Rashmi A. Gedam et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 5, Issue No. 2, 166 - 171
― Performance comparison of multi-coupled chaotic Transceiver system‖ Rashmi A. Gedam Electronics Department G.H. Raisoni college of engineering Nagpur, India panderashmi6@gmail.com
Prof. D .V. Padole, Electronics Department G.H. Raisoni College of Engineering Nagpur, India dineshpadole@rediffmail.com
FORMULATION OF CHAOTIC SECURE COMMUNICATION SYSTEMS A general chaotic system can be described as the following dynamic equation:
T
II.
X = Ax
Keywords— chaos security communication; communication; AWGN channel noise;
wireless
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I INTRODUCTION In recent years, using chaotic signals to address the secure communication problem has received a great deal of attention. a proper modulation of the chosen chaotic dynamical system, the private message is hidden in the transmitter and sent to the receiver. At the receiving side, a synchronous dynamical system is built to synchronize with the transmitter in an objective to recover the original information signal. We have developed a more advanced encryption scheme that seems to yield improved security/privacy because of the use of multiple chaotic signals.[2]. The chaos synchronization between master (transmitter) and slave (receiver) chaotic systems has been an important issue for its potential applications in secure communication. The chaotic security communication didn’t be directly applied to wireless case in early researches. Inspired by the lack of developments in chaotic security communication for wireless environment, a new structure is proposed in this study to make the availability of chaotic secure systems for wireless applications. It is worth noting that global chaos synchronization of three chaotic systems has been studied hardly [2-3]. The formulation of chaotic secure communication system is discussed in Section II. Section III presents the new transmitter-receiver structure and analyses performances of SNR and BER in the AWGN (Additive White Gaussian Noise) channel. Finally, Section IV provides some brief conclusions.
ISSN: 2230-7818
(1)
+ g(x)
Where Ax is the linear part, g(x) is the nonlinear part of this system. In this paper, the chaotic security system is constructed by using Lorenz’s chaotic system which is an autonomous 3-order nonlinear system. The scheme of secure communication can be distributed by a coupled chaotic system. The input message M is masked by the chaotic state and transmitted. The system operation is described by the following equation. The equations of encrypt and decrypt systems are presented as following:
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Abstract— In this paper, a new way to transmit and receive an information bearing signal via chaotic system, a global chaos synchronization scheme of three identical system is investigated, by choosing proper coupling parameters, the state of all the three system can be synchronized. In a three channel transmission method is adopted for the purpose of synchronization and higher security. The transmitter and the receiver are synchronized in the presence of channel noises, and the encoded signal can be recovered by the receiver. To improve the security and accuracy of transmitted information, we proposed a new wireless communication structure based on three coupled chaotic systems. The performances, including SNR and BER in the AWGN channel, are verified.
Encrypt side (master): x = Ax + g(x,v) + Lzx
(2)
Where v = x1 + M
Decrypt side (slave): y = Ay + g(y,v) + Lzy
(3)
Where x € Rn , y € Rn are the state vectors. Ax and Ay are the linear part, g(x ,v) and g( y ,v) are the nonlinear part of this system, L is the controller gain of the system, K>0 is the coupling strength between master and slave system, zx and zy are the feedback signal. T
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X = [ x1 x2 x3 ] , y = [ y1 y2 y3 ] ,
g(x,v) = [ 0 –vx3 vx2 ]T, g(y,v) = [ 0 vy3
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vy2]T
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Rashmi A. Gedam et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 5, Issue No. 2, 166 - 171
III. THE NEW WIRELESS TRANSMITTER-RECEIVER STRUCTURE
e = x – y = [ e1 e2 e3 ]
(4)
And e = x – y = Ae - g(y,v) + L (zx -zy)
(5)
The goal is designing the controller gain L such that the input message M can be recovered in the slave system. To present the main structure in this paper the following theorem is essential to guarantee that the error dynamics is asymptotically stable.
Theorem 1. Suppose K 0 and the elements of the control
L = [ l1 l2 l3 ]T
satisfy:
l1> -a, l2 = a + c l3 = 0
(6)
The error states of eq.(4)are global asymptotically stable in Lyapunov function, and the masking message is Recovered at the same time.
Proof. For determining the elements of
The Lyapunov function is defined as follows:
(7)
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V(e) = (e12 + e22 + e32)/ 2 > 0 The derivative of V(e) from eq.(4) is V(e) = e1e1 + e2e2 + e3e3 = -(a+l1)e12 – (1+K)e22 -be32 + (a+c-l2) e1e1 –l3e1e3
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R v y1 (x1 M) y1 as x1 y1, R M
AWGN Channel
MESSAGE
Chaotic System Tx1
AWGN Channel
(8)
In Eq. (8), system parameters a, b, and c are positive Constants, by choosing control gain L satisfy Eq. (6) Such That V (e)< 0 . From Lyapunov direct theorem, The global asymptotically stability of error eq. (5) can Be guaranteed in the Lyapunov sense. Furthermore, The masking Message can be obtained as recovered Message R shown as Follows:
Chaotic System Tx2 Chaotic System Tx3
AWGN Channel
Chaotic System Rx1
Chaotic System Rx2
Threshol d Detector
Encrypte d Message
Chaotic System Rx3
Figure 1. The proposed wireless communication in AWGN channel
(9)
The Gaussian distribution Noise will be added into the transmitted chaotic signal and damaged its primal state in AWGN (Additive White Gaussian Noise) channel. Therefore, it is necessary to study for the application of chaotic secure communication in wireless environment.
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In Fig. 1, the left side (Transmitter) is the master Lorenz’s system, the right side (Receiver) is the slave ones. In this structure, we transmit message signal on three identical Encrypt/Decrypt systems. In this structure, each decrypt system is coupled to its own encrypt system. The decrypted signal will be linear combined firstly, and then import to the threshold detector. There are three transmitters and three receiver, the information signal is added to the variables(A, M, L, Zx) to be the pretend the chaos signal ,which is transmitted to the receiver ; Adding the AWGN noise for output of the transmitter channel. At the receiver end, with the synchronization occurrence among the three chaos systems, the information signal can be recovered by threshold detector. In this method, the signal is decoded considering chaos signal depending on initial values, obviously, by comparison with the original chaos masking mode, this method has higher security.[4].
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Gain
A. The Proposed structure
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The synchronization error and its error dynamic are defined as follows:
Although wireless is convenient for motivating transmission, nevertheless, the critical distortion will be irretrievable. the encrypted message is difficult to recover the original message in wireless communication. The basic theory is that the message signals is mixed to the chaos drive signal to be the pretend transmitted signal, which is transmitted to the receiver. The information signal is recovered by decoding in the synchronized receiver. Moreover, AWGN effect can’t be ignored. For obtain more precise recovered message in slave system, we propose a concept of Transmitter-Receiver structure in fig.1
Generally, for wireless applications, each Encrypt /Decrypt systems will be still interfered by AWGN channel. Therefore, all recovered message are combined to increase the signal strength to avoid the distortion in the receiver side
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Figure. 3. Recovered one coupled system
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In Fig. 1, between the Transmitter and Receiver, there are three coupled chaotic systems for information transmitting in wireless communication. However, on the receiver side, these coupled chaotic systems should cause signal level of decrypted message increased or decreased. Three different situations are considered in our proposed structure: Case 1: One couple Encrypt/Decrypt system. Case 2: Two couple Encrypt/Decrypt systems. Case 3: Three couple Encrypt/Decrypt systems. In one coupled system we have to given the input message for bit form is fad to the encrypt ( Tx1) block but this chaos transmitter is not given the proper input signal so output of this block some distortions in message and this message is sending to the input of decrypt (Rx1)block but decrypter canâ&#x20AC;&#x2122;t understand itâ&#x20AC;&#x2122;s message or noise so we will get adding to the Gaussian noise after adding the noise decrypter get remove the noise in transmitter but in one coupled system is not given the original message so this system is not proper for secure message it having some variances in this coupling.Fig(3) Then we have to modify this system for adding the again one coupling that is two coupling the same procedure for one coupling but in two coupling system we have to use the double value of the parameter because it has two transmitter and receiver so the output problem of one coupled system is overcome the two coupled system. The variance of the two coupled system is small as compared to one coupled system.Fig(4) So in second system we will not get the original message so we can add again transmitter and receiver to the previous system and the name as three coupled system. In this coupled remove the total noise of the output of decrypter and get original message.Fig.(5). All cases are evaluated by BER performance with SNR from 0dB to 10dB . The original message is given as a square wave shown in Fig. 2,
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B. Numerical simulation
Figure. 2. Original message
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Rashmi A. Gedam et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 5, Issue No. 2, 166 - 171
Figure.4. Recovered two coupled system
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Rashmi A. Gedam et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 5, Issue No. 2, 166 - 171
Figure.5. Recovered three coupled system
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C. Comparison for Original Message With One, Two, Three Coupled System
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D. Bit Error Rate For One , Two and Three Coupled System 0.500000 (ONE COUPLED SYSTEM) 0.280000 (TWO COUPLED SYSTEM) 0.000000 (THREE COUPLED SYSTEM)
In one coupling there will be a large error in recovered message and in two coupling it is less error as compared to the one coupled system but in three coupled there will be no error in the recovered message so it will get original message of three coupled system.
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CONCLUSIONS In this paper, we have investigated the problem of secure Communication scheme For the purpose of increasing communication security, A software simulation model is developed with encrypt and decrypt transmitted signal using three coupled scheme. We have reported global synchronization to a Lorenz chaotic system without any knowledge about the values of its parameters. The communication of information across an AWGN channel has Been carried out by using a pair of synchronized chaotic circuits. Further, the chaotic signals from the same transmitter and receiver pair have been utilized to encrypt and decrypt the Information signal respectively. In the simulation results, the relativity of SNR, BER, and number of Encrypt/Decrypt system analysis is discussed. The security of the system is potentially increased. From those analyses, the wired chaotic security communication can be directly extended to wireless communication with AWGN channel feasibility. Based on the proposed system, more control issues and wireless application can be devised in the further research work. REFERENCES
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Huibin Zhu, Baotong Cui,‖ A new adaptive synchronization scheme of delayed chaotic system for secure communication with channel noises‖,vol.4 .978-1-4244-7164-51 © 2010 IEEE Zhong-Ping Jiang,‖ A Note on Chaotic Secure Communication Systems‖, 1057–7122/02 © 2002 IEEE Li-Xin Yang, Jiangang Zhang,‖ Synchronization of three identical systems and its application for secure communication with noise perturbation‖ 978-1-4244-4994-1/09©2009 IEEE Li-Xin Yang, Jian-Gang Zhang,‖ A new multistage chaos synchronized system for secure communications and noise perturbation‖, 978-0-7695-3853-2/09 © 2009 IEEE DOI 10.1109/IWCFTA.2009.15 Zhengguo Li, Kun Li, Changyun Wen, and Yeng Chai Soh ― A New Chaotic secure communication system‖ IEEE transaction on communications,Vol.51,no.08 AUGUST 2003, 0090-6778/03 © 2003 IEEE
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K. Murali, Haiyang Yu, Vinay Varadan and Henry Leung,‖ SECURE COMMUNICATION USING A CHAOS BASED SIGNAL ENCRYPTION SCHEME”, 0098 3063/00 @ 2001 IEEE [7] Alicia d'Anjou,Cecilia Sarasola, F.JavierTorrealdea,Manuel Graiia,‖ Parameter Adaptive Global Synchronization of Lorenz Chaotic Systems”, 0-7803-5800-7/00-02000 IEEE [8] Alicia d'Anjou, Cecilia Sarasola, F. JavierTorrealdea Manuel Graiia,‖ Parameter Adaptive Global Synchronization Of Lorenz Chaotic Systems‖, 0-7803-5800-7/00/0-2000 IEEE
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