On the Security of a Digital Signature with Message Recovery Using Self-certified Public Key

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1 Informatca 29 (2005) On the Securty of a Dgtal Sgnature wth Message Recovery Usng Self-certfed Publc Key Janhong Zhang 1,2, We Zou 1, Dan Chen 3 and Yumn Wang 3 1 Insttuton of Computer Scence & Technology, Peng Unversty, Beng, P.R.Chna E-mal: hzhs@eyou.com, zouwe@cst.pu.edu.cn 2 College of Scences, North Chna Unversty of Technology, Beng, P.R.Chna E-mal: hzhang@ncut.edu.cn 3 State Key Lab.of ISN, Xdan Unversty, X an, Shaanx, P.R.Chna E-mal: ymwang@xdan.edu.cn Keywords: dgtal sgnature, message recovery, self-certfed publc ey, mproved scheme Receved: Aprl 7, 2005 Self-certfed publc eys are proposed to elmnate the burden of verfyng the publc ey before usng. To allevate relance on system authorty and strengthen the securty of system, Chang et al propose a new dgtal sgnature schemes, no redundancy s needed to be embedded n the sgned messages n ths scheme. Moreover, Chang et al clamed that the schemes are stll secure even wthout the trustworthy system authorty, and only the specfed recpent can recover the message n hs authentcaton encrypton schemes. Unfortunately, In ths wor, we analyze the securty of Chang et al scheme and show that f the system authorty s trustless, the scheme s nsecure, namely, the system authorty can recover the message wthout the prvate ey of the recpent n Chang authentcaton encrypton schemes. Fnally, we propose an mproved scheme to overcome the weaness of Chang et al scheme. Povzete: Predstavlena e tehna dgtalnega certfata z avnm lučem. 1 Introducton In tradtonal publc cryptosystem, each user has two eys, a prvate ey and a publc ey. The user can use hs prvate ey to produce a sgnature for a message, and any verfer can chec whether ths sgnature s vald or not by the user s publc ey. The publc ey of all users s publc n a publc drectory. However, these systems suffer from the well-nown authentcaton problem. In order to ensure the authentcty of publshed publc eys, usually there exsts a certfcate authorty (CA) to ssue a certfcate for every publc ey. Then every user reles on CA to valdate publc eys n the system. Shamr ntroduced n 1984 the concept of dentty-based cryptography[1]. The dea s that the publc ey of a user be publcly computed from hs dentty (for example, from a complete name, an emal address or an IP address). Then, the secret ey s derved from the publc ey. In ths way, dgtal certfcates are not needed, because anyone can easly verfy that some publc ey PK U corresponds n fact to user U. However, the user s prvate ey s chosen by a trusted authorty (TA). Ths approach maes user relance on TA. Based on the above ID-based cryptography s problem, the concept of self-certfed publc ey was frst ntroduced by Grault[10] n In the self-certfed publc ey cryptosystem, each user publc ey s generated by the CA, whle the correspondng prvate ey n only nown to the user. The authentcty of publc eys s mplctly verfed wthout the certfcate. That s, the verfcaton of the publc eys can be carred out n the sgnature verfcaton phase smultaneously. Recently, Tseng[8] et al proposed a new dgtal sgnature scheme wth message recovery and two varants based on the self-certfed publc system above. There exsts a trusted system authorty n Tseng et al schemes; however, the trusted authorty s not exstent n real world. Thereby, Ya-Fen Chang et al [3] propose a new dgtal sgnature schemes wth message recovery, whch provde the same functon as Tseng et al s scheme wthout the assumpton that TA s not necessary to be relable. To demonstrate convenently, we call the scheme of lterature [3] as Chang scheme. In ths wor, we gve a securty analyss of Chang scheme, and show

2 344 Informatca 29 (2005) J. Zhang et al. that the scheme s nsecure, namely, the system authorty can recover the message wthout the prvate ey of the recpent n Chang authentcaton encrypton schemes. Fnally, we gve an mproved scheme to overcome the weaness. The organzaton of ths paper s shown as follows. In Secton 2, we revew Chang et al s dgtal sgnature scheme and authentcaton encrypton scheme. In Secton 3, we gve securty analyss to Chang et al scheme. Our mproved dgtal sgnature scheme s presented n Secton 4. Fnally, we draw some conclusons. 2 Revew of Chang et al Scheme In the secton, we wll bref descrbe Chang et al s dgtal sgnature scheme wth usng self-certfed publc ey and hs authentcaton encrypton, the scheme conssts of three phases: the system ntalsaton phase, sgnature generaton and message recovery phase. 2.1 Sgnature Scheme wth Message Recovery System ntalzaton phase: n ths phase, a system authorty (SA) s responsble for generatng system parameters; note that ths system authorty s trustless. He selects two same sze safe large prmes p and q, whch satsfy p= 2p + 1and q= 2q + 1where p and q also are large prme, and he computes RSA modulus N = p q. Then, he chooses a generator g of the order p q and a publc collson-resstant hash functon h() whch accepts a varant-length nput strng of bts and produces a fx-length output strng of bt as specfed n [2]. Fnally, the system authorty eeps p, qpq,, secret, and publshes g, Nh, () publc. When a user U wth hs dentty ID ntends to on ths system, frst he generates hs publc ey. Therefore, he randomly chooses a number x as hs prvate ey and x computes p = g mod N. Then, the user U sends ( ID, p ) to the system authorty. After recevng ( ID, p ), the system authorty computes the publc ey 1 ( ) y ( ) h ID = p ID modn of the useru, the user U can verfy whether t holds by the h( ID) x equaton p ID g mod N + =. Sgnature generaton phase: When a user sgn a message M, the sgnng procedure s as follows: Step1: the user U chooses a random number. Step2: compute r1 = M g mod n, r 1 r2 = M g mod n and s = r1 x h( r2). The resultant sgnature on message M s ( r1, r2, s ). U wants to Message recovery phase: after the recpent receves the sgnature ( r1, r2, s ), he can verfy the sgnature and recover the message M by the followng steps: Step1: the verfer uses ID and p of the sgner to recover the sgned message M by computng s h( ID ) hr ( 2 ) M = r2 g ( p + ID) modn Step2: after recoverng the message, the verfer checs the recovered message M further by the followng equaton 1 r1 ( r 1 1 M ) modn = r2 M modn After the above verfcatons passes, t means that the sgnature s vald. 2.2 Authentcaton Encrypton Scheme Chang et al proposed two authentcaton encrypton schemes based on the scheme above. One s called authentcaton encrypton scheme whch only allows that a specfed recever can verfy and recover the sgned message; the other s called authentcated encrypton scheme wth message lnages that s used to transmt large message. In fact, the second scheme s the extenson of the frst authentcaton encrypton. We only consder the frst scheme n the followng. The scheme s dvded nto three phases: system ntalzaton phase, sgnature generaton phase, and message recovery phase. System Intalzaton Phase The system ntalzaton phase s the same as one of the above Chang et al s sgnature. Because the space s lmted, we omt t Sgnature Generaton Phase If the user U wants to sgn and encrypt a message M to a specfed recever U, the generaton procedure of the sgnature s as follows. Step1: frst chooses a random number. Step2. compute h( ID ) h( ID ) r1 = M ( p + ID) modn r1 r2 = M ( p + ID) modn and s = r1 x h( r2). Step3: U sends the sgnature ( r 1, r 2, s) to the verfer U Message recovery phase After recevng the sgnature ( r 1, r 2, s ), the verfer U recovers the message M and verfes that the sgnature ( r, r, s) s vald by the followng equatons. 1 2 s h( ID ) hr ( 2 ) x 2 ( ( ) ) mod M = r g p + ID n And the verfer U further checs whether 1 r1 ( r M ) modn = r M 1 modn holds or not. 1 2

3 ON THE SECURITY OF A DIGITAL... Informatca 29 (2005) Securty Analyss of Chang et al Sgnature and Authentcaton Encrypton Chang et al clamed that ther schemes are secure wthout the assumpton that system authorty s trustworthy. In hs authentcaton encrypton scheme, Chang et al clamed that only the specfed verfer can recover the message M from the sgnature. Unfortunately, we show that f the system authorty s trustless, we can attac ths scheme. Frst, we gve a securty analyss to Chang et al prmtve sgnature, and then we analyze the securty of the authentcaton encrypton. Because the authentcaton encrypton s based on Chang et al sgnature scheme, f Chang et al sgnature scheme s nsecure, then authentcaton encrypton and the extenson vson of ths authentcaton encrypton s also nsecure. In the followng, we wll consder the securty of the scheme. Accordng to the above sgnature phase of Chang et al scheme, we now that a sgnature ( r 1, r 2, s) of a message M satsfes r1 = M g mod N, r M g N r 1 2 = mod Supposed that the system authorty s trustless, because the system authorty nows the factorng of n, he also nows pq, whch s the order of the base g. Hence, he can perform as follows. Step1: ths system authorty computes r1 (1 r1 ) α = = g mod N. r 2 1 Step2: compute β = (1 r) mod pq Step3: compute 1 1 (1 r1) β (1 r1) (1 r1) β γ = α mod N = ( g ) mod N = ( g ) mod N = g mod N Step 4: recover the message M as the followng r M = 1 mod N γ The system authorty can recover the message M from the sgnature ( r 1, r 2, s) wthout the nformaton ( ID, p ) of the sgner U. In the followng, we consder how to attac the Chang et al authentcaton encrypton. Accordng to the sgnature phase of the Chang et al s authentcaton encrypton scheme, we now that the sgnature ( r1, r2, s) satsfy the followng relaton h( ID ) r1 = M ( p + ID) modn h( ID ) r1 2 = ( + ) mod r M p ID N Supposed that the system authorty s trustless, the system authorty nows the factorng of n. Accordng to the above way, the attac procedure s as follows: Step1: ths system authorty computes α r 1 h( ID ) (1 r1 ) = = ( p + ID) modn. r2 1 Step2: compute β = (1 r) mod pq Step3: compute β h( ID ) (1 r1 ) β h( ID ) 1 (1 r1)(1 r1) γ = α mod N = ( p + ID ) mod N = ( p + ID ) modn h( ID ) = ( p + ID ) modn 1 Step 4: recover the message M as the followng r M = 1 mod N γ If the system authorty ntercepts the sgnature ( r1, r2, s) of the message M from the channel between the sgner U and the recpent U, then he can recover the message M wthout the prvate ey of the recpent U. Accordng to the way ale, the attac mounts to the second authentcaton encrypton. 4 An Improved Scheme To overcome the weaness of Chang et al scheme, we suggest an mproved scheme. In our mproved scheme, System ntalzaton phase s the same as one of Chang et.al. scheme. The dfference s Sgnng phase and Verfyng phase. [Sgnng phase] If the user U wants to sgn and encrypt a message M to a specfed recever U, the generaton procedure of the sgnature s as follows. Step1: frst chooses a random number. Step2. compute h( ID ) h( M ) h( ID ) r1 r1 = M ( p + ID ) modn r2 = M ( p + ID ) modn and s = r1 x h( r2). Step3: U sends the sgnature ( r 1, r 2, s) to the verfer U. [Verfyng phase] After recevng the sgnature ( r 1, r 2, s ), the verfer U recovers the message M and verfes that the sgnature ( r1, r2, s) s vald by the followng equatons. s h( ID ) h( r2 ) x M = r2 ( g ( p + ID) ) modn And the verfer U further checs whether

4 346 Informatca 29 (2005) J. Zhang et al. ( r M ) mod N = ( r M ) modn 1 r1 1 hm ( ) 1 2 holds or not. Our mproved scheme can extend to the same authentcaton encrypton as Chang et al scheme. Here we omt t for the lmted space. h( ID ) ( ) h M By revsng r 1 nto r1 = M ( p + ID) modn, we prevent the above attac and mae that anyone (except for the sgner and the specfed recever) cannot recover the message M from the sgnature ( r 1, r 2, s ), even f the system authorty can not recover the message. Compared wth the Chang et al scheme, only one more hash functon s requred n the mprovement scheme; however, the hash computaton s neglgble. Therefore the mprovement preserves the Chang et al clamng merts; namely, our scheme s secure wthout a trusted system authorty and effcent. 5 Concluson Self-certfed publc eys are proposed to elmnate the burden of verfyng the publc ey before usng t. However, there exsts a trusted authorty n ordnary selfcertfed publc ey system; the trusted authorty s not guaranteed to be honest n the real world. To strengthen the securty of system, Chang et al propose a new dgtal sgnature schemes, no redundancy s needed to be embedded n the sgned messages. Moreover, the schemes are stll secure even wthout the trustworthy system authorty. In ths wor, we gve a securty analyss to Chang et al scheme and show that f the system authorty s trustless, the scheme s nsecure. Fnally, we propose an mproved scheme to overcome the weaness of Chang et al scheme. References [1] A. Shamr, Identty-based cryptosystem based on the dscrete logarthm problem, n Proceedngs of CRYPTO_84, 1985, pp [2] Zuhua Shao, mprovement of dgtal sgnature wth message recovery usng self-certfed publc eys and ts varants Appled Mathematcs and Computaton 159 (2004) [3] Y.F.Chang, C.C.Chang, H.F.Huang, Dgtal sgnature wth message recovery usng selfcertfed publc eys wthout trustworthy system authorty[j], Appled Mathematcs and Computaton, Vol 161, n 2005, pp [4] P. Horster, M. Mchels, H. Petersen, Authentcated encrypton schemes wth low communcaton costs, IEE Electroncs Letters 30 (15) (1985) [5] K. Nyberg, R.A. Ruppel, Message recovery for sgnature schemes based on the dscrete logarthm, n: Proceedngs of EUROCRYPT_94, 1994, pp [6] R.L. Rvest, A. Shamr, L. Adelman, A method for obtanng dgtal sgnature and publc ey cryptosystem, Communcatons of ACM 21 (2) (1978) [7] A. Shamr, Identty-based cryptosystem based on the dscrete logarthm problem, n Proceedngs of CRYPTO_84, 1985, pp [8] Y.M. Tseng, J.K. Jan, H.Y. Chen, Dgtal sgnature wth message recovery usng self-certfed publc eys and ts varants, Appled Mathematcs and Computaton 136 (2003) [9] W. D.e, M.E. Hellman, New drectons n cryptography, IEEE Transactons on Informaton Theory IT-22 (6) (1976) [10] M. Grault, Self-certfed publc eys, n: Proceedngs of EUROCRYPT_91, n 1991, LNCS, sprnger-verlag, pp

5 Informatca 29 (2005) Obect Groupng and Replcaton Algorthms for Word Wde Web A. Mahmood Department of Computer Scence Unversty of Bahran Kngdom of Bahran E-mal: Keywords: Data mnng, document clusterng, obect replcaton, Web, dstrbuted web-server system, document replcaton. Receved: December 4, 2004 Ths paper presents an algorthm to group correlated obects that are most lely to be requested by a clent n a sngle sesson. Based on these groups, a centralzed algorthm that determnes the placements of obects to a cluster of web-servers s proposed to mnmze latency. Due to the dynamc nature of the Internet traffc and the rapd changes n the access pattern of the World-Wde Web, we also propose a dstrbuted algorthm where each ste reles on some collected nformaton to decde what obect should be replcated at that ste. The performance of the proposed algorthms s evaluated through a smulaton study. Povzete: Gruprane obetov na spletu. 1 Introducton An ever-ncreasng popularty of Word Wde Web has brought a huge ncrease n traffc to popular web stes. As a result, users of such web stes often experence poor response tme or denal of a servce (tme-out error) f the supportng web-servers are not powerful enough. Snce these stes have a compettve motvaton to offer better servce to ther clents, the system admnstrators are constantly faced wth the need to scale up ste capacty. There are generally two dfferent approaches to achevng ths [1]. The frst approach s to use powerful server machnes wth advanced hardware support and optmzed server software. Unfortunately, ths approach s expensve and complcated one and the ssue of scalablty and performance may persst wth ever ncreasng user demand. The second approach, whch s more flexble and sustanable, s to use dstrbuted and a hghly nterconnected nformaton system or dstrbuted web server system (DWS). A dstrbuted web server system s any archtecture of multple stand-alone web server hosts that are nterconnected together and act as a logcally sngle server [2]. A DWS s not only cost effectve and more robust aganst hardware falure but t s also easly scalable to meet ncreased traffc by addng addtonal servers when requred. In such systems, an obect (a web page, a fle, etc.) s requested from varous geographcally dstrbuted. As the DWS spreads over a MAN or WAN, movement of documents between server nodes n an expensve operaton [1]. Mantanng multple copes of obects at varous locatons n DWS s an approach for mprovng system performance (e.g. latency, throughput, avalablty, hop counts, ln cost, and delay etc.) [1-3]. Web cachng attempts to reduce networ latency and traffc by storng commonly requested documents as close to the clents as possble. Snce, web cachng s not based on the users access patterns, the maxmum cache ht rato achevable by any cachng algorthm s bounded under 40% to 50% [4]. A Proactve web server system, on the other hand, can decde where to place copes of a document n a dstrbuted web server system. In most exstng DWS systems, each server eeps the entre set of web documents managed by the system. Incomng requests are dstrbuted to the web server nodes va DNS servers [5-7]. Although such systems are smple to mplement but they could easly result n uneven load among the server nodes due to cachng of IP addresses on the clent sde. To acheve better load balancng as well as to avod ds wastage, one can replcate part of the documents on multple server nodes and requests can be dstrbuted to acheve better performance [8-10]. However, some rules and algorthms are then needed to determne number of replcas of each document/obect and ther optmal locatons n a DWS. Choosng the rght number of replcas and ther locatons can sgnfcantly reduce web access delays and networ congeston. In addton, t can reduce the server load whch may be crtcal durng pea tme. Many popular web stes have already employed

6 348 Informatca 29 (2005) A. Mahmood replcated server approach whch reflects upon the popularty of ths method [11]. Choosng the rght number of replcas and ther locaton s a non-trval and non-ntutve exercse. It has been shown that decdng how many replcas to create and where to place them to meat a performance goal s an NP-hard problem [12,13]. Therefore, all the replca placement approaches proposed n the lterature are heurstcs that are desgned for certan systems and wor loads. Ths paper proposes a sut of algorthms for replca placement n a Web envronment. The frst two algorthms are centralzed n nature and thrd s a dstrbuted one. For dstrbuton of requests, we tae nto account ste proxmty and access cost. A detaled formulaton of the cost models and constrants s presented. Snce most of the requests n web envronment are read requests, our formulaton s n the context of read-only requests. The rest of the paper s organzed as follow: Secton 2 revews some exstng wor related to obect replcaton n the web. Secton 3 descrbes the system model, centralzed and dstrbuted replcatons models and the cost functon. Secton 4 presents an algorthm to cluster hghly correlated obects n a web envronment. Secton 5 presents a centralzed and a dstrbuted algorthm for obect replcaton. Secton 6 presents the smulaton results and secton 7 concludes the paper. 2 Related Wor The problem of replca placement n communcaton networs have been extensvely studed n the area of fle allocaton problem (FAP) [14,15] and dstrbuted database allocaton problem (DAP) [16,17]. Both FAP and DAP are modeled as a 0-1 optmzaton problem and solved usng varous heurstcs, such as napsac soluton [18], branch-and-bound [19], and networ flow algorthms [20]. An outdated but useful survey of wor related to FAP can be found n [14]. Most of the prevous wor on FAP and DAP s based on the assumpton that access patterns are nown a pror and reman unchanged. Some solutons for dynamc envronment were also proposed [21-23]. Kwo et al. [24] and Bsdan Patel [25] studed the data allocaton problem n multmeda database systems and vdeo server systems, respectvely. Many proposed algorthms n ths area try to reduce the volume of data transferred n processng a gven set of queres. Another mportant data replcaton problem exsts n Content Delvery Networs (CDN). Unle FAP and DAP, n a CDN, a unt of replcaton/allocaton s the set of documents n a webste that has regstered for some global web hostng servce. In [26], the replca placement problem n CDN s formulated as an uncapactated mnmum K-medan problem. In [27], dfferent heurstcs were proposed based on ths K-medan formulaton to reduce networ bandwdth consumpton. The authors of [28] tae storage constrant nto consderaton and reduce the napsac problem to replca placement problem n CDNs. L [11] proposed a sut of algorthms for determnng the locaton of replca servers wthn a networ. The obectve of ths paper s not to determne the placement of obects themselves but to determne the locatons of multple servers wthn a networ such that the product of dstance between nodes and the traffc traversng the path s mnmzed. Wolfson et al. [29] proposed an adaptve data replcaton algorthm whch can dynamcally replcate obects to mnmze the networ traffc due to read and wrte operatons. The proposed algorthm wors on a logcal tree structure and requres that communcaton traverses along the paths of the tree. They showed that the dynamc replcaton leads to convergence of the set of nodes that replcate the obect. It, however, does not consder the ssue of multple obect replcatons. Further, gven that most obects n the Internet do not requre wrte operaton, the cost functon based on read and wrte operatons mght not be deal for such an envronment. Bestavros [30] consdered the problem of replcatng contents of multple web stes at a gven locaton. The problem was formulated as a constrant-maxmzaton problem and the soluton was obtaned usng Lagrange multpler theorem. However, the soluton does not address the ssue of selectng multple locatons through the networ to do replcaton. In [31], the authors have studed the page mgraton problem and presented a determnstc algorthm for decdng on where to mgrate pages n order to mnmze ts access and mgraton costs. Ths study, however, deals only wth page mgraton assumng that the networ has copes of a page. In addton, t does not address the problem of addng and deletng replcas to the system and presents no specal algorthm for replca selecton. It only assumes that the reads are done only from the nearest replca. Tensaht et al. [13] present two greedy algorthms, a statc and a dynamc one, for replcatng obects n a networ of web servers arranged n a tree-le structure. The statc algorthm assumes that there s a central server that has a copy of each obect and then a central node determnes the number and locaton of replcaton to mnmze a cost functon. The dynamc verson of the algorthm reles on the usage statstcs collected at each server node. A test s performed perodcally at each ste holdng replcas to decde whether there should be any deleton of exstng replcas, creaton of new replcas, or mgraton of exstng replcas. Optmal place of replca n trees has also been studed by Kalpas at el. [3]. They consdered the problem of placng copes of obects n a tree networ n order to mnmze the cost of servng read and wrte requests to obects when the tree nodes have lmted storage and the number of copes permtted s lmted. They proposed a dynamc programmng algorthm for fndng optmal placement of replcas.

7 OBJECT GROUPING AND REPLICATION... Informatca 29 (2005) The problem of documents replcaton n extendable geographcally dstrbuted web server systems s addressed by Zhuo et al [1]. They proposed four heurstcs to determne the placement of replca n a networ. In addton, they presented an algorthm that determnes the number of copes of each documents to be replcated dependng on ts usage and sze. In [32] the authors also proposed to replcate a group of related documents as a unt nstead of treatng each document as a replcaton unt. They also presented an algorthm to determne the group of documents that have hgh coheson, that s, they are generally accessed together by a clent n a sngle sesson. Xu el al. [33] dscussed the problems of replcaton proxy placement n a tree and data replcaton placement on the nstalled proxes gven that maxmum M proxes are allowed. The authors proposed algorthms to fnd number of proxes needed, where to nstall them and the placement of replcas on the nstalled proxes to mnmze the total data transfer cost n the networ. Karlsson et al. [34] developed a common framewor for the evaluaton of replca placement algorthms. Heddaya and Mrdad [35] have presented a dynamc replcaton protocol for the web, referred to as the Web Wave. It s a dstrbuted protocol that places cache copes of mmutable documents on the routng tree that connects the cached documents home ste to ts clents, thus enablng requests to stumble on cache copes en route to the home ste. Ths algorthm, however, burdens the routers wth the tas of mantanng replca locatons and nterpretng requests for Web obects. Sayal el al. [36] have proposed selecton algorthms for replcated Web stes, whch allow clents to select one of the replcated stes whch s close to them. However, they do not address the replca placement problem tself. In [37], the author has surveyed dstrbuted data management problems ncludng dstrbuted pagng, fle allocaton, and fle mgraton. 3 The System Models A replcated Web conssts of many stes nterconnected by a communcaton networ. A unt of data to be replcated s referred as an obect. Obects are replcated on a number of stes. The obects are managed by a group of processes called replcas, executng at replca stes. We assume that the networ topology can be represented by a graph G(V, E), n whch N = V s the number of nodes or vertces, and E denotes the number of edges (lns). Each node n the graph corresponds to a router, a swtch or a web ste. We assume that out of those N nodes there are n web servers as the nformaton provder. Assocated wth every node v V s a set of nonnegatve weghts and each of the weghts s assocated wth one partcular web server. Ths weght can represent the traffc traversng ths node v and gong to web server ( = 1,2,,n). Ths traffc ncludes the web access traffc generated at the local ste that node v s responsble for and, also, the traffc that passes through ths t on ts way to a target web server. Assocated wth every edge s a nonnegatve dstance (whch can be nterpreted as latency, ln cost, or hop count, etc.). A clent ntates a read operaton for an obect by sendng a read request for obect. The request goes through a sequence of hosts va ther attached routers to the server that can serve the request. The sequence of nodes that a read request goes through s called a routng path, denoted by π. The requests are routed up the tree to the home ste (.e. root of the tree). Note that a route from a clent to a ste forms a routng tree along whch document requests must follow. Focusng on a partcular sever, the access traffc from all nodes leadng to a server can be best represented by a tree structure f the transent routng loop s gnored [11,13,29]. Therefore, for each web server, a spannng tree T can be constructed rooted at. Hence, m spannng trees rooted at m web servers represent the entre networ. The spannng tree T rooted at a ste s formed by the clents that request obects from ste and the processors (clents) that are n the path π of the requests from clents to access obect at ste. 3.1 The Obect Replcaton Models In ths paper, we consder two obect replcaton models: centralzed and dstrbuted. In the centralzed model, each read request for an obect s executed at only one of the replcas, the best replca. If ℵ s the set of stes that LC C, have a replca of obect and denotes the cost of accessng obect at ste from the least cost ste (denoted by LC ), then LC LC =, f a replca of s locally avalable at =, otherwse such that C, s mnmum over all ℵ That s, for a gven request for an obect at ste, f there s a local replca avalable, then the request s servced locally ncurrng a costc,, otherwse the request s sent to ste havng a replca of obect wth the least access cost. In the centralzed model, there s a central arbtrator that decdes on the number of replcas and ther placement based on the statstcs collected at each ste. Upon determnng the placement of replcas for each obect, the central arbtrator re-confgures the system by addng and/or removng replcas accordng to the new placement determned by the arbtrator. The locaton of each replca s broadcasted to all the stes. In addton each ste eeps the followng nformaton:

8 350 Informatca 29 (2005) A. Mahmood LC : The least cost ste to that has a replca of obect. C, : The cost of accessng obect at ste from ste on π., f : The access frequency of obect at ste from ste on π. ℵ : The set of stes that have a replca of obect In the dstrbuted model, there s no central arbtrator. Smlar to centralzed model, for a gven request for an obect at ste, f there s a local replca avalable, then the request s servced locally ncurrng a costc,, otherwse the request s sent to ste havng a replca of obect wth the least access cost. After every tme perod T, each ste maes the decson about acqurng or deletng a copy of an obect based on the local statstcs The Cost Model Determnng an optmal replcaton nvolves generatng new allocatons and determnng ther goodness. The evaluaton s done n terms of an obectve functon subect to system constrants. The desgnaton of an obectve functon reflects the vew of goodness of obect replcaton wth respect to system desgn goals. It s not feasble to completely descrbe a system wth ust one obectve functon; nstead the obectve functon should only capture the crtcal aspects of the system desgn. Also, the form and the parameters of the obectve functon should be proper. That s, f the obectve functon ndcates that an allocaton s better than the other one then the actual measurements should concur. Keepng n mnd these consderatons, we develop the obectve functon for obect replcaton problem as follow: Suppose that the vertces of G ssue read requests for an obect and copes of that obect can be stored at multple vertces of G. Let there are total n stes (web servers) and, m obects. Let f s the number of read requests for a certan perod of tme t ssued at ste for obect to ste on π. Gven a request for an obect at ste, f there s a local replca avalable, then the request s servced locally wth a costc,, otherwse the request s sent to ste havng a least access cost replca of obect wth a cost LC C, as explaned earler. If X s an n m matrx whose entry x = 1 f obect s stored at ste and x = 0 otherwse, then the cost of servng requests for obect ( 1 m) at ste ( 1 n) s gven by TC = ( 1 x ) f C + x, LC,, LC f, C (1) The cost of servng requests for all the obects at ste s: TC = = m = 1 TC = = m [ + ], LC, LC,, 1 x ) f C x f C = 1 ( (2) Hence, the cumulatve cost over the whole networ for all the obects can be wrtten as: n m = =, LC, LC,, CC( X ) = (1 x ) f C + x f C 1 1 LC Now, the replca placement problem can be defned as a 0-1 decson problem to fnd X that mnmzes (3) under certan constrants. That s, we want to n m = =, LC, LC,, mnmzecc( X ) = mn (1 x ) f C + x f C 1 1 LC (4) Subect to n = 1 m = 1 x x 1 for all1 m s TS x {0,1, for all, for all1 m The frst constrant specfes that each obect should have at least one copy. If s denotes sze of obect and TS s the total storage capacty of ste then the second constrant specfes that the total sze of all the obects replcated at node should not exceed ts storage capacty. 4 Obect Groupng Almost all the proposed obect/document placement and replcaton algorthms for web on web servers decde about the placement/replcaton of a complete web ste or ndvdual obects comprsng a web ste. Both of these methods are not realst. It has been shown n varous studes that each group of users generally accesses a subset of related pages durng a sngle sesson. Therefore, t s logcal to group documents whch have hgh correlaton that s, the documents that are very lely to be requested by a clent n a sngle sesson. Ths would reduce the HTTP redrecton throughout a HTTP sesson and hence mprove the response tme. Each group then can be replcated on web servers as a unt hence reducng the search space. In ths secton, we propose an algorthm to group obects that are hghly correlated n the sense that they have hgh (3) (5) (6) (7)

9 OBJECT GROUPING AND REPLICATION... Informatca 29 (2005) probablty of beng accessed by a clent n a sngle sesson. The proposed algorthm s an adaptaton of the algorthm proposed n [38]. The maor dfference s that the algorthm n [38] produces non-overlappng groups, that s, each document s placed n a sngle group but the proposed algorthm may nclude an obect n more than one group. Ths s partcularly mportant snce dfferent users may request for dfferent correlated obects durng each sesson. Also, we use multple sessons, nstead of a sngle sesson, orgnatng from a clent to obtan obect groups for the reasons explaned. The proposed algorthm groups the obects nto correlated obect clusters based on the user access patterns whch are stored n the system access log fles. An access log fle typcally ncludes the tme of request, the URL requested, and the machne from whch the request orgnated (.e. IP address of the machne). Below, we explan maor steps of the algorthm. 1. Frst the log fle s processed and dvded nto sessons where a sesson s a chronologcal sequence of document requests from a partcular machne n a sngle sesson. We assume that each sesson spans over a fnte amount of tme. It s mportant to note that the log fle may have multple sessons for the same user. Ths gves a better pcture of the usage pattern of a user. Also, note that we have to mae sure that each request from a machne should be recorded n the log fle to obtan an accurate access pattern of users. Ths can be accomplshed by dsablng cachng, that s, every page sent to a machne contans a header sayng that t expres mmedately and hence browsers should load a new copy every tme a user vews that page. 2. In step 2, we create a correlaton matrx. The correlaton between two obects O 1 and O 2 s the probablty that they are accessed n the same user sesson. To calculate correlaton between O 1 and O 2, we scan the log fle and count the number of dstnct sessons n whch O 1 was accessed after O 2 (count(o 1,O 2 )) and calculate p(o 1 O 2 )=count(o 1,O 2 )/s(o 1 ), where p(o 1 O 2 ) s the probablty of a clent vstng O 1 f t has already vsted O 2 and s(o 1 ) s the number of sessons n whch O 1 was accessed by a clent. Smlarly, we compute p(o 2 O 1 )=count(o 2, O 1 )/s(o 2 ), where p(o 2 O 1 ) s the probablty of O 2 beng accessed after O 1 n a sesson, count(o 2, O 1 ) s the number of sessons n whch O 2 s accessed after O 1 and s(o 2 ) s the total number of sessons n whch O 2 s assessed. The correlaton between O 1 and O 2 s the mn(p(o 1 O 2 ), p(o 2 O 1 )) to avod mstang a asymmetrc relatonshp for a true case of hgh correlaton. 3. At step three, we frst create a graph correspondng to correlaton matrx n whch each obect s a vertex and each non-zero cell of the correlaton matrx s mapped to an edge. The length of an edge s equal to the correlaton probablty between two vertces. The edges wth a small value are removed from the graph. We then group documents by dentfyng clques n the graph. A clque s a subgraph n whch each par of vertces has an edge between them. The algorthm to dentfy clques f gven n fgure 1. The algorthm always starts wth a par of vertces that have the longest edge between them. Both of these vertces are ncluded n the group and edge s removed. Then we examne the rest of the vertces that have not been ncluded n the group and select the next best vertex (a vertex wth the hghest edge value) that s connected to the vertces already ncluded n the group and nclude t n the group. In ths way we choose the obects that are hghly correlated. The sze of the clque s bounded by the longest sesson of ts members snce there s no need of ncludng an obect to a group f t s not accessed n the longest sesson. Each vertex that s not ncluded n any of groups s ncluded n a separate group havng that vertex as ts only member. R = {vertces connected to at least one edge whle (R φ) { Fnd the longest edge n R wth vertces O 1 and O 2 V = { O 1, O 2 G = R \ V, C = φ l=maxmum sze of V whle ( V l ) { for (each vertex O n G) { f (O s connected to all vertces n V ){ Record the shortest edge between o and vertces n V Add O to V f (C φ ) { Choose the vertex O shortest edge to V s longest Add O to V Delete O from G and R C = φ l=l+1 Fgure 1.Obect groupng algorthm whose else { delete O 1 and O 2 O 1 and O 2 from G and R brea Construct a group for each remanng vertex

10 352 Informatca 29 (2005) A. Mahmood 5 Obect Placement and Replcaton Algorthms The replca placement problem descrbed n the prevous secton reduces to fndng 0-1 assgnment of the matrx X that mnmzes the cost functon subect to a set of constrants. The tme complexty of ths type of problems s exponental. In the next secton, we present our proposed centralzed obect replcaton algorthms. 5.1 Centralzed Greedy Algorthm Our frst algorthm s a polynomal tme greedy algorthm that s executed at a central server and decdes the placements of replcas for each obect. The algorthm proceeds as follows: Frst all the obects groups are organzed n descendng value of ther densty to mae sure that the obects that are heavly accessed are assgned to the best server. For each obect, we determne the number of replcas that should be assgned to varous servers usng the algorthm proposed n [32] (R denotes the number of replca each obect should have). The frst obect n a group s assgned to most sutable server and then all the other obects n the same group are allocated to the same server f t has enough capacty. The dea s that the documents n the same group have hgh probablty of beng accessed n the same sesson by a clent; therefore, eepng them together wll mprove the response tme. If an obect cannot be assgned to the same server then we fnd a server wth mnmum access cost and assgned the obect on that server. After a copy of an obect s assgned, then we assgn the remanng replca of each obect to best servers not havng a copy of that obect and have the capacty for that obect. The complete algorthm s gven n fgure Dstrbuted Obect Replcaton Algorthm The algorthm presented n the prevous secton are centralzed n the sense that a central arbtrator collects all the necessary statstcs, determnes the placement of the obects, and reconfgures the system n accordance wth the newly determned allocaton. Ths mght nvolve removng/deletng replcas and addng or mgratng replcas by the central arbtrator. However, n the dstrbuted model, there s no central arbtrator. Rather, each ste determnes for tself whch obects t should add/remove based on the current replca placement and Group obects usng obect group algorthm Arrange obect groups n descendng order of ther densty Arrange obects n each group n descendng order of ther densty Determne the number of replcas for each obect for (=1; <= no_of_obects; ++) replca_assgned =0 for g = 1 to no_of_groups { whle (G φ ) { = frst_obect_n _G A = // set of obects allocated to f ( has not been allocated) { = ste wth mnmum value of (2) such that no constrant s volated f a replca of s allocated to Allocate at replca_assgned = replca_assgned + 1 G = G - whle ( has capacty and G φ and ) { = frst_obect_n _G Allocate at replca_assgned = replca_assgned + 1 G = G - A= A for ( each n A ) { for (r= replca_assgned ; r R ; r++) { Fnd a ste not havng a replca of and has mnmum value of replca of s assgned at and no constrant s volated Assgned at replca_assgned = replca_assgned + 1 Fgure 2: Proposed replcaton algorthm (algorthm 1) C, and f a

11 OBJECT GROUPING AND REPLICATION... Informatca 29 (2005) K ) { for (each obect If (server s the only server havng a replca of obect ) proft = a_max_number else proft =,, ( TC f C ) / s // TC then the cost of servng requests for obect // at ste from the least cost ste for (each obect ) { proft = ( TC locally collected statstcs as descrbed n secton 3.1. Our proposed dstrbuted obect replcaton algorthm s a polynomal tme greedy algorthm where each ste eeps the replcas of those obects that are locally evaluated to be the best replcas. Assume that X (an n m matrx) represents the current obect replcaton. Intally X can be determned by usng the algorthm proposed n the prevous secton. If K and ξ s the set of obects that are replcated at ste and the set of obects that are not replcated at ste respectvely then each ste, after every tme perod t, determnes whch obects t should add/remove based on the current replca placement and locally collected statstcs usng the followng proposed algorthm. The algorthm frst calculates the unt loss/proft of removng the local replcas and then the unt proft of havng replcas of those obects whch are not avalable locally. It then sorts all the obects n descendng values of ther proft and replcates top n obects whch t can accommodate wthout volatng the constrants. The complete algorthm s gven n fgure 4. 6 Expermental Results Ths secton presents some performance measures obtaned by smulaton of the proposed algorthms. We have run several smulaton trals. In each smulaton run, we model the web as a set of trees havng stes. The total obects to be replcated were 2000 n all the smulaton runs. We use dfferent obect szes whch follows a normal dstrbuton. The average obect sze s taen as 10 KB and maxmum sze was taen as 100KB. About 64% obects szes were n the range of 2KB and 16KB. The storage capacty of a server was set randomly n such a way that total storage of all the servers was enough to hold at least one copy of each obect at one of the servers. In each tral, we run the replca placement algorthms for 200,000 requests for dfferent obects. We created log fles by generatng requests for obects for ξ f, C, ) / s C, LC / Sort all the obects n K ξ n descendng order of ther proft values. Replcate the obects from the sorted lst one by one untl there s space avalable on server. Fgure 4. The proposed dstrbuted algorthm (algorthm 2) s multple sessons. Ths log fle was used to group obects. The same log fle was used by the proposed algorthms to collect varous statstcs. Durng a smulaton run, each ste eeps a count c of the total number of requests t receves for an obect. The latences are updated perodcally for each replca usng the formula T = 1/( µ λ) where λ s the average arrval rate and µ s the average servce tme. Exponental servce tme s assumed wth an average servce rate of 100 transactons/second. The value of T s propagated to the clents n the shortest path spannng tree. The cost (latency) at dfferent stes s computed as follows: At the replca ste, the average arrval rate s computed and the latency T = 1/( µ λ) s broadcast to all the stes of the tree rooted as ths replca. At a ste of the tree, the communcaton cost (set randomly) at the neghborng ste from whch T s propagated s added to T. Ths qualty wll be the cost of accessng the replca from ste. At the end of every 20,000 requests, the mean latency requred to servce all the 20,000 requests s calculated and used as a performance measure of the smulated algorthms. We studed the performance of our proposed algorthms and compared t wth that of random allocaton algorthm [28] and greedy algorthm [13]. The random algorthm stores replcas at randomly selected nodes subect to system constrants. The number of replcas for each obect was determned by densty algorthm [1]. We pc one replca at a tme wth unform probablty and one node also wth unform probablty; and store that replca at that node. If the node already has a replca of that obect or allocaton of replca at that node volates any of the constrants then another node s selected randomly untl the replca s placed at a node. Snce the obect placement problem s NP-Complete and hence optmal soluton cannot be obtaned for large problems n a

12 354 Informatca 29 (2005) A. Mahmood reasonable amount of tme, the random algorthm provdes a good basc on whch we can determne how good a heurstc performs than that of a smple random algorthm. Fgure 5 shows the average latency for all the smulaton runs for dfferent tree szes. The fgure shows that the average latency decreases for all the algorthms as the number of stes ncreases n the system. Ths s because of the fact that as the number of stes ncreases, more replca of an obect can be placed. Also, note that the performance of algorthm 1 and algorthm 2 s comparable demonstratng the effectveness of the dstrbuted algorthm. The fgure 6 shows the average performance of the algorthms for all the system confguratons. It s evdent that the proposed algorthms perform, on average, better than the greedy and the random algorthm. To demonstrate how algorthm 2 adapts to the access patterns, we performed a set of experments. The ntal allocaton was obtaned by randomly placng replcas of each obect as explaned before. After each requests, the algorthm s run on each ste. We observed the mprovement n latency, frst by calculatng the latency f no reallocaton of obects s done and then by allowng the algorthm to adust the replcaton usng the statstcs. The results are shown n fgure 7. It s evdent from the fgure that the algorthm reduces the latency every tme t s executed. Intally the mprovement s sgnfcantly hgh snce the ntal allocaton was obtaned randomly. After a number of runs, the performance of algorthm 2 s comparable wth that of algorthm 1. 7 Conclusons Obect replcaton on a cluster of web servers s a promsng technque to achevng better performance. However, one needs to determne the number of replcas of each obect and ther locatons n a dstrbuted web server system. Choosng rght number of replcas and ther locaton s a non-trval problem. In ths paper, we presented an obect groupng algorthm and two obect replcaton algorthms. The obect groupng algorthm groups web obects based on the clent access patterns stored n access log fle. The documents that are correlated and have hgh probablty of beng accessed by a clent n a sngle sesson are put nto the same group so that they can be allocated, preferably on the same server. The frst proposed for obect replcaton s a centralzed one n the sense that a central ste determnes the replca placement n a graph to mnmze a cost functon subect to the capacty constrants of the stes. The second algorthm s a dstrbuted algorthm and hence does not need a central ste for determnng obect placement. Rather, each ste collects certan statstcs and decsons are made locally at each ste on the obects to be stored at the ste. Taen each algorthm ndvdually, smulaton results show that each algorthm mproves the latency of the transactons performed at dfferent stes as the number of stes s ncreased. A comparson of the proposed algorthms wth greedy and random algorthms demonstrates the superorty of the proposed algorthms. Average Latency Average Latency % Improvement # of stes Alg. 1 Alg. 2 Greedy Random Fgure 5. Mean latency for dfferent tree szes Alg. 1 Alg. 2 Greedy Random Fgure6. Average latency for all smulaton runs Run# Fgure 7. Average % mprovement n latency acheved by algorthm 2 References [1] ZHUO, L., WANG, C-L. and LAU, F. C. M., Document Replcaton and Dstrbuton n Extensble Geographcally Dstrbuted Web Servers, J. of Parallel and Dstrbuted Computng, Vol. 63, 2003, No. 10, pp [2] PHOHA, V. V., IYENGAR S. S. and KANNAN, R., Faster Web Page Allocaton wth Neural

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