DENIAL OF SERVICE ATTACK IN DISTRIBUTED WIRELESS NETWORK BY DISTRIBUTED JAMMER NETWORK: A BIRTH-DEATH RANDOM PROCESS ANALYSIS

Transcription

1 Jourl of Coputer Sciece 0 (8): , 04 ISSN: Sciece Publictios doi:0.3844/jcssp Published Olie 0 (8) 04 ( DENIAL OF SERVICE ATTACK IN DISTRIBUTED WIRELESS NETWORK BY DISTRIBUTED JAMMER NETWORK: A BIRTH-DEATH RANDOM PROCESS ANALYSIS R. Dhsekr d G. Sigrvel Deprtet of DCE, K.S. Rgsy Istitute of Techology, Tiruchegode Nkkl, Tildu, Idi Deprtet of IT, K.S.R College of Egieerig, Tiruchegode Nkkl, Tildu, Idi Received ; Received ; Accepted ABSTRACT Lrge uber of low power, tiy rdio jers re costitutig Distributed Jer Network (DJN) is used owdys to cuse Deil of Service (DoS) ttck o Distributed Wireless Network (DWN). Usig NANO techologies, it is possible to build huge uber of tiy jers i illios, if ot ore. The Deil of Service (DoS) ttcks i Distributed Wireless Network (DWN) usig Distributed Jer Network (DJN) cosiderig ech of the s seprte Poisso Rdo Process. I itegrted pproch, i this study, we dvocte the ore turl birth-deth rdo process route to study the ipct of Distributed Jer Network (DJN) o the coectivity of Distributed Wireless Network (DWN). We express tht the Distributed Jer Network (DJN) c root phse trsitio i the perforce of the trget etwork. We use Birth-Deth Rdo Process (BDRP) route for this phse trsitio to evlute the collisio of Distributed Jer Network (DJN) o the coectivity d globl percoltio of the trget etwork. This study cofirs the globl percoltio of Distributed Wireless Network (DWN) is defiite whe the Distributed Jer Network (DJN) is ot ore sigifict. Key words: DWN, DJN, Birth-Deth Rdo Process, BDRP, Network Architecture, DoS Attcks. INTRODUCTION Miituriztio of jers is possible, copred to wireless sesors, due to the fct tht jers eit A ifesttio of the developet of rdio oly oise sigls without requirig coplex techology is the trsitio fro huge vcuu tube odultios, filterig, sclig d other sigl rdios to icro otube rdios. This i its wke hs processig fuctios. Distributed Jer Network ushered i rdicl chges i the desig d use of rdio (DJN) hs y pplictios i the defese scerio of devices. Distributed Jer Network (DJN) cosists coutry. New devices such s otube rdio y fid their pplictio i the jig dust. Distributed of huge uber of tiy low powered Jers Jer Network (DJN) fors irror ige to the distributed iside trget etwork, with the purpose of Distributed Wireless Network (DWN). Distributed jig the trget Distributed Wireless Network jer etwork c be deployed to for low power (DWN) (Hug et l., 0). Recet dvces i ir-bor jig dust, to disrupt the couictio Micro-Electro Mechicl Syste (MEMS) d NANO cpbilities of dversry, which is ore dvtges techologies (Otis et l., 004; Weldo et l., 008) becuse the ked eye cot eve see the otube ke it possible to build sufficiet uber of NANO jers, with uch reduced effect o self-iterfce. jers tht the Distributed Jer Network (DJN) The dvtge of self-iterfce free jig hs bee tkes the for of dust cloud i the ir, clled jig ply d purposefully see i the secod Irq wr s dust of icro sesors (Kh et l., 999). reported i the Wshigto post. Correspodig Author: R. Dhsekr, Deprtet of DCE, K.S. Rgsy Istitute of Techology Sciece Publictios 397

2 R. Dhsekr d G. Sigrvel / Jourl of Coputer Sciece 0 (8): , 04 Civili pplictios of distributed jer etwork iclude the silecig of cell phoes usig jers i resturt, thetres d coversio hlls i y coutries where it is legl. Although owig or usig jers is illegl i USA. I Itly, jers re reportedly used i exitios cetre to void udesirble ctivities. Secod ture of religious services is preserved i teples d churches usig jers. Deployig low-power distributed jer etwork i the plce of high-power jers is clerly preferble due to the helth cocers. Distributed Jer Network is differet fro trditiol jers (Rich et l., 00) used by the ilitry, which re trditiolly locted outside the trget distributed wireless etwork d produce iferece by beig high-power rdio sigl over log distces usig directiol te (Hug et l., 0). As etwork with lrge uber of tiy odes, Distributed Jer Network (DJN) i huge etwork perspective hs proiet effect o y Distributed Wireless Network (DWN). Distributed Jer Network (DJN) hs siple redudcy, hrd to detect bility, selfiterferece free cpbilities d low power cosuptio. Give tht the totl power cosuptio is costt, the gi of usig lrge uber of jers hs bee brought out i (Hug et l., 0). The wide usge of the wireless ediu leves it vulerble to itetiol iterferece ttcks, typiclly referred to s jig. This itetiol iterferece with wireless edius c be used to itroduce the Deil of Service (DoS) ttcks o wireless etworks. Typiclly, jig hs bee ddressed uder exterl thret odel (Pelechriis et l., 0). The ope ture of the wireless etworks, it hs ultiple security threts. Ayoe with trsceiver c evesdrop o wireless trsissios, iject spurious essge or j legitite oes. While evesdroppig d essge ijectio c be preveted usig cryptogrphic ethods, jig ttcks re uch hrder to couter (Proo d Lzos, 0)... Geerl Discussio d Relted Work Wireless etworks hve bee used i y pplictios, such s hoe utotio, ilitry surveillces d etity trckig systes. The wireless odes hve low coputtiol cpbilities d re highly resource costried. Routig protocols of wireless etworks re proe to vrious routig ttck, such s blck hole, rushig d Deil of Service (DoS) ttcks (Rchdr d Shug, 0). There is iproved risk of security ttcks, to defet coceled ttcks there is ecessity to utheticte both ccess poits d wireless sttios (Moorthy d Sthiyb, 0). Floodig is oe of the types of Deil of Service (DoS) ttck i obile d-hoc etwork. This kid of ttck cosues bttery power, storge spce d bdwidth. Floodig the excessive uber of pckets degrde the perforce of the etwork (Mdhvi d Duriswy, 03). Previous works o jig cocetrtes o ilitry pplictios (Hug et l., 0). Rdio iterferece ttcks re serious thret to the opertios of wireless etwork. Jig ttcks, it is iportt to uderstd the differet thret odels. The couter esures tht y be eployed to defed gist jig ttcks. Our work tkes, Deil of Service (DoS) ttcks i Distributed Wireless Network (DWN) by Distributed Jer Network (DJN) s Birth-Deth Rdo Process X () where is the re of lysis d is the uber of liked odes. The Birth-Deth Rdo Process (BDRP) cofirs tht the globl percoltio i Distributed Wireless Network (DWN). This study is rrged s follows: (). Mterils d Methods re i sectio-. (b). The Mtheticl bsis of Birth-Deth Rdo Process (BDRP) is i sectio-3. (c). Results re i sectio-4. (d). Coclusio d future work re i sectio-5 d Refereces follow i sectio-6.. MATERIALS AND METHODS.. Rdo Process The theory of probbility ttepts to qutity the chce of occurrece of evet of rdo experiet. I cotext where the discussio cot be restricted to oe rdo vrible, we re cofroted with fily of rdo vribles. A stochstic process (lso clled rdo process) {X(t), tεt} is fily of rdo vribles, ech of which is fuctio of tie. The set of ll vlues X(t) of the process costitute its stte spce. If t y prticulr poit of tie t 3 is X(t) = 3, the process is sid to be t stte x, t tie t. The set of ll tie poits costitute the tie spce of the process. A rdo process with discrete stte spce d cotiuous tie spce is clled discrete rdo process. Birth-deth rdo process is discrete rdo process where discrete stte spce represets the uber of coected trsitter odes i the re of iterest (clled birth) d deth deotes the deise the lik i the re with respect to DWN/DJN eviroet. If is the uber ctive likges i re d if, s the there exists the globl coectivity for the Distributed Wireless Network (DWN) i-spite of the Distributed Jer Network (DJN). Sciece Publictios 398

3 R. Dhsekr d G. Sigrvel / Jourl of Coputer Sciece 0 (8): , MATHEMATICAL BASIS 3.. Birth-Deth Rdo Process Birth-Deth Rdo Process (BDRP) is discrete rdo process stisfyig the birth-deth postultes (Veerrj, 004; Abrowitz et l., 0; Bruce d Westwig, 00) if P () = P{X() = } = probbility tht the ctive liks of Distributed Wireless Network (DWN) i re is, i birth-deth rdo process stisfies the differece-differetil Equtio: P = λ P λ + P + P for (3..) + + (where, is derivtive w.r.t ) d: P 0 = λ 0P 0 + P for 0 (3..) where, λ, re the e birth/deth rtes whe ctive odes re i the Distributed Wireless Network (DWN). Figure shows, whe birth occurs, the process goes fro stte to +. Whe deth occurs, the process goes fro stte to -. The process specified by birth rtes λ where = 0 d deth rtes where =. Solvig (3..) d (3..) we get P () [ 0] which gives P{X() = }, the probbility distributio of X(). If P is sll d λ = λ d = the (3..) gives: ( λ + ) + λ = (3..3) P P P Lier Birth-Deth Process If we ssue lier birth-deth rdo process by tkig λ = λ d =, birth-deth Rdo Process equtios re for : = ( ) λ ( λ + ) ( ) P P P P + + Ad: + (3..) = (3..) P P It c be show (Veerrj, 004), tht the siple birth-deth rdo process: = { α}{ β}{ β} (3..3) P for 0 With: = α (3..4) P Also the e d vrice of populr size i lier birth-deth process X() re give by: ( λ ) { } = (3..5) E x e Ad: Ad this is secod order differece equtio with costt coefficiets with the geerl solutio [C d C re rbitrry costts]: λ + Vr X e e λ ( λ ) ( λ ) { } = { } (3..6) P = C + C (3..4) where,, re the roots of: ( λ + ) + λ = (3..5) 0 Agi, whe o jers re preset the process is pure lik process with the differece-differetil syste (for the lier cse) s: = ( ) λ λ (3..7) P P P Give by: For d with the solutios: λ, = ( λ + ) ± ( λ ) =, where, λ = : (3..6) λ λ P = e e ; (3..8) Also for the siple birth process {X()}: = ( + ) (3..7) P C C e Sciece Publictios 399 { } E X = e λ (3..9)

4 R. Dhsekr d G. Sigrvel / Jourl of Coputer Sciece 0 (8): , 04 Fig.. Birth-deth rtes for ctive odes Ad: λ { } Vr X = e (3..0) = ( ) λ ( ) + ± λ λ + (4..5) 4. RESULTS 4.. Birth-Deth Rdo Process Alysis The rdo process X() deotes the uber of ctive liks i the DWN with P () = P {X() = }, the probbility distributio of X(), where is the re uder cosidertio where ctive liks re preset. Whe λ d re the birth d deth rtes, the probbility distributio of X(t) re govered by the differece differetil syste give by (3..) d (3..). We propose to give the geerl solutio of this syste for severl specil cses. dp If P is sll (P = c be cosidered s d probbilistic esure of the rte of chge of w.r.t d whe P is sll, we c iterpret it s tht the DJN effect is ot sigifict). We get the differece Equtio: λ P ( λ + ) P + P = 0 ( ) (4..) + + Ad: P 0 = λ 0P 0 + P (4..) The geerl solutio of (3..) is: = (4..3) P Ae +B where,, re the roots of: ( λ + ) + λ = (4..4) d whe the discriite is positive. I the specil cse λ = λ, = for ll, (4..5) gives: λ = ( λ + ) ± ( λ ) = = With: Ad: λ P = Ae +Be = P 0 i geerl s X (4..6) Hece globl percoltio of DWN is defiite whe the DJN effect is ot ore sigifict. 4.. Lier Model Whe λ = λ, = I this cse the rdo process results re: { } E X e( λ ) = (4..) { } λ + ( λ+ ) ( λ+ ) Vr { X( )} = e e λ Cse : λ >, (4..) The (4..) gives tht s, E{X()}. Hece wheever the jig rte is less th likig rte globl percoltio of the DWN is defiite. Sciece Publictios 400

5 R. Dhsekr d G. Sigrvel / Jourl of Coputer Sciece 0 (8): , 04 Cse : λ =, The E{x()} = irrespective of the vlue of. Hece for equl jig d likig rtes globl percoltio of the DWN is ipossible. Also: ( λ ) Lt Lt e Vr{ X( )} = ( λ + ) = = λ λ λ λ Idictig lrge vrice s d is iterpreted s hugely dispersed lik less isolted Distributed Wireless Network (DWN) odes. Cse 3: > λ: S + λ + + λ = 0 (4.3.6) With: = [S + λ + ], (4.3.7) With geerl solutio: S L = Ae + B (4.3.8) where, A, B,, re costts. E(x) = e λ 0 s Tkig Iverse Lplce Trsfors (ILT): Hece the Distributed Wireless Network (DWN) dies out crshig due to superior jig effect of the Distributed Jer Network (DJN). Jig of couictios i eey territory is doe due to powerful Distributed Jer Network (DJN) let loose o their Distributed Wireless Network (DWN) Model with λ = for Ay Vlue of. Geerl Cse. The differece differetil Equtio is: P = +λp λ + P + P ; (4.3.) + Lplce trsfors solutio (Widder, 00). Let: = (4.3.) LP L S The: LP = SL Where P 0 = 0 Whe (4.3.3) O tkig LT, (4.3.) gives: ( S + λ + ) L = λ L + L + (4.3.4) ( + λ + ) + λ = (4.3.5) L S L L This is secod order differece equtio with costt coefficiets, with uxiliry Equtio: P = A δ ( + ) + B e δ (4.3.9) where, δ is the direct delt fuctio. Usig (4.3.4) oe c copete E{X()} for this odel, uericlly or by siultio. 5. CONCLUSION The Deil of Service (DoS) ttck i Distributed Wireless Network (DWN) by Distributed Jer Network (DJN) s birth-deth discrete rdo process X() where is the re of lysis, where E{X()} is the e uber of liked odes of Distributed Wireless Network (DWN) whe λ d re the e likig/jig rtes per uit re whe liked odes re i the re. The differece differetil equtio for P () = P{X() = } hs bee lyzed with E{X()} d Vr {X()} for vrious cse of λ, vlues d iterpreted. The qutified results of this Birth-Deth Rdo Process (BDRP) theticl odel, cofirs the theoreticl hypothesis tht the globl percoltio of Distributed Wireless Network (DWN) is defiite whe the Distributed Jer Network (DJN) effect is ot ore sigifict. I future, lyze this study usig, the topology eployed i the etwork, ediu used for dt ccess d dt trsfer rte (tie) rther th liked odes () d re () tht is i our pproch. Sciece Publictios 40

6 R. Dhsekr d G. Sigrvel / Jourl of Coputer Sciece 0 (8): , REFERENCES Abrowitz, M. d I.A. Stegu, 0. Hd Book of Mtheticl Fuctios: With Foruls, Grphs d Mtheticl Tbles. st Ed., Courier Dover Publictios, New York, ISBN-0: , pp: 046 Bruce, R.K. d E.A. Westwig, 00. Mtheticl Physics: Applied Mthetics for Scietists d Egieers. d Ed., Joh Wiley d Sos, ISBN- 0: , pp: 689. Hug, H., N. Ahed d P. Krthik, 0. O ew type of deil of service ttck i wireless etworks: The distributed jer etwork. IEEE Trs. Wireless Cou., 0: DOI: 0.09/TWC Kh, J.M., R.H. Ktz d K.S.J. Pister, 999. Mobile etworkig for srt dust. Proc. ACM Mobi Co, Uiversity of Clifori. Mdhvi, S. d K. Duriswy, 03. Floodig ttck wre secure AODV. J. Coput. Sci., 9: DOI: /jcssp.03 Moorthy, M. d S. Sthiyb, 0. Effective uthetictio techique for distributed deil of service ttcks i wireless locl re etworks. J. Coput. Sci., 8: DOI: /jcssp.0 Otis, B.P, Y.H. Chee, R. Lu, N.M. Pletcher d J.M. Rbey, 004. A ultr-low power MEMS-bsed two-chel trsceiver for wireless sesor etworks. Proceedigs of the Syposiu o Digest of Techicl Ppers VLSI Circuits, Ju. 7-9, IEEE Xplore Press, pp: 0-3. DOI: 0.09/VLSIC Pelechriis, K., M. Iliofotou d V.S. Krishurthy, 0. Deil of service ttcks i wireless etworks: The cse of Jers. IEEE Cou. Surveys Tutorils, 3: DOI: 0.09/SURV Proo, A. d L. Lzos, 0. Pcket-hidig ethods for prevetig selective jig ttcks. IEEE Trs. Depedble Secure Coput., 9: 0-4. DOI: 0.09/TDSC.0.4 Rchdr, S. d V. Shug, 0. Ipct of sybil d worhole ttcks i loctio bsed geogrphic ulticst routig protocol for wireless sesor etworks. J. Coput. Sci., 7: DOI: /jcssp.0. Rich, A., C. Scheideler, S. Schid d J. Zhg, 00. A jig-resistt MAC protocol for ulti-hop wireless etworks. Proceedigs of the 4th Itertiol Coferece o Distributed Coputig, Sept. 3-5, Spriger-Verlg Berli Heidelberg, Cbridge, USA., pp: DOI: 0.007/ _7 Veerrj, T., 004. Probbility, Sttistics d Rdo Process. st Ed., Tt McGrw Hill, ISBN-0: , pp: 693. Weldo, J., K. Jese d A. Zettl, 008. Noechicl rdio trsitter. Physic Sttus Solidi, 45: DOI: 0.00/pssb Widder, D.V., 00. The Lplce Trsfor. st Ed., Dover Publictios. Sciece Publictios 40