基于忆阻蔡氏电路的保密通信.doc

Secure Communication Based on Chua’s Circuits withMemristors#5101520253035WEN Shiping, ZENG Zhigang**(College of Automation, Huazhong University of Science and Technology)Abstract: In this paper, a new way is proposed to transmit and retrieve an information-bearing signalwhich is achieved by using the conventional synchronization of chaos and digital encryptionapproaches. A memristor-based Chua’s circuit is employed to generate a digital key. By consideringappropriate circuit configuration, the simulation results are presented.Key words: Secure communication; chaos; memristor0 IntroductionMemristor was postulated by Chua in 1971 [1] and realized by Williams’s Team in 2008 [2]. Itohand Chua derived several chaotic systems from Chua’s systems by replacing Chua’s diodes withmemristors characterized by a monotone-increasing and piecewise-linear nonlinearity [3].Memristor-based applications have attracted great attention recently [4, 5]. In this paper, a novelway via chaotic systems based on piecewise memristors is investigated to transmit and retrievedigital information signals by using the conventional synchronization of chaos and digitalencryption approaches. This signal along with the digital information signal is used to generate theencrypted signal .Then the encrypted signal is masked by one of the memristor-based chaoticsignals of the transmitter and is transmitted through the channel to the receiver as well as used todrive the chaotic transmitter system using the concept of self-modulation. At the receiver end,suitable feedback loop is constructed to unmask and then to recover the information signal. Bothmathematical analysis and simulation results are presented, which demonstrate the feasibility ofthe memristor in this application.1 Basic principleAt present, synchronizing chaotic systems and its potential usefulness in secure communicationshave attracted increasing interest [6, 7, 8]. Great efforts have been made to use chaotic systems toenhance certain features of communication and encryption systems. In this paper, a chaotic digitalkey is generated from one of the memristor-based chaotic signals, and a small amplitude versionof this signal along with the digital information signal is added to one of the chaotic variables andfurther encoded or modulated within the memristor-based chaotic system by using the property ofself-modulation. This signal is transmitted via the channel to synchronize certain memristor-basedchaotic system at the receiver end. Under suitable values of the parameters, the variables of thechaotic receiver system synchronize with that of the transmitter, consequently, the chaotic key canbe regenerated. Therefore the information signal is recovered by employing the decryption rule onFoundations: This work was supported by the Natural Science Foundation of China under Grant 61125303,National Basic Research Program of China (973Program) under Grant 2011CB710606, Research Fund for theDoctoral Program of Higher Education of China under Grant 20100142110021, the Excellent Youth Foundation ofHubei Province of China under Grant 2010CDA081.Brief author introduction:Shiping Wen, 1982, male, doctor, memristor, neural networksCorrespondance author: Zhigang Zeng, 1971, male, He is a professor in School of Automation, HuazhongUniversity of Science and Technology, Wuhan, China, and also in the Key Laboratory of Image Processing andIntelligent Control of Education Ministry of China, Wuhan, China. His current research interests include neuralnetworks, switched systems, computational intelligence, stability analysis of dynamic systems, pattern recognitionand associative memories. zgzeng527@-1-c(t ) f1 (... f1 ( f1 (s(t ), k (t )), k (t )),..., k (t )) , f1 (a, b)(a b),  h (a b) h,r(t ) f1 (... f1( f1 (cr (t ),k (t )),k (t )),...,k (t )) ,the encrypted digital signal with the regenerated chaotic key. Schematic diagram of the digital40 signal transimission scheme is shown in Fig. 1.Signals(t)Recovered signalr(t)Cipher c(t)Decipher cr(t)k(t)Chaotic system 1 kr(t)d(t)TransmitterPublic channel d(t) Chaotic system 2ReceiverFig 1 Schematic diagram of the memristor-based chaotic digital signal transimission scheme.And the proposed memristor-based digital chaotic encryption system using chaos synchronizationcan be described as follows.45 Transmitter:dx(t)dt  f ( x(t)) (d (t) x1(t)), (1)Encrypter:k (t ) g ( xi (t )), i 1, 2,..., N , (2)n nwhere x(t ) ( x1 (t ), x2 (t ),..., xN (t )) T are the state variables, d (t ) x1 (t ) pc(t ) is the50 chaotic signal to mask the encrypted signal c(t ) , and s(t ) is the digital information signal,there p , is the real number set. This method can mask and generate the key signalk (t ) with appropriate linear or nonlinear function g() . There c(t ) is an n -shift cipher toencrypt the plain signal, where h is chosen to make s(t), k (t) lie within (h, h) . Andf1 (,) is the following nonlinear f。