Analysis of Data Dependency Based Intrusion Detection System *

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1 nalyss of Data Dnny Bas Intuson Dtton Systm * Ymk ugmanov 1, Bajna ana 1, an Y Hu 2 1 Comut Sn an Comut Engnng Datmnt Unvsty of kansas ayttvll, R {ynugmano,bana}@uak.u 2 Comut Sn Datmnt othn Kntuky Unvsty Hghlan Hghts, KY huy1@nku.u bstat. Ths sah fouss on analyzng th ost fftvnss of a atabas ntuson tton systm that uss nns among ata tms to tt malous tansatons. Th mol suggst n ths a onss th man fatos: th qualty of ntuson tton, th obablty of ntuson, an th ost stutu of an oganzaton whos ata s ott by th ntuson tton systm. W vlo a st by st aoah that hls n tmnng th otmal onfguaton xss by th sons statgy an th thshol valu. Th xmntal sults show that ou mol s aabl of fnng th otmal onfguaton whl takng th ost stutu of an oganzaton nto onsaton. Kywos: Databas ntuson tton, smant analyz, ost analyss, sons statgy. 1 Intouton lthough th xst many suty tools fo ottng omut systms fom attaks, as [1], non of thm an ov absolut suty. Thfo, all motant vnts that ou n a omut systm must b suvs an xamn fo a ossbl sn of malous atvty by ntuson tton systms. Of th two unvsally ognz mols fo ntuson tton [2, 14], msus tton an anomaly tton, th latt tyally uss a thshol to fn whh vnts a ons nomal an whh a ons ntusv [3, 4, 15]. By hangng th thshol, an oganzaton may fn th otmal balan btwn sussful ttons an fals alams. Howv, fnng of th otmal onfguaton s a ffult task. Som nt woks hav fous on th otmzaton thnqus fo anomaly tton systms * Rsah of Ymk ugmanov an Bajna ana was suot n at by OSR un gant Rsah of Y Hu was suot n at by th KY S ESCoR ogam. E. Gus, J. Vaya Es.: Data an latons Suty 2009, LCS 5645, , II Intnatonal aton fo Infomaton ossng 2009

2 112 Y. ugmanov, B. ana, an Y. Hu [4, 5]. t snt, th majoty of xstng host-bas anomaly tton systms a nfftv n ttng attaks on atabass, sn thy a fous on takng an analyzng vnts that ou n oatng systms an alatons, an not on th atabas tslf. lthough a fw mols hav bn vlo fo ttng malous atvts n atabass, to th bst of ou knowlg, non of ths mthos hav bn analyz fo th ost fftvnss. Th objtv of ths wok s to valuat th ata nny bas atabas ntuson tton systm [12] fo otmzaton bas on sons statgy an thshol valu. 2 Bakgoun lmt sah has bn on to ass th oblm of malous tansaton tton n atabas systms. In [6] an ahttu fo ntuson-tolant atabas systms s oos. n ntuson-tolant atabas managmnt systm s abl to oat an lv ssntal svs vn n as of attaks. Howv, ths aoah s mo fous on th loalzaton of attaks an ovy of th amag, than on vlong a sf ntuson tton systm. atabas ntuson tton shm bas on ata nny ul mnng s snt n [11]. smla mtho that uss wght squn mnng thnqus s off n [7]. Th majo awbak of ths tton mtho s that th wghts of attbuts must b assgn manually. Th mtho snt n [8] tts ntuson n atabass that mloys ol-bas ass ontol an t uss aïv Bays Classf to t th ol whh th obsv SQL omman most lkly blongs to, an omas t wth th atual ol. If th ols a ffnt, th SQL statmnt s ons llgal. n ntuson tton systm fo al-tm atabas systms has bn suss n [9]. Rsahs n [10] oos a msus tton systm fo atabass bas on th obsvaton that th xst tan gulats n ass attns of uss. Ou sah s bas on th mol snt n [12] that tts malous atvts n a atabas managmnt systm by usng ata nny latonshs. Rgang th fftvnss of ntuson tton, a stuy snt n [3] show that suh mthos a subjt to th bas-at fallay, omng to th onluson that n o to ahv substantal valus of th Baysan tton at, w hav to ahv a low fals alam at. H foun that n most ass suh a at s unattanabl. ollowng that, sahs n [13] vlo th thnqus fo bulng an ntuson tton systm on th bass of ost-snstv mols. Th fst omhnsv stuy on th ost fftvnss of ntuson tton systms aa n [5], whh asss th oblm of fnng th otmal onfguaton of a sngl ntuson tton systm, an vaous ombnatons of multl ntuson tton systms. n otmzaton shm bas on gam thoy has bn off n [4]. 3 Th Mol 3.1 Data Dnny Bas Intuson Dtton Mol In ths ston, w vy bfly suss th ata nny bas atabas ntuson tton mol, whh was snt n [12]. Ths mol has two omonnts,

3 nalyss of Data Dnny Bas Intuson Dtton Systm 113 namly, th stat smant analyz an th ynam smant analyz. Th stat smant analyz s mloy to analyz th atabas alaton ogam statally to sov nta-tansaton ata nns snt by th a, -wt, an ost-wt st. If a tansaton os not onfom to th a, -wt, o ost-wt sts, t wll b ntf as a malous tansaton. Ths s tat as th fst ln of fns. In as, th malous tansatons a wll-aft an a omlant wth th ata nns sov by th stat smant analyz, th ass attns to ths sts an b us to sov malous tansatons. Th ass obablts fo ths sts n on th xuton ath of th atabas alaton an th nomal us ass attns of th atabas. Th ynam smant analyz s sgn to alulat th ass obablty bas on th atabas log. To hav a btt unstanng on th ata nny bas atabas ntuson tton mol, w llustat an xaml h. Suos ung nomal atabas oaton has, two tansatons T 1 an T 2 a gnat by th atabas alaton. ssum that w hav th SQL statmnts n T 1 an T 2 as shown n Tabl 1. Tabl 1. T 1 T 2 Uat Tabl1 st m j wh Uat Tabl1 st m wh Uat Tabl1 st n m k wh Uat Tabl1 st t m q wh Th stat smant analyz wll gnat th a, -wt, an ost-wt sts as llustat n Tabl 2. Lt us us ata tm m to llustat th uos of ths sts an how thy an b us to ntfy malous atabas tansaton. Data tm m has non-mty a st an ost-wt st. Th a st stats that bfo ata tm m s uat by th tansaton, th ata tms n {, j} o {, } hav to b a by th tansaton. Th ost-wt st stats that aft m s uat, ata tm n an t hav to b uat by th sam tansaton. las not that th wh lauss hav bn gno to k ths xaml shot an may not b so n alty. If a tansaton uats ata tm m wthout omlyng wth uls sf by th a st an ostwt st, t wll b ntf as an anomalous tansaton. Tabl 2. Ra St -Wt St ost-wt St m { {, j}, {, } { } { {n,t}} n { {m, k} } { {m} } { } t { {m,, q} } { {m, n} } { } If an attak s tansaton s wll-aft an onfom to th ata nns sf, th ynam smant analyz thn sts n. Say, n alty, th ass obablts of {, j} an {, } n th a st of m a ffnt fo nomal us

4 114 Y. ugmanov, B. ana, an Y. Hu tansatons an st {, } s only nfquntly us fo uatng m n sal oasons. If th attak s tansaton uatng m as {, } nsta of {, j} bfo mofyng m, th ass obablty of th a st gnat by th ynam smant analyz an b us to ntfy ths anomalous tansaton. o mo nfomaton on th ata nny bas atabas ntuson tton mol, ntst as may f to [12]. s th qumnt of th ata nny bas atabas ntuson tton mtho, th an b only two tys of uss: nomal uss an ntus. omal uss a authoz uss, who onnt to th atabas only though th atabas alaton an, thfo, an gnat only lgal tansatons. Intus a unauthoz uss, who onnt to th atabas fom a mot tmnal masquang as nomal uss. Th a many ways to tn to b a nomal us. o xaml, an ntu an obtan a asswo of th lgtmat aount o tak ontol of a nomal us s atabas onnton. In any as, n o to gt an ass to th atabas, an ntu must fn som vulnablty an xlot t. 3.2 obablty of Intuson Th a th man fatos that ontbut to th ost of anomaly tton. Ths fatos shoul b takn nto onsaton n th analyss of th otmal onfguaton of a ata nny bas ntuson tton systm. Th fst fato s th tton at of th systm. Th mtho sb n [4] was aat to stmat ths aamt. Th son fato s th ato of ntusons to lgal atvts. W assss ths valu by assumng that th numb of ntusons ns on th numb of vulnablts n th omut systm that may allow an attak to stablsh a onnton to th atabas ott by th systm. Bays fomula fo osto obablty s us to fn th atual obablty of attak n sn o absn of an alam sgnal. Th last fato s th losss nu by an oganzaton n ffnt outoms of a sngl attak. Ths valus fn whh sons statgy th oganzaton ns to aly. Th otmzaton ontons fo th sons statgy a foun by mans of lna ogammng. Th otmal valu of thshol s v omutatonally. If both val an llgal tansatons a gnat at th sam at, th xt at of ntusons among all tansatons an b xss th as follows: αψ λ αψ ϕ wh α s th ooton of sussfully xlot vulnablts to all sov vulnablts, ψ s th at at whh vulnablts a sov an ϕ s th at at whh nomal uss stablsh onntons to th atabas. Th valu of ϕ an b asly tv by analyzng th atabas log. In o to fn ψ, t s nssay to fn out what sot of vulnablts an b us by an ntu to stablsh a onnton to th atabas. o xaml, f th oatng systm on whh th atabas alaton s loy has a vulnablty that allows gttng unauthoz ass to ths systm, th ntu fnally wll b abl to stal th asswo of a lgtmat atabas us an stablsh a onnton to th atabas. Thn, usng th nfomaton sul by th vno o oth oganzatons suh as Comut Emgny Rsons

5 nalyss of Data Dnny Bas Intuson Dtton Systm 115 Tam, w an stmat th at at whh suh vulnablts a sov. Th most ffult s to valuat th valu of α whh ns on a lag numb of vaous fatos. Th obablty that tan vulnablty wll b sussfully us fo an attak s gatly nflun by th sonalty of th nvual who fst sov ths vulnablty. If th vulnablty was sov by th vno, t wll vy lkly not b announ bfo th hot fx s las. If th vulnablty s sov by a otntal ntu, vythng ns on th ntu s bhavo: a hak an th onut an attak o ublsh th sov vulnablty. W an assum that, n th fst as, th s always a ossblty that nsta of attakng a sngl tagt, th hak an anomly hoos a tagt o fom a mass attak aganst all known uss of th vulnabl softwa o hawa. If th vulnablty s ublsh, th obablty that ths vulnablty wll b us aganst a sngl oganzaton onsably nass. ll ths fatos sgnfantly omlats th alulaton of α. Hn, to smlfy th oblm, w assum that α s th faton of vulnablts sussfully utlz by haks bfo th ath has bn al by a vno. Thus, lyng on th statsts of sussful attaks w an stmat th valu of α, whh, n tun, allows us to fn th ntuson at. 3.3 Evaluaton of th Data Dnny Bas Databas Intuson Dtton s xlan al, th ata nny bas ntuson tton systm uss th nns among th ata tms n th atabas. Bfo a ata tm s uat n th atabas, som oth ata tms a a o wttn, an aft th uat, oth ata tms an b wttn too. Malous tansatons a tt by omang a, -wt an ost-wt sts aganst ata tms atually a o wttn by us tansatons. lso th ass obablty fo ths sts an b us to ntfy malous tansatons. Wthout loss of gnalty w an fomulat ata nny bas ntuson tton mtho as th followng two uls: 1. Stat Dtton Rul: Eah uat oaton of a tansaton must onfom to th ata nns snt by th a, -wt, an ost-wt sts; 2. Dynam Dtton Rul: Eah uat oaton of a tansaton must onfom to th nomal us ass attns of ffnt sts n th a, -wt, an ost-wt sts. omally th uat oatons of a tansaton a squntally tst fo omlan wth both th uls. Th tansaton s ons llgal f any of ts uat oatons os not onfom to at last on of th uls. Howv, fo th uoss of analyss w assum that ntally all of th uat oatons of a tansaton a tst fo omlan wth th fst ul. W all ths ou stat tton. Thn, th uat oatons a tst fo omlan wth th son ul, whh w all ynam tton. Th tansaton s ons llgal f any of ts uat oatons fals to ass th th stat o th ynam tton ou. It s obvous that ou aoah ous th ntal sults wth th ognal tton mtho. Eah tansaton that gos though th stat analyz auss th aton of th ata nny whh th tansaton onfoms to. In oth wos, tansatons that w us to gnat th ata nns a always ntf as lgal by th

6 116 Y. ugmanov, B. ana, an Y. Hu stat tton. Sn, by fnton, th stat analyz taks nto onsaton all tansatons that an b gnat by th atabas alaton, w an assum that th fals ostv at of th stat tton quals to zo. tually, ths assumton sms to hol n most al-lf stuatons, as th tansatons whh w omtt ung th stat analyss a lkly to b val lat, n ous of gnatng th log fl fo ynam analyss. Th xmnts onut by [12] ov th mal vn of ths assumton, sn, aong to th sults, th fals ostv at always quals to zo, whn th tton s bas only on th sults of stat smant analyss. ot that th tansatons ntf as malous by th stat tton wll b lassf as llgal galss of th sult of th ynam tton. Thfo, f w not ST as th tu ostv at of th stat tton, thn th agggat tton at of both stat an ynam tton an b alulat as follows: 1 T ST wh DT s th at at whh th ynam tton otly ntfs ntusons mslassf by th stat tton. Th stat tton annot b ma mo o lss stt, so that ST s a onstant valu unlss th atabas alaton s mof. ST an b xss as th ooton of th tansatons ntf as llgal by th stat tton to all llgal tansatons. To obtan ths ooton, w n to onstut a st of saml ntusons an tst th stat tton ou aganst ths st. If th slt samls a sntatv, w wll gt an natv ST valu. Unlk th stat tton, th ynam tton an b ma mo o lss stt by gulatng th thshol valu. Ths mans that th xsts a Rv Oatng Chaatst ROC uv whh lots DT aganst fals ostv at. lthough th ROC uv an also b v mally, w wll n to onut a lag amount of tsts. Thfo, t s btt to us an analytal mtho fo fnng onomally otmal onfguaton of ynam tton. omally, th ynam analyz omuts th total us obablty fo ah ata tm st an maks t as nfquntly us f th valu s lss than th thsholτ. In o to omly wth ata nns, a tansaton ns to ass all ata tms of at last on ata tm st of ah a, -wt an ost-wt sts that snt ths ata nns. Th ynam tton gnats an alam sgnal whn th tansaton nlus at last on ata tm st whh s mak as nfquntly us. Lt us mak som altatons of ths mtho. Suos, th ata nns at by th stat analyz altogth ontan ata tm sts, D 1, D 2,,D. Insta of makng ata tm sts as nfquntly us, th ynam analyz assoats ah ata tm st wth ts total us obablty M D, 1. ow, suos that tansaton T asss all mmbs of K ffnt ata tm sts, K. Dung th analyss of T, th ynam tton fns th mnmum μ of th valus assoat wth ah of K ata tm sts, ST DT μ mn{ M, M,..., M }. D1 D2 DK

7 nalyss of Data Dnny Bas Intuson Dtton Systm 117 Thn, ths valu s oma aganst th thshol τ. If μ s gat than o qual to τ, thn tansaton T os not nlu any nfquntly us ata tm,.., all K ata tms hav th total us obablty that a gat than th thshol an th tansaton s nomal. If μ s lss than τ, thn th tansaton nlus at last on nfquntly us ata tm, so that an alam sgnal s gnat. Evn though th altatons w ma o not hang th outom of th ynam tton, thy aang ths ou to th fom to whh w an aly an analytal mtho. Th only xton s that th sult s nvt wth ga to th thshol valu, so that w n to hang th lmts of ntgaton. s a sult, usng th bas fomulas fom [17], w xss DT an as follows: DT τ μ σ τ μ σ x 1 2 U x x x, 2π τ μ L σ τ μ L σ L x 1 2 U x x x ; 2π L 2 2 wh τ s th tton thshol, μ L s th man valu of μ fo lgal tansatons, μ s th man valu of μ fo ntusons, σ L s th vaan of μ fo lgal tansatons, σ s th vaan of μ fo ntusons, an Ux s th obablty nsty funton fo both nomal an malous atabas tansatons. Sam vaan fo nomal an malous atabas tansaton s assum. So ssntally, DT o snts th ntgaton of th nomal nsty funton. gu 1 llustats a saml omutaton of DT an. g. 1. Comutaton of DT an

8 118 Y. ugmanov, B. ana, an Y. Hu Bfo fomng analytal analyss w n to stmat th valus of μ L, an σ L, μ an σ. Th fom two valus an asly b v fom th log fl. In o to obtan th latt two valus w n to fn llgal tansatons that a lassf as lgal by th stat tton an bul a st of saml ntusons. Th samls must b sntatv; othws, th omut valu wll not nat th al fals ostv at. 3.4 Otmal Rsons Statgy n oganzaton may o may not hav to son to th alam sgnal gnat by th ntuson tton systm. Th sons usually onssts of manual nvstgaton of th vnt whh aus th alam. If th vnt s n malous n natu, th manual nvstgaton allows ovng a at of th amag aus by th ntuson. Howv, th nvstgatons a ostly, sn thy ngag sous, both ol an qumnt, an oftn ntf wth th ongong wok. Thfo, an oganzaton must to nvstgat an alam sgnal, only f th s a gat lklhoo that th alam was aus by an ntuson. In o to mak a ason son, an oganzaton ns to fn th obablty of ntuson gvn oun of alam, whh s xss, n as of ata nny bas ntuson tton, by th followng fomula: I I I I I I I Tλ λ 1 λ wh λ s th ntuson at. In fat, an oganzaton may to launh an nvstgaton vn f th s no alam sgnal, assumng that th ntuson tton systm ou a fals ngatv outom. In ths as, th oganzaton wll n to valuat lablty of ts ntuson tton systm by omutng th osto obablty of ntuson gvn th absn of an alam sgnal, as follows: I I I I I I I 1 T T 1 T λ λ 1 1 λ If an nvstgaton fns that a susous tansaton n fat s llgal, th oganzaton stats ovy ou to sto th ata amag by ths tansaton. Sn nvstgatons a ostly, an oganzaton may sk th nvstgaton ou an mmatly stat th atabas amag assssmnt an ovy ous to anl out th ffts of th tansaton whh aus an alam sgnal. That s, th oganzaton fully ls on th son ma by th ntuson tton systm. Howv, n as of tton o, th oganzaton wll nu losss by ollng bak a lgal tansaton. In ontast, a manual nvstgaton always lafs th tu ty of a tansaton, so that th ovy that follows a manual nvstgaton nvolvs only llgal tansatons. Lt not th ost of manual nvstgaton, snt th ost of a ollbak oaton, snt th amag aus by a sussful ntuson, an not th loss aus by a ollbak oaton ov a lgal tansaton. Thn, th xt ost of a tansaton whn an alam s gnat s tmn by th followng quaton:

9 nalyss of Data Dnny Bas Intuson Dtton Systm 119 ; 1 1, wh s th faton of manually nvstgat alam sgnals, an s th at at whh th tansatons ntf as llgal a automatally oll bak by mloyng a atabas ovy ou. Ths funton, howv, os not flt th nt xt ost, as t os not tak nto onsaton th losss nu n th absn of th alam, whh a omut as follows: ; 1 1, wh s th at at whh tansatons lassf as lgal a nvstgat, an s th at at whh tansatons lassf as lgal a automatally oll bak. gu 2 llustats th ossbl sonss n both alam an no alam ass. g. 2. ossbl Rsonss om th xt osts of a tansaton n both alam an no alam ass, w an tmn th total ost as th athmt man of ths valus: T T T λ λ λ λ Th vaabls,,, fn th otmal sons statgy an must b hosn to ov mnmal valus of an. Th otmzaton ontons wth ga to ths funtons a ntal, sn both of thm a xss by th sam fomula; th only xton s th ffnt obablty aamts. W xamn th otmzaton ontons by th xaml of. Tansaton lam o lam Invstgat Invstgat Rollbak Rollbak Do nothng 1- Do nothng 1- -

10 120 Y. ugmanov, B. ana, an Y. Hu Th task of fnng th mnmal ost an b snt as th oblm of lna ogammng [16] wth an objtv funton, that s a subjt to th followng nqualty onstants: 0 1, 0 1, an 0 1. Ths nqualts follow fom th fat that an snt th ootons of sonss to th v alam sgnals. s shown n gu 3, thy ou th gon of ossbl solutons lmt by both oonat axs an th ln xss by funton 1. g. 3. Soluton Rgon fo It s known that at last on of th vts of fasbl gon snts th otmal soluton [16]. In ou as, th xst th ossbl solutons that oson to th vts of th tangl-sha gon: 1. 0, 0; 2. 1, 0; 3. 0, 1. Eah of ths solutons boms otmal un tan ontons. Ths ontons a fn by th offnts of th vaabls an. o smlty, w snt ths offnts as follows: a, b In ths as, w an snt as., a b. It s obvous that 0 an 0 s th otmal soluton f a 0, b 0. W an ov t by ontaton. st, lt us fn th mnmal valu of th xt ost:

11 nalyss of Data Dnny Bas Intuson Dtton Systm 121 0,0 a 0 b 0. ow, lt us assum that th xst suh an that, s lss than,.. a b <. In ths as, th followng onton s nssay to hol: a b < 0. Sn th nqualty onstants vnt an fom atng ngatv valus, ths onton ontats to th ntal onton that both a an b a gat than o qual to zo. 1 an 0 s th otmal soluton f a < 0, a b. In ths as th mnmal valu fo, s 1,0 a 1 b 0 a. Lt us assum th xst suh an, > 0, 1,that, ats a lss valu,.., Knowng that a b < a. a a 1, w an snt th vous nqualty n th fom of a a b < a. Smlfyng t, w wll gt a > b, whh ontats to a b. 0 an 1 s th otmal soluton f b < 0, b < a. W an ov ths onton n th sam way as th vous on. ow w an alulat what ato of th al valus ah otmal soluton osons to. om a 0, follows that.., 0, om b 0, follows that 0,.

12 122 Y. ugmanov, B. ana, an Y. Hu.., om.., a b, follows that, Thus, th otmzaton ontons fo an b fomulat as shown n Tabl 3... Tabl 3. Otmzaton ontons an 0 0 < < an an 1 0 < 0 1 Th sam ontons fo a ahv by lang wth. To sum u, th oganzaton s atons to otmz th tansatons shoul onsst of th followng sts: 1. Slt a sntatv st of known llgal tansatons an tst th stat tton aganst th st to stmat ST as th ooton of th tansaton ntf as ntusons to all tansatons n th st; 2. n μ fo ah of th llgal tansatons ntf as lgal by th stat tton, omut man μ an vaan σ ; 3. Slt th sntatv st of known lgal tansatons an fn μ fo ah of ths tansatons; omut man μ L an vaan σ L. 4. Dtmn α, ψ an ϕ an alulat th at of ntusons λ; 5. Dtmn th oganzaton s ost mts xss by,,, ; 6. n th otmal onfguaton,.. th valus of T, τ,,,, ; 7. St th thshol to τ ; 8. ollow th sons statgy fn by,,,. Sn many of th ntal vaabls hang th valus n ous of tm, th oganzaton must oally at ths oatons to uat th otmal onfguaton.

13 nalyss of Data Dnny Bas Intuson Dtton Systm Exmntal Rsults s mnton n Ston 3.2, th a th fatos afftng th ost of th ntuson tton. Changng of any of ths fatos las to th altaton of th fnal outom. Howv, as Tabl 3 nats, th absolut valus of th ost mts xss by,, an a lss motant than th ootons of ths fou vaabls. Th ootons of th fst two aamts a unlkly to hang wth tm; moov, th valus of an a xt to b of th sam magntu, as both th nvstgaton of an alam sgnal an th ovy fom an onous ollbak qu human ntaton. In ontast, th valu of may sgnfantly vay, as th amag aus by an attak ns on th natu of th ata sto n th atabas. Gvn that th ollbak s on of th ky fatus of atabas managmnt systms, s xt to b muh small than an. om ths onsatons, th followng vaants of th ost mts w slt fo tstng: 1. 1, 100, 10000; 2. 1, 100, 50000; 3. 5, 100, 50000; In th fst vaant, w assum that th amag aus by a sussful ntuson s 100 tms gat than th ost of nvstgaton an th ost of ovy fom a falsly onut ollbak, whh, n tun, a 100 tms gat than th ost of a ollbak oaton. In th son vaant w nas th otntal amag, whl oth aamts man th sam. In th th vaant w atonally nas th ost of a ollbak oaton. Th qualty of ntuson tton s xss by ST, μ L, μ,σ L an σ. Ths aamts shoul not sgnfantly hang wth tm, unlss th ntuson tton systm has bn loy wthout a o tanng. W tst th ogam aganst ffnt sts of th aamts, an slt thos whos tst sults a mo llustatv: ST 0.4, μ L 0.6, μ 0.4, σ L 0.2, σ 0.2. In o to show how th obablty of ntuson nfluns th otmal onfguaton, w hos th valu of λ to vay fom 10-5 to gu 4 llustats th total xt ost fo all th vaants of ost mts. Th x-axs of th gah s a logathm sal sntng th valus of λ. It must b not that th ata ov n ths fgu s a small subst of that obtan though th xmnt; u to ag lmtaton, w oul not ou th nt sult h. s gu 4 nats, n st of th fat that n th son vaant, th valu of otntal amag s fv tms gat than that n th fst on, th maxmum valu of th ost funton os not nas sgnfantly. Howv, a lag valu of nass th gowth at of th ost funton. In ontast, th ost of ovy fom an onous ollbak affts th maxmum valu of th ost funton. uthmo, as gu 4 ts, th osts stat to ln at som ont. lthough t sms atyal, th xlanaton fo ths hnomnon s that th gowth of ntuson at ass

14 124 Y. ugmanov, B. ana, an Y. Hu Cost Vaant 1 Vaant 2 Vaant Intuson at g. 4. Total Cost fo Dffnt Vaants of Cost Mts th untanty of ntuson tton oss. In oth wos, hgh ntuson at mts mo auat sons, thus, fftvly sonng to th attaks. 5 Conlusons In ths a, w hav snt a mol that an b us to tmn th onomally otmal onfguaton of th ata nny bas ntuson tton systm. Th man aamts a takn nto onsaton n ou mol: th ntuson at, th qualty of th ntuson tton, an th ost mts of an oganzaton. W snt a st by st mthoology that hls n fnng th otmal onfguaton, xss by th sons statgy an th thshol valu. Ou xmntal sults suggst that th valu of otntal amag os not ootonatly afft th total ost funton. Howv, th ovy ost assoat wth an onous ollbak sgnfantly affts th maxmum valu of th ost funton. uthmo, th xmnt llustat that th ynam tton s usful only at hgh ntuson ats. Thfo, whl th xt at of ntuson mans asonably low, an oganzaton may smly ly on th stat tton an stll mantan a low total xt ost of th ntuson tton. s at of ou futu wok, w lan to onut futh xmnts to ntfy otmal sons statgy un vaous umstans. knowlgmnt Ths sah has bn suot n at by US OSR un gant an th KY S ESCoR ogam. W a thankful to D. Robt. L. Hklotz an Jffy Mossy fo th suot, whh ma ths wok ossbl.

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