Research On The Memcapacitor Chaotic System And Its Application In The Mail Encryption

As early as 1970 s,memristor was proposed,but the authenticity of memristor was proved by HP laboratory in 2008.Memristor is a nonlinear element with memory function,and it has broad application prospects in the fields of non volatile impedance memory?RRAM?and neural network.The generalized memristor,memcapacitor and meminductor were proposed in 2009,and the research of memcapacitor has greatly attracted attention.At present,the research on the characteristics of memcapacitor in nonlinear circuit is still dependent on the mathematical models and equivalent circuits.In this paper,the mathematical models and equivalent circuits of memcapacitor are studied and applied to a new chaotic oscillator which based on charge-controlled memcapacitor.The dynamical characteristics affected by system parameters and initial values for the charge-controlled memcapacitor-based chaotic system are analyzed.The simulation circuit is designed for the reduced order system,and a kind of chaotic attractors is obtained.Finally,the chaotic-DES encryption algorithm is designed by replacing the secret key sequence of DES with chaotic sequence of memcapacitor,and applied to the e-mail security software.The contents of the study include the following aspects:?1?The mathematical definitions of the memristor,memcapacitor and meminductor,and the port characteristics of HP laboratory TiO₂ memristor are analyzed.Then the cubic smooth curve model of charge-controlled memcapacitor and the quadratic smooth curve model of voltage-controlled memcapacitor are given,and the corresponding equivalent circuits are designed to verify the characteristics of the hysteresis loop.?2?The classical one dimensional discrete Logistic mapping and continuous Lorenz chaotic system are introduced,and the analysis methods of chaotic system are given.A new three dimensional chaotic system is proposed.In order to research the dynamic characteristics of new chaotic system,the equilibrium point,bifurcation diagram and Lyapunov spectrum are studied.The state distribution of new system is described by dynamic map.The results show that the existence of coexisting attractors is the most prominent feature of new chaotic system.System trajectories converge to different attractors under different variable initial values combination when system parameters are fixed.?3?An autonomous chaotic oscillation system is constructed based on the charge-controlled memcapacitor,and the dynamic characteristics of the system are analyzed by dynamic map,bifurcation diagram and Lyapunov exponent with varying parameters.In addition,bifurcation diagram and Lyapunov exponent spectrum of the varying initial values are analyzed when system parameters are fixed.We found that the chaotic system has the characteristic of coexistence oscillation,and there exist many kinds of coexisting attractors.The four order systems are integrated to get the reduced order system,and the type of coexisting attractors of reduced order system is less,which means the coexistence oscillation of reduced order system is weakened.The realization circuit of three order chaotic system is designed by actual device,and a kind of chaotic attractors is obtained.?4?In order to study the application value of chaotic system in the field of communication,this paper analyzes the relation between chaos and cryptography,and introduces the traditional DES encryption algorithm.The chaotic sequence of the memcapacitor has passed all the test indexes of NIST,which indicates that the chaotic signal of the memcapacitor has good randomness.The chaotic-DES encryption algorithm is designed by replacing the secret key sequence of DES with chaotic sequence of memcapacitor.E-mail security software is designed by this encryption algorithm.