cryptography community.Chaos is a class of inherent randomness in deterministic nonlinear systems.There is no doubt that taking chaotic systems as new driving components has many advantages,such as high safety in theory and outstanding hardware implementation efficiency.This dissertation focuses on the bottleneck frontier problem "dynamical degradation of chaotic systems realized on finite-state automata",which troubles the field of chaotic cryptography community.The main work is to make a thorough study of systematic theory of chaotic degradation,construction of non-degenerate digital chaos,secure synchronization scheme and application of stream cipher.Nearly all the existing methods to solve dynamical degradation of chaotic systems are aimed at improving performance of system to resist degradation.These methods lack of systematic analysis theory.To solve this problem,this dissertation proposes a unified mechanism for designing and analyzing schemes of counteracting dynamical degradation based on symbolic dynamics and topological theory.The mechanism provides a theoretical explanation for these schemes from the perspective of space extension.Additionally,sufficient conditions are given to judge if a scheme fits our mechanism and can truly counteract the dynamical degradation.Based on the mechanism,a scheme which can recover ideal characteristics of digital chaotic systems is proposed.Focusing on the research gap of directly constructing non-degenerate digital chaos which can be strictly proved in theory and realized effectively on finite-state automata,this dissertation proposes an analog-digital hybrid model.In the model,the analog chaotic system is adopted to control any digital system.Based on the model,a general construction method of non-degenerate digital chaos is demonstrated.In theory,aiming at the limitation of classical symbolic dynamics,the concept and method of generalized symbolic dynamics are proposed.Further the non-degenerate digital chaotic system in the analog-digital hybrid model is proved to be chaotic in strict mathematical sense.In practice,the circuit prototype of the hybrid model is completed on the platform of field programmable analogy array(FPAA)and field programmable gate array(FPGA).Analog chaotic system is the critical component to construct non-degenerate digital chaos.However,analog systems are usually unstable.In order to successfully achieve processes of encryption and decryption,synchronization should be performed.Focusing on the problem that transmission of synchronization signals in the channel is not only susceptible to noise,but also leaks characteristic information of system,this dissertation proposes a method of utilizing the local constructed non-degenerate digital chaotic system to impulsively control the analog chaotic system and achieve synchronization.Then an analog-digital hybrid model with bidirectional control is built.Theoretical analysis and experimental results indicate that the model successfully constructs non-degenerate digital chaos and simultaneously achieve safe synchronization without synchronization signals transmitted in the channel.In addition,this dissertation discovers a previously unknown chaotic attractor under such mutual control.In the end,to meet the need for highly secure stream cipher and requirement for secure and controllable chaotic driving source,a high-dimensional digital chaotic system based on time-delay coupling is firstly proposed.Then,a complicated analog-digital hybrid chaotic system based on parameter-varying mechanism is proposed by applying the analog-digital hybrid model to the high-dimensional digital chaotic system.On the basis,a highly secure non-degenerate chaotic stream cipher is proposed.Compared with other stream ciphers,the cryptosystem has the unique advantage of immunity to chaos degradation,and ability to resist various chaos-based attacks and cryptanalytic attacks.