A Novel Design Architecture of Secure Communication System with Reduced-Order Linear Receiver

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A Novel Design Architecture Reduced

Professor, Department of Electrical Engineering

ABSTRACT In this paper, a new concept about secure communication system is introduced and a novel secure communication design with reducedlinear receiver is developed to guarantee the global exponential stability of the resulting error signals. Besides, the guaranteed exponential convergence rate of the proposed secure communication system can be correctly calculated. Finally, some numerical simulations are given to demonstrate the feasibility and effectiveness of the obtained results. Key Words: Chaotic system, secure csystem, reduced-order linear receiver 1. INTRODUCTION As we know, because chaotic system sensitive to initial value, the output behaves like a random signal. Frequently, chaos in many dynamic systems is an origin of the generation of oscillation and an origin of instability. Several kinds of chaotic systems have been widely applied in various applications such as secure communication, slave chaotic systems, image encryptionsystems, chemical reactions, system identificationand ecological systems; see, for instancethe references therein. In recent years, numerous secure communications have been extensively explored; see, for example, [12] and the references therein. Generally speakingsecure communication is composed of transmreceiver and reduced-order linear receivermerits of low price and easy implementation.Therefore, searching a lower-dimensional order linear receiver for the secure chaotic communication system constitutes an important area for practical control design.

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A Novel Design Architecture of Secure Communication System Reduced-Order Linear Receiver

Yeong-Jeu Sun Electrical Engineering, I-Shou University, Kaohsiung

In this paper, a new concept about secure communication system is introduced and a novel secure communication design with reduced-order linear receiver is developed to guarantee the global exponential stability of the resulting error signals.

guaranteed exponential convergence rate of the proposed secure communication system can be correctly calculated. Finally, some numerical simulations are given to demonstrate the feasibility and effectiveness of the obtained results.

Chaotic system, secure communication

chaotic system is highly the output behaves like a , chaos in many dynamic

systems is an origin of the generation of oscillation everal kinds of chaotic

have been widely applied in various applications such as secure communication, master-

image encryption, biological system identification,

instance, [1-3] and

, numerous secure communications have been extensively explored; see, for example, [4-

erally speaking, a secure communication is composed of transmitter and

order linear receiver has the s of low price and easy implementation.

dimensional reduced-secure chaotic

constitutes an important area

In this paper, we will propose a new communication system and acommunication system with receiver will be developed resulting error signals can converge to zero in some exponential convergence rateguaranteed exponential convergence rateproposed chaotic secure communication system be accurately estimated. Finally, simulations are proposed to exhibitfeasibility of the main results. This paper is organized as follows. The problem formulation and main results 2. Several numerical simulations are3 to illustrate the main result. Finally, remarks are drawn in Section paper, nℜ denotes the n-dimensional Euclidean space,

xxx T ⋅=: denotes the Euclidean norm of the

vector x, and a denotes the

number a. 2. PROBLEM FORMULATION AND MAIN

RESULTS In this paper, we develop the following communication system with simple linear receiver and its block diagram is shown in Figure 1. Transmitter:

( ) ( ) ( ),3211 txtxatx =& ( ) ( ) ( ),23122 txatxatx +=& ( ) ( ) ( ),21543 txtxaatx +=& (1c)

( ) ( ) ( ),2716 txatxaty += ( ) ( ) ( ) .0,1 ≥∀+= ttmtxCt mmφ

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Secure Communication System with

Kaohsiung, Taiwan

we will propose a new idea about secure a novel design of secure

communication system with reduced-order linear to guarantee that the onverge to zero in some

convergence rate. Meanwhile, the guaranteed exponential convergence rate of the proposed chaotic secure communication system can

Finally, some numerical exhibit the capability and

This paper is organized as follows. The problem are presented in Section

simulations are given in Section to illustrate the main result. Finally, conclusion

in Section 4. Throughout this dimensional Euclidean space,

the Euclidean norm of the column

he absolute value of a real

ROBLEM FORMULATION AND MAIN

the following new secure communication system with simple reduced-order

and its block diagram is shown in

(1a) (1b)

(1d) (1e)

International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456


Receiver:

( ) ( ) ( ),1

62

6

71 ty

atz

a

atz +−= (2a)

( ) ( ) ( ),6

223

6

722 ty

a

atza

a

aatz +

−−=& (2b)

( ) ( ) ( ) ,0,2 ≥∀−= ttzCttm mmφ (2c) where ( ) ( ) ( )[ ] 2

21: ℜ∈= Ttxtxtx is the partial of transmitter, ( ) ℜ∈ty is the output of transmitter

( ) ( ) ( )[ ] 221: ℜ∈= Ttztztz is the state vector

( ) 11

×ℜ∈ qtm is the information vector,

( ) 12

×ℜ∈ qtm is the signal recovered from Nq ∈ . It is noted that the chaotic Sprott B

the special case of the system (1) with 153321 =−=−=== aaaaa . In the sequel, we adopt the

same parameters of the chaotic Sprott B 076 >aa . Apparently, a good secure communication

system means that we can recover the message in the receiver system; i.e., the error vector

( ) ( ) ( )tmtmte 12: −= can converge to zero in some sense. Before presenting the main result, let us introduce a definition which will be used in the main theorem Definition 1: The system (1) with (2) is called secure communication system with exponential convergence type if there are positive numbers k and

( ) ( ) ( ) ( ) 0,exp: 12 ≥∀−≤−= ttktmtmte α .

In this case, the positive number α exponential convergence rate. Now we present the main resultscommunication system of (1) with (2). Theorem 1: The system (1) with (2) is a secure communication system with exponential convergence type. Besides, the guaranteed

convergence rate is given by 6

71a

a+=α .

Proof. Define ( ) [ ] [ ] 2

221121 ℜ∈−−== TT zxzxwwtw .(3) Thus, from (1)-(3), one has

( ) ( ) ( )tztxtw 222 &&& −=

( ) ( ) ( )

( )tya

a

tzaa

aatxatxa

6

2

1236

722312

−

−++=

in Scientific Research and Development (IJTSRD) ISSN: 2456


partial state vector of transmitter,

is the state vector of receiver,

is the information vector, 2×ℜ∈ qmC , and

from ( )tm1 , with haotic Sprott B system is

the special case of the system (1) with . In the sequel, we adopt the

chaotic Sprott B system with , a good secure communication

system means that we can recover the message ( )tm1 in the receiver system; i.e., the error vector

can converge to zero in some sense.

let us introduce a which will be used in the main theorem.

The system (1) with (2) is called secure communication system with exponential convergence

and α such that

is called the

s for secure

tem (1) with (2) is a secure communication system with exponential convergence

exponential

( ) ( )

( ) ( )[ ]txatxaa

a

aa

aatxatxa

27166

2

36

722312

+−

−++=

( )

( ) ( )[ ]tztxaa

aa

a

aatxa

a

aa

2236

72

6

7223

6

72

−

−−=

−+

+−=

( )

( )twaa

aa

a

aatxa

a

aa

236

72

6

7223

6

72

−−=

−+

+−=

( ).1 26

7 twa

a

+−=

This implies that

( ) ( )

+−⋅= t

a

awtw 1exp0

6

722 .

From (1)-(4), it is easy to see that( ) ( ) ( )tztxtw 111 −=

( ) ( )

( ) ( )

+−−

−=

tya

tza

a

txa

aty

a

62

6

7

26

7

6

1

1

( ) ( )[ ]

( )twa

a

tztxa

a

26

7

226

7

−=

−−=

( )

+−⋅−= t

a

a

a

wa1exp

0

6

7

6

27

Hence, from (3)-(5), it results

( ) ( ) ( )

( )0226

27

26

22

21

wa

aa

twtwtw

⋅+≤

+=

.0,1exp6

7 ≥∀

+−⋅ tt

a

a

Thus, it can be readily obtained that( ) ( ) ( )

( ) ( ) ( ) (( )twC

xCttzCt

tmtmte

m

mmmm

⋅≤

+−−=

−=

φφ12

( )

,0,1exp

0

6

7

226

27

26

≥∀

+−⋅

⋅⋅+≤

tta

a

Cwa

aam

in view of (1), (2), and (6). This

in Scientific Research and Development (IJTSRD) ISSN: 2456-6470

Dec 2018 Page: 1155

( )tz23

( )tza 23

−

( )tza 23

−

(4)

), it is easy to see that

. (5)

(6)

t can be readily obtained that

( )t

This completes the proof.



Remark 1: It should be emphasized thatreceiver of (2) is linear and with lower dimensthan that of the transmitter. Consequentlyproposed receiver of (2) has the superioritiesprice and easy implementation by electronic circuit 3. NUMERICAL SIMULATIONS Consider the novel secure communication system of (1)-(2) with 176 == aa and [ ]11 −=mC . By Theorem 1, the synchronization of signals ( )tm1 and proposed secure communication (1)achieved with guaranteed convergence The real message ( )tm1 , the recovered message and the error signal are depicted in Figure 2respectively, which clearly indicates message ( )tm1 is recovered after 3 seconds. 4. CONCLUSION In this paper, a new concept about secure communication system has been introduced and a novel secure communication design with order linear receiver has been developed to guarantee the global exponential stability of the resulting error signals. Meanwhile, the guaranteed exponential convergence rate of the proposed secure communication system can be correctly calculated. Finally, some numerical simulations have been offered to show the feasibility and effectiveness of the obtained results. ACKNOWLEDGEMENT The author thanks the Ministry of Science and Technology of Republic of China for supporting work under grants MOST 106-2221MOST 106-2813-C-214-025-E, and MOST E-214-030. Besides, the author is grateful to Professor Jer-Guang Hsieh for the useful

( ) ( )daSystem 11 −

channelchannel

( )tz

( )ty( )tx

Transmitter

( )tmφ++

( )tm2

+−

( )tm1

mC

mC

Systems (2a)-(2b)

Figure 1: Secure-communication scheme information vector and ( )tm2 is the recovered vector)



It should be emphasized that the proposed lower dimensions

Consequently, the superiorities of low

by electronic circuit.

novel secure communication system of . By Theorem 1, and ( )tm2 for the

proposed secure communication (1)-(2) can be rate of 2=α . message ( )tm2 , ure 2-Figure 4, that the real

seconds.

In this paper, a new concept about secure communication system has been introduced and a

cation design with reduced-has been developed to guarantee

the global exponential stability of the resulting error signals. Meanwhile, the guaranteed exponential convergence rate of the proposed secure

ectly calculated. Finally, some numerical simulations have been offered to show the feasibility and effectiveness of the

Ministry of Science and of Republic of China for supporting this

2221-E-214-007, , and MOST 107-2221-

grateful to Chair for the useful comments.

Transmitter

Receiver

scheme ( ( )tm1 is the

is the recovered vector).

Figure 2: Real message of transmitter of (1)

Figure 3: Recoverd message of receiver of (2)

Figure 4: Error signal of

0 5 10 15 20 253.5

4

4.5

5

5.5

6

6.5

t (sec)

m1(

t)

0 5 10 15 20 253.5

4

4.5

5

5.5

6

6.5

t (sec)

m2(

t)

0 50

0.05

0.1

0.15

0.2

0.25

t (sec)

m2(

t)-m

1(t)


Dec 2018 Page: 1156

Real message of ( )tm1 described in the

transmitter of (1).

Recoverd message of ( )tm2 described in the

receiver of (2).

Error signal of ( ) ( )tmtm 12 − .

30 35 40 45 50t (sec)

30 35 40 45 50t (sec)

10 15t (sec)



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A Novel Design Architecture of Secure Communication System with Reduced-Order Linear Receiver

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