The Application In Image Encryption Of The Memristors Chaotic Circuit

Chaotic signal is considered to has very high application value in the field of secure communications, due to the the characteristics of high complexity, unpredictability, extreme dependence on initial value, and easy to implement,etc. The chaotic sequence built by chaotic signal generated by chaos system and corresponding encoding has become the focus of one of the digital image encryption methods. And the memristor which was first put forward by Chua has become a popular device of constructing chaotic circuit system because of its unique nonlinear characteristic.In this paper, simulation experiments of classical chaotic system for image encryption was made to verify that the high-dimensional chaos systems are more privacy and can cause a much more greater damage to the distribution characteristics of original image pixels than the low dimensional chaotic systems.According to the general polynomial format of memristor, a relatively simple charge-controlled memristor model is proposed in this paper, whose relation between memristance M and charge q can be described by a quadratic nonlinearity curve.The simulation experiments verify that the charge-controlled memristor has the core traits of memristor: it will show a similar "8" glyph of volt-ampere characteristic curve in cycle bipolar signal, and its volt-ampere characteristic curve will change with parameter itself and amplitude, frequency, phase of the cycle bipolar signal. Then derive a four dimensional continuous charge-controlled memristor-based chaotic circuits from Chua’s oscillators by replacing Chua’s diodes with this charge-controlled memristor model.And it turns out some dynamical characteristics including portrait diagrams, time domain wavetorms,Lyapunov exponent and dimension. Those dynamical characteristics are all able to verify that the charge-controlled memristor-based chaotic circuits will be in a chaotic state driven by the initial value and some certain parameter configurations. Varying initial value and proving the dynamical track of this chaotic system will make a huge difference when a tiny change happen to initial state. Further more, the stable condition eliminated the influence of zero characteristic root of this charge-controlled memristor chaotic system in equilibrium points is judged by Routh criterion.And then make a digital image encryption simulation experiment for the four dimensional continuous charge-controlled memristor-based chaotic circuits in this paper. Setting control parameters and the initial value of charge-controlled memristor-based chaotic system, calculating the trajectory of the chaotic system, setting up reasonable interval, drawing a discrete sample from the four dimensional continuous chaotic system and discrete sample, putting forward a coding way to construct a discrete chaotic sequence which is a mixture of the chaotic systems’ tracks in four dimensions, using the gray encryption algorithm for image encryption, getting the ideal effect of encryption. Finally analysis from the following several aspects: gray histogram, key space, key sensitivity, noise interference and shear attack. And summarize that the charge-controlled memristor-based chaotic system can completely destroy the distribution characteristics of original image pixels and has a strong confidentiality when used for digital image encryption; The size of key space can resist brute force attack; the encrypted image can’t be decrypt when key appears very tiny difference; it has good robustness, and can withstand a certain degree of noise interference and shear attack.