A Novel Approach to Security Enhancement of Chaotic DSSS Systems

Transcription

1 A Nove Approach to Security Enhancement of Chaotic DSSS Systems Nguyen Xuan Quyen 1, Chuyen T. Nguyen 1, Pere Baret-Ros 2, and Reiner Dojen 3 1 Schoo of Eectronics and Teecommunications, Hanoi University of Science and Technoogy, Vietnam 2 Department of Computer Architecture, UPC BarceonaTech, Spain 3 Department of Eectronic and Computer Engineering, University of Limeric, Ireand 4 Emai: {quyen.nguyenxuan, chuyen.nguyenthanh}@hust.edu.vn, pbaret@ac.upc.edu, reiner.dojen@u.ie Abstract In this paper, we propose a nove approach to the enhancement of physica ayer security for chaotic directsequence spread-spectrum (DSSS) communication systems. The main idea behind our proposa is to vary the symbo period according to the behavior of the chaotic spreading sequence. As a resut, the symbo period and the spreading sequence vary chaoticay at the same time. This simutaneous variation aims at protecting DSSS-based communication systems from the bind estimation attacs in the detection of the symbo period. Discrete-time modes for spreading and despreading schemes are presented and anayzed. Mutipe access performance of the proposed technique in the presence of additiona white Gaussian noise (AWGN) is determined by computer simuations. The increase in security at the physica ayer is aso evauated by numerica resuts. Obtained resuts show that our proposed technique can protect the system against attacs based on the detection of the symbo period, even if the intruder has fu information on the used chaotic sequence. Index Terms Chaotic direct-sequence spread-spectrum (DSSS); Chaos-based spread-spectrum; Physica ayer security. I. INTRODUCTION In the two ast decades, a arge number of studies have been devoted to the design and anaysis of communication systems based on chaotic direct-sequence spread-spectrum (DSSS) [1]- [5]. The main goa of the appication of chaotic sequences to spread-spectrum communications is the enhancement of physica ayer security [6]-[9]. However, severa recent studies have shown that chaotic sequences can be recovered by different bind detection methods [10]-[13]. A detection method based on noninear time series anaysis is presented in [10], where mutua information and fase nearest neighbor methods are used for estabishing optima embedding parameters for the attractor reconstruction from the experimenta time series. The reconstruction of chaotic attractor is aso investigated in [11] by expoiting intrinsic geometry of chaotic attractor sets. Based on the reconstructed attractor, the chaotic sequence used can be recovered by an approximation agorithm. The study in [12] shows that the equivariant adaptive separation via independence (EASI) agorithm in fixed-point arithmetic can recover successfuy the chaotic sequences. The obtained resuts of the above studies aso pose a new security chaenge, that is, if an intruder can recover the chaotic spreading sequence, he wi empoy the recovered sequence to detect the symbo period [13, 14]. With the recovered sequence and detected period, he can totay recover the origina data. It means that the security of chaos-based DSSS systems is totay broen. This paper proposes a nove chaos-based DSSS technique for overcoming the security weaness aforementioned. In the proposed technique, the period of the data symbo is varied according to the behavior of the chaotic spreading sequence. Because both the spreading sequence and the symbo period vary chaoticay at the same time, the bit energy aso varies according to the chaotic behavior. As a resut, it is not easy for an intruder to detect the symbo period by using energy detection methods [13, 14]. In fact, the idea of chaos-based variation of the symbo period in spread-spectrum communication systems has aso been presented in [15] and [16]. However, the spreading sequences investigated in these studies are binary sequences, i.e., PN and NRZ-chaos sequences, which have ony two eves, +1 or -1. Obtained resuts point out that the performance of mutipe-access system with the simutaneous variation of the symbo period and the spreading sequence gets worse when the variation range of the symbo period is increased. But in return, our technique can protect the system from attacs based on detecting the symbo period at the physica ayer, even if the attacer fuy nows the chaotic sequence. The rest of this paper is structured as foows: in Section II, the proposed approach is described via the anaysis of discretetime modes for spreading and despreading schemes. Mutipe access performance over the AWGN channe is estimated by numerica resuts in Section III. Section IV presents an investigation using computer simuations on the abiity of the proposed technique in resisting the symbo period detection attacs. Finay, our concusion with remars is given in Section V. II. DESCRIPTION OF PROPOSED APPROACH A. Spreading Scheme with Variabe Bit Period The boc diagram of the spreading scheme is shown in Fig. 1. The puse chain with variabe inter-puse intervas, denoted by {p } is generated by the variabe interva puse generator (VIPG) whose input is the chaotic sequence {x }. In the VIPG, the input sequence {x } is samped at each instance 2016 IEEE. Persona use of this materia is permitted. Permission from IEEE must be obtained for a other uses, in any current or future media, incuding reprinting/repubishing this materia for advertising or promotiona purposes,creating new coective wors, for resae or redistribution to servers or ists, or reuse of any copyrighted component of this wor in other wors. DOI /CCE

2 triggered by the input puse, i.e., p = P (t t ), (1) Data Buffer p b c e with P (t) = { 1 0 t τ, 0 otherwise, (2) f( ) β x where t is the instance to generate the th puse. The output sampe x is then converted into a positive integer β by using a transformation function, i.e., β = f(x ). Here, the function f( ) is determined so that when the sequence {x } varies in a nown range of [x min, x max ], {β } aso varies in a corresponding range of [in = f(x min ) = 0, ax = f(x max ) = ]. In order to determine the function f( ), we first choose a fixed vaue for. The range of [x min, x max ] is then divided into ( +1) vaue intervas, i.e., [x min +jγ, x min +(j+1)γ], with j varying from 0 to. γ is a constant defined by r =e +n Correator c VIPG p x Chaotic Generator Σ s b Buffer Output Data γ = (x max x min )/( + 1). (3) VIPG If the input vaue x fas into the range of [x min +jγ, x min + (j + 1)γ], the corresponding output vaue β is determined by the function f( ) as foows: x x min β = f(x ) =, (4) γ with being the foor function. Depending on the vaue of β, the ( + 1) th puse is generated at the output of VIPG at the instance t +1 given by t +1 = t + (β + β )τ, (5) Data 1 Data i x Synchronized Chaotic Generator Transmitter 1 Transmitter i r e (1) e (i) n r Receiver 1 Receiver i Output Data 1 Data i here τ is chip period of the chaotic sequence {x } and β is a fixed integer whose vaue is predetermined. We can see from Eq. (5) that the intervas between inter-puses of {p } vary according to the chaotic sampe vaues {x } and aways equa to a mutipe of chip period τ. With the trigger of each puse of {p }, the data buffer shifts the binary vaue of next symbo, i.e., b = {±1}, to its output. It means that the period of th symbo, denoted by T, is determined from Eq. (5) as foows: T s = t +1 t = (β + β )τ. (6) The spread-spectrum process is performed by directy mutipying the variabe-period bits {b } with the chaotic sequence {x }. Eq. (6) shows that there are (β +β ) chips in the period of th bit. It means that the sum, i.e., (β + β ) is aso the spreading factor of the th bit. In the spreading process, the number of symbo tends to infinite, β varies in the range of [0, ], thus the spreading factor, (β + β ), varies in the range of [β, ]. The predetermined constants, β and, are considered as the initia vaue and the variation width of the spreading factor, respectivey. The output signa of the spreading scheme in the period of the th bit can be expressed as e = b x. (7) Data K Transmitter K e (K) (c) Receiver K Data K Fig. 1. Boc diagrams of Spreading scheme, Despreding scheme, and (c) DS-CDMA system. It is noted that in the specia case of the variation width = 0, the symbo period T s = βτ is unvaried in the spreading process. The proposed technique in this case becomes the conventiona chaotic DSSS technique. B. Despreading Scheme The boc diagram of the despreading scheme is dispayed in Fig. 1. The oca chaotic sequence is regenerated and synchronized with the incoming signa by means of the synchronized chaotic generator (SCG) whose scheme is shown in Fig. 1(c). This synchronization scheme reies on the scheme presented in [30] for the conventiona chaotic DSSS technique with a modification. In particuar, instead of repeating the correation process after a fixed symbo period as usua, the correation process is controed by the trigger puses from the VIPG. In the SCG, the chaotic generator and the VIPG are identica to those of the spreading scheme. The synchronized

3 chaotic sequence is used for the despreading process and data recovery. The incoming signa is the sum of the transmitted signa and the noise of AWGN channe, we have r = e + n, (8) here n is an AWGN sampe with zero mean and variance N 0 /2. The despreading process is simpy performed by using a correator. The output signa of the correator is samped by the trigger of each pue of {p }. The sampe vaue at the instance t is determined by s = = r x = (e + n )x (b x + n )x = b (x ) 2 + n x. Based on this sampe vaue s, the binary vaue of th symbo is recovered by { 1 s 0, b = (10) 1 s < 0. At the trigger instance of each puse of {p }, the recovered bits are shifted into the buffer. C. Mutipe-access Operation Fig. 1(c) shows a typica DS-CDMA communication system based on the proposed DSSS technique. K users are distinguished from each other by different chaotic sequences, which can be produced by using the same chaotic map with different initia vaues. At the input of the i th receiver, the incoming signa is expressed as r = K e (i) + n = K (9) b (i) + n (11) The correation vaue at output of the samper is given by s (i) = r = = ( K ( K = b (i) e (i) + n ) b (i) + n ( )2 + ) K,i j b (i) x(j) + n (12) Simiary, based on this sampe vaue s (i), the vaue of b (i) is recovered by the comparison as in Eq. (10). P(Evb ) E vb β=32, =10 β=32, =5 β=32, β =0 β=16, =10 β=16, =5 β=16, β 5 m = β=16, =0 β=16, =5 β=16, =10 β=32, =0 β=32, =5 β=32, = E vb Fig. 2. Resuts obtained by numerica computation: Variation of symbo energy, Histograms of symbo energy distribution. III. SIMULATION RESULTS In this section, PC simuations for the chaotic DS-CDMA system based on the proposed DSSS technique are carried out with different system parameters. The chaotic map used for generating chaotic sequences is the Chebyshev poynomia function of order 2 given by with [x min, x max ] = [ 1, 1] and E c = E [ x 2 ] = x = f(x 1 ) = 2x 2 1 1, (13) x 2 ρ(x)dx = 1 1 x 2 1 π 1 x 2 dx = 1 2, (14) Fig. 2 and Fig. 2 show respectivey the variation of bit energy and the histograms of the bit energy distribution, obtained by numerica computations for cases of β = 16, 32 with = 0, 5, 10. Each histogram is potted by means of 1000 casses which are cacuated statisticay from sampes of bit energy. It can be ceary observed that the bit energy varies aperiodicay, where the average energy increases aong with the increment of the initia spreading factor β, and the variation range of the bit energy becomes wider with the increment of variation width. In Fig. 3, we evauate the effect of two parameters, i.e., β and, on the performance of the mono-user system under the same vaue of E ab N 0 = 9dB. We can find that the cacuated resuts totay agree with the simuated ones. Both of them point out that the system performance increases with the vaue of β. For exampe with the same = 10, when β increases from 4 to 64, the BER vaue reduces from 2 to , respectivey. In contrast, when increases, the system performance gets worse. Specificay, at the same

4 = 40 ρ (α) (db) T s=32τ BER = 20 = 10 = 5 = β K=5 K=4 K=3 ρ (α) (db) BER K=1 K=2 ρ (α) (db) E b /N 0 (db) Fig. 3. BER performance of the DS-CDMA system using the proposed DSSS technique: Mono-user system with increment of β and at the same E ab /N 0 = 9dB; Muti-user system with increment of K at β = 16 and = 10. β = 16, the BER vaue increases from to corresponding to varying from 0 to 40. In return, the increment of contributes to enhance the system security at the physica ayer. This enhancement wi be anayzed in Section IV. The dependence of the system performance upon the number of users K for β = 16, = 10 is dispayed in Fig. 3. It can be ceary observed that the system performs worse with the increment of K. For exampe with the same vaue of E ab N 0 = 10dB, the BER vaue increases from to 6 corresponding to K increasing from 1 to 5. (c) Fig. 4. Fuctuation graphs obtained by PC simuations for the first scenario in cases of PN-DSSS technique, Chaotic DSSS technique, and (c) Proposed DSSS technique. IV. IMPROVEMENT OF PHYSICAL LAYER SECURITY In this section, we investigate the security abiity of the proposed chaos-based DSSS technique by means of PC simuations. Let s suppose that an intruder uses the we-nown attac method proposed in [13, 14] to detect the typica parameters, i.e, symbo period T s and sequence period T S, of the spreading sequence from the received signa r(t). The attac method used reies on the computation of the fuctuation of the auto-correation vaue. In order to compute the fuctuations, the received signa is divided into L tempora windows with W being the window width. By appying an autocorreation estimator to each window, the correation vaue is computed by R n rr(α) = 1 W W 0 r(t)r (t α)dt, (15)

5 ρ (α) (db) 10 1 T s=32τ where R n rr(α) is the correation vaue of the n th window, r (t α) is the compex conjugate of r(t α), and α is the shifted duration. The fuctuation vaue is then determined as foows: { ρ(α) = Ê Rn rr(α) 2} = 1 L 1 L R rr(α) n 2. (16) 0 T =34.5τ as (c) T =127 S (d) T =127τ S (e) Fig. 5. Fuctuation graphs obtained by PC simuations for the second scenario in cases of Chaotic DSSS technique, Proposed DSSS technique with = 5, (c) Proposed DSSS technique with = 10, (d) Proposed DSSS technique with = 20, Proposed DSSS technique with = 40. By potting the graph of ρ(α) versus α, caed fuctuation graph, the symbo period or sequence period can be determined by measuring the duration between pea vaues in the graph. To compare the security eve, we simuate the attac process of the intruder with respect to three techniques, i.e., PN- DSSS, chaotic DSSS, and chaotic DSSS with variabe symbo period. The simuation parameters are chosen as foows: fixed spreading factor β = 32 for the cases of PN and chaotic DSSS techniques, β = 32 and = 5, 10, 20, 40 for the case of the proposed technique, sequence period T S = 127τ, window width W = 1000τ, and window number L = Here, the attac simuations are carried out for two scenarios: (1) the intruder has no information about the transmitting side. He performs a bind detection using the aforementioned method; (2) the intruder has fu information on the spreading sequence. The received signa is mutipied with this nown sequence. The output product is then used as the input signa of the detection method above. Fuctuation graphs obtained by the simuations for the first scenario are shown in Fig. 5. For the case of the PN-DSSS technique, by measuring the cyce of periodic the curve of the graph in Fig. 4, the intruder can easiy detect the symbo period, T s = 32τ, and the sequence period, T S = 127τ. With respect to the cases of the chaotic DSSS and our proposed techniques with = 10, Fig. 4 and Fig. 4(c) ceary show that the intruder just detects the sequence period T S = 127τ and there is no sign of the symbo period. These resuts point out an important feature, that is, the DSSS systems are protected from the attac method described above by repacing PN sequences by chaotic ones. Fig. 5 presents the simuated fuctuation graphs for the second scenario. We can see from Fig. 5 that the intruder can detect both of the symbo and sequence periods in the case of the conventiona chaotic DSSS technique. For the case of the proposed DSSS technique, Fig. 5, Fig. 5(c), Fig. 5(d), and Fig. 5(e) show that the intruder can detect the sequence period T S = 127τ but cannot detect exacty the variation of the symbo period. With respect to the case of = 5, the intruder may detect the average symbo period, i.e., T as = (β + /2)τ = 34.5τ, even so this average vaue is not enough to recover the origina data. For the case of = 10, the sign of the average period starts to disappear. There is no sign of the symbo period for the cases of = 20 and = 40. It means that our technique can hide the information of the symbo period, thus its security cannot be broen by the intruder who has fu information on the chaotic sequence used.

6 V. CONCLUSIONS This study has proposed and investigated a nove chaosbased DSSS technique, where the symbo period is varied according to the behavior of the chaotic spreading sequence used. Mathematica modes in discrete time domain for the spreading scheme with variabe symbo period and the despreading scheme with sequence synchronization are presented and anayzed. The BER performance of the proposed technique in DS-CDMA communication systems over an AWGN channe is estimated with the use of numerica simuation. The robustness against the attac of symbo period detection of the proposed technique in comparison with that of the conventiona techniques is evauated in two different scenarios by means of the numerica simuations. The obtained resuts show that: (1) the use of chaotic sequences instead of PN sequences heps to protect DSSS-based communication systems from bind estimation attacs to detect the symbo period; (2) the mutipe access performance gets better when the initia spreading factor β is increased. With the chip period being fixed, this increment eads to the reduction of the symbo rate. On the other hand, the increment of variation width of the spreading factor, i.e.,, maes the performance worse, but in return the physica ayer security is enhanced significanty. Therefore, the vaues of β and have to be propery predetermined to guarantee the trade-off between performance, data rate and security of the system; (3) it is cear that the spreading, despreading and synchronization schemes of the proposed technique are more compicated than those of the conventiona ones and they operate based on the process of discrete-sampe processing. Therefore, these schemes are suitabe to be impemented easiy on high speed programmabe integrated circuits. A the noticeabe remars above mae the chaos-based DSSS with variabe symbo period be a promising and robust technique for enhancing the physica ayer security of DS-CDMA communication systems. [8] A. N. Miiou, I. P. Antoniades, S. G. Stavrinides, A. N. Anagnostopouos, Secure communication by chaotic synchronization: Robustness under noisy conditions, Noninear Anaysis: Rea Word Appications, vo.8, no. 3, pp , [9] N. X. Quyen, T. Q. Duong, A. Naanathan, Modeing, anaysis and performance comparison of two direct samping DCSK receivers under frequency nonseective fading channes, IET Communications, doi: /iet-com , [10] S. Kodba, M. Perc, and M. Marh, Detecting chaos from a time series, Europen Journa of Physics, vo. 26, pp , [11] G. K. Rohdea, J. M. Nichos, and F. Buchotz, Chaotic signa detection and estimation based on attractor sets: Appications to secure communications, Chaos: An Interdis. Jour. of Noni. Science, vo. 18, , [12] S-J. Kimy, K. Umenoyz, and R. Taahashiz, Recovery of chaotic signas using on-ine ICA agorithm, 2007 Int. Symp. on Noni. Theory and its Appi. (NOLTA 07), Vancouver-Canada, Sept. 2007, pp [13] G. Bure, Detection of spread spectrum transmissions using fuctuations of correation estimators, IEEE-ISPACS, Nov. 2000, pp. B B [14] H. Xu, Z. Huang, Y. Zhou, Bind estimation of the symbo period of a ong-code DS-SS signa, Int. Conf. on Micro.and Mii. Wave Techno. (ICMMT 07), Changsha-China, Apr. 2004, pp.1-4. [15] N. X. Quyen, V. V. Yem, T. M. Hoang, A chaos-based secure directsequence/spread-spectrum communication system, Abstract and Appied Anaysis, 11 pages, doi: /2013/764341, [16] N. X. Quyen, V. V. Yem, T. Q. Duong, Design and anaysis of a spread-spectrum communication system with chaos-based variation of both phase-coded carrier and spreading factor, IET Communications, vo. 9, no. 12, pp , REFERENCES [1] C. C. Chong and S. K. Yong, UWB direct chaotic communication technoogy for ow-rate WPAN appications, IEEE Trans. Veh. Techno., vo. 57, no. 3, pp , [2] G. Kaddoum, P. Charge, and D.Roviras, A generaized methodoogy for bit-error-rate prediction in correation-based communication schemes using chaos, IEEE Comm. Letters, vo. 13, no. 8, pp , [3] N. X. Quyen, L. V. Cong, N. H. Long, V. V. Yem, An OFDM-based chaotic DSSS communication system with MPSK moduation, Proc. Int. Conf. Communications and Eectronics (ICCE 14), Danang-Vietnam, 2014, pp [4] S. M. Berber, Probabiity of error derivatives for binary and chaos-based CDMA systems in wide-band channes, IEEE Trans. Wire. Commun., vo. 13, no. 10, pp , [5] M. K. Pate,, S. M. Berber, K. W. Sowerby, Adaptive RAKE receiver in chaos based piot-added DS-CDMA system, Physica Communication, vo. 16, pp , [6] N. X. Quyen, V. V. Yem, T. M. Hoang, and K. Kyamaya, MxNary chaotic puse-width-position moduation: An effective combination method for improving bit rate, Int. Jour. for Computation and Mathematics in Eectrica and Eectronic Engineering, vo. 32, no. 3, pp , [7] J. Yu and Y.-D. Yao, Detection performance of chaotic spreading LPI waveforms, IEEE Trans. Wireess Commun., vo. 4, no. 2, pp , 2005.