Dynamic Analysis Of Digitized Chaotic System And Algorithm Design Of Pseudorandom Sequence Generation

Pseudorandom sequences are widely used in communication,cryptography and computer fields.The nonlinearity,initial value sensitivity,aperiodicity,ergodicity and noise like properties of chaotic system provide a solid theoretical basis for the design of chaotic pseudorandom sequence generation algorithm.However,most of the chaotic systems are constructed over the real number field.When the chaotic system over the real number field is realized by digital circuit,the chaotic system will eventually collapse to the finite field,and show the degradation behavior of the chaotic system dynamics,which makes the chaotic pseudorandom sequence no longer have the aperiodicity,ergodicity and initial value sensitivity.For the degenerated chaotic system over the finite field,that is,the digitized chaotic system,will generate sequences with short period,it has a certain security risk to directly apply the digitized chaotic system in the field of digital information,and hinders the widespread application of the chaotic digital hardware encryption.Therefore,it is of great significance to analyze the dynamic behavior of digitized chaos and construct a good digitized chaotic pseudorandom sequence by using the digitized chaotic system over the finite field.Starting from the analysis of the dynamic behavior of digitized chaotic system and focusing on the complex periodic behavior of digitized chaotic system,this paper systematically studies the principle and structure of several algorithms for generating digitized chaotic pseudorandom sequences over the finite field by constructing chaotic system with the same structure,introducing additional parameters and optimizing Boolean function.The main work of this paper is as follows:(1)According to the classical definition of chaos,the chaotic system over the real number field,the chaotic system over the symbol space and the degenerated chaotic system over the finite field are strictly distinguished.According to the theory of state transition graph on finite state machine,the theoretical model of digitized chaotic system based on floating point and fixed point representation is established.Based on the analysis of the reasons for the formation of periodic orbits in degenerated chaotic systems over the finite fields,two inherent limitations of digitized chaotic systems are obtained,that is,short period behavior and multiple period behavior.(2)In order to overcome the short period behavior and increase the period,the cascading method is used to construct the digitized chaotic pseudorandom sequence.According to the period three theorem,a general method of designing one-dimensional polynomial chaotic system is proposed.By calculating the coefficient variable,a large number of chaotic systems with the same structure can be constructed.Furthermore,a generation algorithm of reconfigurable one-dimensional cascaded digitized chaotic pseudorandom sequence is designed by using the same structure.After reconfiguration,the number of digitized chaotic systems needed by one-dimensional cascaded digitized chaotic pseudorandom sequence generation algorithm is significantly reduced,and the generated sequences have good randomness.Based on Jacobi matrix method,a general method for designing a class of high-dimensional polynomial chaotic systems is proposed.By calculating the coefficient variable matrix,a large number of high-dimensional chaotic systems with the same structure can be constructed,and a generation algorithm of reconfigurable high-dimensional cascaded digitized chaotic pseudorandom sequences is designed by using the same structure.After reconfiguration,the number of digitized chaotic systems needed by high-dimensional cascaded digitized chaotic pseudorandom generation algorithm is significantly reduced,and the generated sequences have good randomness.(3)In order to overcome the short period behavior and increase the period,the perturbation method is used to construct the digitized chaotic pseudorandom sequence.A method of introducing additional parameters is proposed to make the digitized Logistic chaotic map always show chaotic behavior.By introducing the disturbance source m sequence,a algorithm of digitized chaotic pseudorandom sequence generation is designed,which combines the m sequence and the digitized Logistic chaotic map.When the precision of the digital system is N,the period and nonlinear complexity of the sequence generated by the generation algorithm of the digitized Logistic chaotic map disturbed by the m sequence are greatly improved,and it shows good balance and randomness.(4)In order to overcome the short period behavior and make the period reach the upper limit of the theoretical maximum,the Boolean function optimization method is used to construct the digitized chaotic pseudorandom sequence.According to the Boolean logic relation of classical digital circuit,the Boolean function characteristic of digitized chaotic system is analyzed in detail.By introducing the control term to optimize the Boolean function of the digitized chaotic system,the period of the digitized chaotic pseudorandom sequence is greatly improved,the short period orbit and the multiple period orbit of the digitized chaotic system are eliminated,and the output sequence of the digitized chaotic system reaches the upper limit of the theoretical maximum value.In addition,taking the digitized Logistic chaotic map as an example,the Boolean function is optimized.The algorithm of pseudorandom sequence generation based on the optimized digitized Logistic chaotic map not only achieves the minimum of resource consumption required by algorithm structure,but also reaches the upper limit of the theoretical maximum period of the sequence.