Erasure Codes-based Storage-aware Protocol for Preserving Cloud Data under Correlation Failures

Transcription

1 Internatonal Journal of Grd Dstrbuton Computng, pp Erasure Codes-based Storage-aware Protocol for Preservng Cloud Data under Correlaton Falures Zhqang Ruan and Zh L Department of Computer, Scence Mnang Unversty, Fuzhou, Chna Insttute of Informaton Engneerng, Chnese Academy of Scence, Beng, Chna rzq_9@63.com, lzh@e.ac.cn Abstract Dstrbuted storage of cloud data mposes a great challenge for assurng data avalablty and relablty n the face of stochastc falures and attacks. Although redundancy scheme such as erasure codes or network codng schemes can be used to mprove storage effcency, they do not consder the scenaro that the network may be splt up nto several regons due to correlated falures of storage components, whch may not successfully reconstruct the orgnal data. Furthermore, the stored data on the faled node need to be recovered to keep the same redundancy of network data whle ntroducng low overhead. In vew of ths, we frst devse an effcent algorthm that guarantees resdual network has enough data segments to recreate the orgnal data under correlated falures. Second, an effcent data recovery scheme s presented to repar the data stored on the faled nodes n case of Byzantne falures or polluton attacks. The proposed protocol benefts from several key features such as less storage cost, compettve communcaton cost, and much better data robustness comparng to the state of the art dstrbuted storage systems. Keywords: Cloud computng, dstrbuted storage, correlated falures, fault-tolerant, relablty. Introducton Cloud computng has enabled ndvduals and enterprses to preserve ther data from local to remote data centers n a dstrbuted manner []. One key ssue to consder n such dstrbuted storage system s mantanng avalablty of data and ensurng relablty n the presence of random falures of storage node (SN). Many works have been proposed n the lterature wth the assumpton that falures occur ndependently at any SNs of the system. Ths assumpton greatly smplfes the analyss; however, t s not realstc for the type of falures occurrng n dstrbuted storage systems such as grd computng, peer-to-peer (P2P) networks, large-scale dstrbuted computng systems. Because the communcaton network and the fact that such falures can change the topology of the system n a random fashon. Snce erasure coded based storage systems have hgh fault tolerance wthout requrng a large number of replcas that ncrease the storage cost [2, 3], they have been extensvely used for ensurng dependable and fault tolerant desgn of dstrbuted data storage, where a set of data symbols/segments s generated and dstrbuted across the network so that one may recover the orgnal data even f a few of these symbols are lost or erased. Formally, n (N, K) erasure code storage system, N coded symbols of sze M /K are generated from the orgnal data M and assgned to n storage nodes n the network. The orgnal data M can be reconstructed when accessng and decodng any K out of N symbols (N K) [3]. However, ths requrement alone s not suffcent for successfully recreate the orgnal data when the network do exhbt some type of spatal and / or temporal correlaton of anomales. Josh et al., analyzed statstcs of falures n large-scale systems and concluded that such systems are affected by frequent, correlated machne crashes and network falures ISSN: IJGDC Copyrght c 205 SERSC

2 Internatonal Journal of Grd Dstrbuton Computng that reduce the relablty of the entre system [4]. A smlar concluson was obtaned ndependently by Gallet, et al., [5]. For smplcty, we assume that the defectve SNs are confned to a certan range. Such falures are generally happened n dsaster scenaros, ether manmade or natural, whereas only the SNs located at the dsaster zone are affected. As a consequence, the network s probably gettng dsconnected because of these powerful but localzed falures. In spte of more than K symbols resdual, none of them exst n the same regon. In order to restore the orgnal data, one has to make sure that at least one of the connected regons has more than K symbols. Therefore, t s extremely mportant to desgn a robust data dstrbuton scheme to overcome such falures. The followng problem s accurate repar the data preserved n the dsabled SNs so that the same redundancy and functonalty of the network can be acheved. The conventonal countermeasure has to frst reconstruct the ntal data and then regenerate the data that conserved n the faled one [6-8]. Unfortunately, ths approach would ntroduce tremendous of overhead by retrevng the whole N symbols of the ntal data, only to regenerate a small fracton of symbols stored n that dsabled SN. Moreover, prevous works manly encompass sudden collapse behavors of SNs, whereas lack of consderng wth Byzantne falures [9] or polluton attacks, n whch the preserved data can be tampered and eventually lead to ncorrect data reconstructon and / or recovery. Thus, t s mperatve that effcent data regeneraton scheme s presented for mnmzng the number of data symbols retreve from the network whle ensurng the ntegrty of stored data. Therefore, ths work seeks to devse a redundant data storage scheme such that the data can be recovered after correlated falures. Snce storage of the data symbols nvolves cost, the data symbol dstrbuton scheme should mnmze the total storage requrement over the storage system. In addton, a smple yet effcent data recovery scheme wth ntegrty check of data has to be consdered. In partcular, the maor contrbutons of the work n ths paper can be summarzed as follows: A robust data dssemnaton approach explotng (N, K) erasure codng for guaranteeng that even though the network s break up nto dfferent sectons because of correlated falures of some SNs, there are at least one remanng parts wll have more than K symbols to recreate the ntal data. The explorng of data recovery scheme that allows exact reproduce of orgnal data wth low computaton and communcaton cost. The remanng sectons are structured as follows: Secton 2 dscusses related work on geographcal correlaton falures; Secton 3 presents the system model and gves problem formulaton; Secton 4 descrbes the performed approaches and solutons; Secton 5 shows the expermental results; Secton 6 gves the analyss; Secton 7 presents the conclusons. 2. Related Work Issue of relablty and correlated falures have been well studed n cloud storage systems, wde-area storage, dstrbuted fle systems and computer networks. Some of the prevous works nterested n correlated falures manly concentrate on () dentfyng the vulnerablty of the system to such dsasters [0, ] (e.g., estmatng damage locatons that have the maxmum mpact on network operaton [0]), or the effect of such dsasters [], () analyzng network capacty or evaluatng ts robustness [2], and measurng ts relablty [8, 3]. They are a few studes [4-6] stress how to dstrbute coded symbols of source SN to a subset of nodes n the network n order to ensure that each of them has one pece of data. The prmary goal of ths lne of research s explct establshment of a stable topology so that the orgnal data can be recreated by vstng at least K SNs. Our work s partly nspred by that of lteratures [4, 5], whch consder stochastc falures and utlze error-correctng codes to replace the data on the dsabled SN. However, there exsts a consderably dfferent between our research and that of [4, 5]. Despte [4, 5] solve the regeneraton problem and seek to get a trade off between communcaton 6 Copyrght c 205 SERSC

3 Internatonal Journal of Grd Dstrbuton Computng and storage overhead, they do not consderng correlated falures n the network, whereas our work drectly towards the obectve of developng a robust data dstrbuton scheme that allow a few SNs dysfuncton due to such falure and perform accurate reparng of data on arbtrary network topology. 3. Models and Problem Formulaton 3.. The System Model We assume a cloud data storage servce that provdes user data outsourcng servce, data retreval, and repar servce. The network ncludes the cloud server, a trust thrd party (TP) and ndvdual customers. The customers outsource ther data to the connected storage server (source SN), whch then encodes the data M nto N fragments and assgns to n SNs. After the data outsourcng servce, a customer can retreve the data anytme and anywhere. However, n order to release the customer from the burden of beng onlne, we suppose that TP responsble the outsourced data reconstructon and repar works for the customers. Ths s reasonable as sometmes the customer has prvacy concerns, and requres a neutral thrd party to manage data. Table summarzes the notons to be used throughout the paper. Table. Lst of Notatons Notaton Descrpton λ The number of symbols saved n each SN β The number of symbols retreve from each SN, where β λ n The total number of SNs n the network d The number of survvng SNs n the network μ The maxmum symbols stored n each SN l The number of largest regons remanng n the network φ The set of SNs n a largest remanng regon Ф The set of l largest remanng components of network G r Radus of fault regon (N,K) Erasure codes encode K nformaton symbols to a coded vector <a 0,...,a N- > Ψ A set of N dstnct colors C The lst of colors assgned to SN The number of dfferent colors requred by set φ, l k 3.2. Problem Formulaton The network s descrbed as a connected graph G=(V, E) where V s the set of n SNs and E represents the set of lnks between them. Let the two dmensonal layout of G on a plane be LG=(P, L) where P={p,...,p n } represents the set of ponts and L={l,...,l w } are straght lnes. We focus on a regon n a two dmensonal plane R wth radus r, because of the correlated falure model most of the SNs or lnks confned to the falure event are destroyed. As a result, the survvng network may compose of several dsconnected parts. The aggregate number of such dfferent regons that has to be consdered s l=o(n 2 )[7]. Let = { R,... R } denotes the set of dfferent regons, for the data M, a SN SN Î V enabled l to store up to μ data symbols. We ntend to dstrbute N encoded symbols of data M from source SN to n storage locatons of the network so that the largest secton of the remanng network has more than K dfferent symbols to recreate the ntal data. Let represents the set of SNs n the maxmum remanng secton n G after regon R fals, where Î [, l ], and let F = {,..., } denotes the set of l largest remanng area of l network G. Assume each SN receved λ symbols after dstrbuton of the coded symbols, where 0 λ μ. Snce storng every sngle symbol nvolves cost, the goal s to mnmze the Copyrght c 205 SERSC 7

4 Internatonal Journal of Grd Dstrbuton Computng total storage requrement n the network. Suppose Y = { c,..., c } are a set of N dfferent N colors, we can formulate the data dstrbuton problem as color dstrbuton problem where each color ndcates a symbols and assgnng a color c, Î [, N ], to a SN SN, Î [, n ]. On the other hand, the data recovery problem can be formulated as choosng dstnct color c, Î [, N ] from the survvng SNs n. 4. The Proposed Scheme 4.. Data Encodng Frst, a message authentcaton code (MAC) s appended to the orgnal data by the source SN for data ntegrty. In ths work, we take advantage of Cyclc Redundancy Check (CRC) because t s easy to mplement and needs lower redundancy. Thereafter, we assume that CRC checksum has been attached to the ntal data. Second, the customer uploads the data to the source SN, whch splts the data nto M / q segments so that each of whch represents an element n GF(2 q ). Then the M / symbols are further dvdes nto M / q K nformaton sequence m m,..., m, we 0 K arrange the nformaton sequence nto an nformaton matrx U wth dmenson of λ d such that U=B B 2, where 殞 m m m L m m m m L m B = M m m m L m 薏 0 2 l - l l l l l l l ( l ) / 2, 殞 m m L m m m L m B = 2 M m m L m 薏 l ( l l ( l l ( l l ) / 2 ) / 2 ) / 2 l ( l l ( l l l ( l l ) / 2 ) / 2 ) / l ( l l l ( l l K ) / 2 ) / Let the elements of U be w, we precsely construct B and B 2 as a symmetrc vector, n partcular, we have ì w = m for # l z ï w = í ï w m fo r l 2l ( - l ) = z + # ïî 2 where z ( )( ) ( ) / 2 and z ( )( / 2 ) ( ) / 2 ( ) 2. After ths constructon, B and B 2 are symmetrc matrces wth sze λ λ. In the process of encodng, each row of U has a codeword of length N. Besdes, for the -th row of U, the correspondng codeword s 0 N [ W ( ), W ( ), L W ( )] () where W (x) s a polynomal wth all elements n the -th row of U as coeffcents, namely, W ( ) w x, where α s the generator of GF(2 q ). We have T = U? G, where d 0 殞 L 0 N - a a L a N - 2 G = ( a ) ( a ) L ( a ) M ( a ) ( a ) L ( a ) d d N d 薏 and T s the codeword vector wth sze of λ N. Next, the -th column of T s assgned to SN by usng the method below. Fnally, the orgnal data s securely erased. q 4.2. Coded Symbol Dstrbuton Algorthm Symbol Dstrbuton Algorthm Input: Ψ={c,...,c N }, μ, r, K, and N. Output: C ={c,...,c λ } begn Compute = { R,... R } and derve resdual graph set l 2 Intalze G?, C?, "? [, n], k =K, "? [, l] F= {, L, } l 8 Copyrght c 205 SERSC

5 Internatonal Journal of Grd Dstrbuton Computng 3 repeat 4 Compute ρ, [, n] ; 5 f u p =0 then 6 No feasble soluton exst; return 7 else select SN p wth hghest ρ n Ф 8 p 9 foreach : SN p do 0 D and D C k k - 2 f k =0 then Ф Ф\φ 3 end 4 C C c p p 5 u p u p - 6 untl 7 for to do 8 for =λ to do 9 f C \c stll has a feasble soluton then C C \c 20 end We want to assgn N encoded symbols (or colors) to total number of n SNs n such a way that the remanng network has more than K symbols to reproduce the data. For each SN (say SN ), the number of coded symbols t receves s λ, where 0 λ μ. Note that μ s a system parameter, whch s used to ensure that the encoded symbols stored n sparse rather than cumulatng on a few storage nodes. Step : each source SN produces all the dfferent regons 좱 = { R, R } l of radus r on the graph layout LG usng the method n [2], and fnds the largest component F= {, L, } l of the resdual graph for each faulty zone. Let C records the lst of colors dstrbuted to SN. k denotes the number of dfferent colors demanded for set. Intally, C =?, and k =K (as shown n Algorthm, lne ). Step 2: for each?, lne 3-6 arranges a new color to a SN. Let ρ, Î [, n] represents the number of tmes SN appears n all sets n Ф. The bgger the value of ρ means SN s a better opton for allocatng a new color. In each teraton, lne 4 chooses a SN, say SN p, for whch ρ s largest and at least cache one color. The for-loop from lne 9-3 scan all the sets φ that contans SN p, among whch lne 0 selects the set of colors D that has not been assgned to any storage node n φ, and the values of k s decreases n lne when a new dfferent colors s found for φ, f any φ satsfed all color requrement n lne 2, t s removed from Ф. Lne 4 pcks up the color c whch s lowest n all the colors I : u D p Î wthn the for-loop and dstrbutes c to the storage node v p. It should be noted that selectng the mnmum color c Î I D : u Î ensures that all the sets φ get a new dfferent color. Lne p 5 reduces up by and the lne 5 ndcates that f u p =0 for S N V at any teraton, all the p SNs have been dstrbuted colors meet ts threshold. Otherwse, f some sets? can not satsfy the colorng constrants of havng K dfferent colors, the algorthm termnates wthout havng a feasble soluton. Step 3: lne 7-20 delete redundant colors dstrbuted to the SNs. The double for-loop works by the lst of the colors allocated to the SNs n reversed order and removes a color from a SN f deletng the color from that one stll has a feasble soluton. Copyrght c 205 SERSC 9

6 Internatonal Journal of Grd Dstrbuton Computng 4.3. Data Reconstructon Wthout loss of generalty, we assume that TP accesses k storage nodes S N, S N,, S N 0 k - Frst, the nformaton sequence m s recovered by solvng the lnear equatons: where L L k 0 G ( ) ( ) ( ) k M ( ) ( ) ( ) k k k d L. U = T? G - (2) G s the frst d columns of G and G - s the nverse of G. The procedure s descrbed as follows: Step : TP ntalzes =k, and randomly selects k storage nodes out of d survval storage nodes, where L = { a, a, L, a } ; then t sets U = T. 0 ( k- ) Step 2: TP apples U = T? G - to derve the nformaton sequence m ; f m passed the CRC test, the CRC checksum can be removed from m to recover the orgnal data block T 0. The procedure returns T 0 and the data reconstructon succeeded; otherwse, go to step 3. Step 3: TP adds =+2, two more encoded symbols a x, a y from survvng SNs (SN x and SN y ) are requred and attached to prevously receved symbols to generate a new codeword, L L a a, then, TP decodes the new codeword to gan the K symbols. Ths decodng x y 2 {, } procedure s repeated untl n-or the decodng algorthm faled to reproduce decoded symbols. Step 4: If n-, the data reconstructon fals due to too much errors occurs, n ths crcumstance, decodng falure s reported; otherwse, TP starts next round of data recovery and go to step 2. Algorthm 2 Symbol Regeneraton Algorthm Input: Output: S begn 2 TP randomly selects d storage nodes S N, S N, L, S N 0 d - 3 Each selected node takes ts symbols as a (β λ) vector and multply t by g n Eq. (3) 4 TP forms the resultant vector as a ( b d ) matrx Y 5 d 6 repeat 7 Perform error correctng code on each row of Y to derve T 8 Perform M = T? G and obtan nformaton symbol S from M 9 f CRCTest(S)=true then 0 return S else Two addtonal storage nodes are retreved 4 Each storage node perform the same operaton as step 3 5 TP forms a new matrx Y b 6 untl n-2 7 return false 8 end 20 Copyrght c 205 SERSC

7 Internatonal Journal of Grd Dstrbuton Computng 4.4. Regeneratng Lost Symbols Suppose node be the dsabled node to be renewed. Durng restorng, TP retreves k ( d # k n - ) SNs S N, S N, L, S N 0 k -. Each retreved node operates the nner product of λ symbols and g = [, ( a ), ( a 2 ), L, ( a ) ] (3) l where g can be obtaned by the generator α and ndex, then the resultant symbol a, a, L a s returned to the TP to generate the codeword T 0 k -, where T = g 利 ( U G ) = ( g 利 U ) G. (4) If ( n - k ) + 2t < n - d +, where t represents the number of ncorrectly decoded data bts n k resultant symbols, g U can be recovered by multplyng T and G, whch s equvalent to g?[ B B ] [ g 利 B g B ] (5) 2 2 Snce transpose of g s the -th column of G, B and B 2 are symmetrc matrces, we have ( g B ) T = B g, for =,2. The λ symbols saved n SN T can be computed by ( g B ) l + ( a - ) ( g B ) 2 (6) T T The decodng procedure n data reconstructon can be appled to decode a, a, L a. Frst, 0 k - TP retreves d SNs and obtans λ and T by (3). Next, the CRC checksum s extracted and verfed. If t s passed, the regeneraton return true; otherwse, two extra SNs are randomly vsted, TP decodes the retreved a 0, a..., a d+ agan to obtan T and λ. The process s repeated untl correctly receved suffcent data fragments to restore the faled node. The symbol recovery algorthm s descrbed n Algorthm Analyss We analyze the fault-tolerant capablty, securty strength, storage cost, and communcaton overhead of the proposed scheme n the followng subsecton. 5.. Fault-tolerant Capablty There are two types of falures, namely crash-stop falures and Byzantne falures, are consdered n analyzng fault-tolerant ablty. Crash-stop falures can be regarded as removng the code elements from codeword. As our symbol dstrbuton scheme enable each set has at least K dfferent symbols, the crash-stop falures that can be allowed n data reconstructon s at most N-K. Durng recovery a sngle symbol, d nodes have to be retreved. Therefore, the fault-tolerance of regeneraton s n-d. In respect of Byzantne falure, we assume that the erasure code s utlzed to obtan the CRC checksum and the number of errors s confned to the maxmum number of falures the RS code can manage. In the crcumstance, the mnmum erroneous node that the RS code can tolerant to restore the CRC checksum s ( n d ) / 2. Therefore, the effcency of data reconstructon can be defned as the probablty of successful decodng Pr rec, we have N K ( n d ) / 2 N N K N ( K ) e e (7) 0 0 K N ( 2 K ) P r ( ) rec where e represents the error probablty of data, and number of SN vsts Securty Strength K N ( K ) K N ( 2 K ) denotes the In analyzng the securty strength, colluson among polluters s consdered. In other words, the polluters can forge data cooperatvely durng the data reconstructon or regeneraton process. Ths s useful when the polluters had compromsed a small set of SNs but stll tamper the data on other SNs and eventually leads to vald but ncorrect data Copyrght c 205 SERSC 2

8 Internatonal Journal of Grd Dstrbuton Computng reconstructon. The securty strength s thus the mnmum number of polluters to forge the data n data reconstructon. Suppose 0,,..., p- be the polluters who collude to forge the nformaton symbols, let y : represents the forged column n m, and y = y + m, where m ndcates the real nformaton symbols. Then, based on the RS encodng procedure, we have = + = + = g + c, (8) : : yg ( y m ) G y G mg where γ s the modfed data symbol made by the polluters and χ s the ntal data symbol stored n SNs. Let the mnmum Hammng dstance of the RS code n γ s θ, obvously, θ n-k+, so we suppose that θ=n-k+ for the worst case. The attacker has to compromse k SNs and make them store the forged nformaton symbols n yg so as to successfully fake nformaton symbols. If TP happens to retreve these polluted SNs, data can be forged successfully. Otherwse, suppose b<k SNs are polluted, that s, q where n - d 薏 2 - b = n - d + - b? n - d 薏 2 s the error correctng capablty of the RS code, the decodng procedure s possble to recover the receved vector to yg. Consderng the mnmum of the securty strength for data reconstructon s 殞 n - d + 2 m n { k, } - 薏 2. 殞 n - d + 2 b = 薏 2 In the case of forgery attack on data regeneraton, the adversary prefer to make the fraudulent data wth all zero redundant bts rather than break the CRC checksum of the faled node, because of lnear operaton ntroduced n computng the CRC checksum. Therefore, the securty strength for data regeneraton s 5.3. Redundancy Rato 殞 n - d + 2 m n { d, } - 薏 2 CRC checksum ncurs extra storage and communcaton overhead, recall that each nformaton vector s added wth the extra r 0 bts n data constructon so that t can be verfed after reconstructon. Suppose that ( N, K ) RS code s appled to encode the CRC checksum nto N fragments and assgned to n SNs, where = 薏 r / 0 q and q = [ n ) 2 ]. Each SN has to keep the encoded CRC symbols for other n- nodes, whch requres addtonal storage of nq bts. Durng data regeneraton, TP must gather the assocated CRC checksum for the faled node to prove the valdaton of reproduced data. At least d SNs need to be retreved, the accessed data and the assocated CRC checksum of the faled node are provded to TP. Each pece of CRC has q bts, the extra communcaton overhead s dq, and the total communcaton cost for reparng the βλ symbols kept n the faled node s βqd. 6. Performance Evaluaton In the smulatons, we set up wth the parameters as follows: [, 2 / ] K m Î, β=, N=4, K=2, r=300. The prevous erasure codes based scheme wthout consderng regon-based fault n the network used as a baselne scheme for comparson. Each smulaton ncludes a data (symbol) dstrbuton phase and a collecton phase. In the prevous phase, each source SN performs the consdered storage protocol to dstrbute the data over the network. Whle n the collecton phase, TP gathers data from these SNs and returns to the customer. We frst nvestgate the mpact of fault regon (radus r) on the network robustness wthout error data n the network. Here, robustness means that after data dstrbuton, the probablty of TP successfully retreves the data. Fgure shows the robustness s decreases wth the ncreases of fault regon r. As we can see, when r grows to 400, our scheme stll has 90% robustness. The reason that we have better performance than exstng schemes s we consder a more realstc case, where the network can get dsconnected due to SN falures. In other words, such falures are.,, 22 Copyrght c 205 SERSC

9 Normalzed cost of storng one byte Robustness Internatonal Journal of Grd Dstrbuton Computng correlated and have greater mpact on data survval compared to ndependent falure of SN. We devse a robust data dstrbuton algorthm that guarantees each remanng zone has at least of K symbols to reconstruct the orgnal data. Contrary, snce Baselne scheme wthout consderng correlated falures, there are probably have not enough symbol n the network for TP to recreate the ntal data. Fgure 2 shows how storage overhead vares when r grows, where we defne the storage overhead as how many bytes are stored for each useful byte. As can be observed, the normalzed cost of two approaches ncreases as r grows, and the proposed scheme outperforms baselne scheme. Based on Fgure and Fgure 2, t can be concluded that our scheme s reslent to correlated falures Baselne Ours fault regon (r) Fgure. Impact of r on Network Robustness Baselne Ours fault regon (r) Fgure 2. Impact of r on Storage Overhead Next, we nvestgate the mpact of parameter K on the total storage requrement, keepng N=4 and r=300 constant. Fgure 3 shows the storage overhead ncurred by the compared schemes. As we can see, the storage requrement of both schemes ncreases wth K. The reason s straght; the hgher K ndcates that TP needs more dstnct symbols to reconstruct the data, whch results n hgher storage requrement for the data symbols. However, the storage overhead of Baselne scheme s much hgher than us. Even for the low rate case,.e., K=7, the Baselne scheme has at least 20% of storage overhead more than us. Ths s one of the maor benefts of the proposed scheme. In the second set of experments, we study the repar effcency of regeneratng data on the faled node. We fal one node at random and start the data repar process. Note that correlated falures do exhbt when ndvdual SN faled, however, the repar work has to be performed separately on each faled SNs. Therefore, there are no dfferences between ndependent falures and correlated falures durng data regeneraton. Copyrght c 205 SERSC 23

10 Average communcaton cost Normalzed cost of storng one byte Internatonal Journal of Grd Dstrbuton Computng K Baselne Ours Fgure 3. Impact of (N, K) on Storage Overhead Baselne CESR error probablty (e) Fgure 4. Average Communcaton Cost vs. Error Probablty n Data Regeneraton Fgure 4 measures the average communcaton cost ncurred by data regeneraton after the repar s fnshed. We can see that the average communcaton cost ncreases as the error probablty ncreases. In our scheme, when the error probablty e s small, the number of symbol retreves s lnear (close to K) then monotoncally ncreases as e ncreases. Furthermore, the Baselne scheme s on average 2-3 tmes more overhead than us. Ths s because, n the conventonal RS codng countermeasure, the orgnal data s frst reconstructed and then regenerate the symbol n the faled node. Consequently, t has to access the entre N symbols of the ntal data, only to reproduce a small fracton of symbols saved n the faled SN; ths greatly ncreases the transmtted message. Snce we conduct ncremental RS decodng, t s not surprsng that we can reduce such unnecessary transmssons. Fgure 5 shows the mpact of error probablty e on the probablty of successful decodng Pr rec for the above mentoned schemes. As we can see Pr rec decreases as e ncreases for two schemes. The reason s qute ntutve: the hgher error of data, the lower chance of successful decodng. However, the proposed scheme sgnfcantly outperforms baselne scheme, even for the hgh rate case (.e., e=0.7), the proposed scheme s on average -2 tmes more relable than Baselne scheme. Ths s because we ensure that each resdual component has more symbols than those correlated falure unaware schemes under the same e, whch means that we have more opportuntes to reconstruct the orgnal data. Another reason s that we utlze CRC for data ntegrty check, ths can mprove the accuracy of data meanwhle decrease the communcaton overhead, as verfed n Fgure Copyrght c 205 SERSC

11 Probablty of successful decodng (Pr rec ) Internatonal Journal of Grd Dstrbuton Computng Baselne Ours error probablty (e) Fgure 5. Probablty of Successful Decodng vs. Error Probablty 7. Conclusons Ths paper proposes an effcent data storage and recovery protocol for dstrbuted storage of cloud computng, whch ensures robustness n data dstrbuton and recovery process by effcently managng data among resdual SNs n the network n case of geographcally correlated falures. Analyss and performance results show that the proposed scheme has lower overhead when compared wth exstng works and can accomplsh compettve data robustness. Addtonally, under scenaros wth Byzantne falures, t performs much better than state-of-the-art RS codng scheme. In the future, we wll explore the mplements of the proposed protocol n real storage systems. Acknowledgments The authors acknowledge support from the Natural Scence Foundaton of Fuan Provnce (Grant number: 204J05079), the Scentfc Research Foundaton of Fuan Provncal Educaton Department (Grant numbers: JK203043, JA3248), the Scentfc Research Proect of Mnang unversty (Grant number: YKQ3003), and the Mnstry of educaton of Internet applcaton nnovaton open platform demonstraton base (meteorologcal cloud platform and applcaton) fund (Grant number: KJRP30). References [] R. Buyya, C. S. Yeo, S. Venugopal, J. Broberg and I. Brandc, Cloud computng and emergng IT platforms: vson, hype, and realty for delverng computng as the 5th utlty, Future Generaton Computer Systems, vol. 25, no. 6, (2009). [2] A. Dmaks, V. Prabhakaran and K. Ramchandran, Decentralzed erasure codes for dstrbuted networked storage, IEEE Transactons on Infromaton Theory, vol. 52, no. 6, (2006). [3] Z. Ruan, X. Sun and W. Lang, Hsao-Hwa Chen, Securng sensor data storage and query based on k- out-of-n codng, Internatonal Journal of Communcaton Systems, vol. 26, no. 5, (203). [4] P. Josh, H. S. Gunaw and K. Sen, Prefal: A programmable falure-necton framwork, Techncal Report No. UCB/EECS-20-30, (20) Aprl 22, [5] M. Gallet, N. Ygtbas, B. Javad, D. Kondo, A. Iosup and D. Epema, A model for space-correlated falures n large-scale dstrbuted systems, Proceedngs of the 6th Internatonal Conference on Parallel Processng. (200) August 3-September 3, Berln, Germany. [6] R. Rodrgues, B. Lskov, K. Chen, M. Lskov and D. Schultz, Automatc reconfguraton for large-scale relable storage systems, IEEE Transactons on Dependable and Secure Computng, vol. 9, no. 2, (202). [7] J. E. Pezoa and M. M. Hayat, Relablty of heterogeneous dstrbuted computng systems n the presence of correlated falures, IEEE Transactons on Parallel and Dstrbuted Computng, vol. 25, no. 4, (204). [8] N. Cao, S. Yu, Z. Yang, W. Luo and Y. T. Hou, Lt codes-based secure and relable cloud storage servce, Proceedngs of 3st IEEE Internatonal Conference on Computer Communcatons (INFOCOM), (202) March 25-30, Orlando, FL, USA. Copyrght c 205 SERSC 25

12 Internatonal Journal of Grd Dstrbuton Computng [9] G. Lang, B. Sommer and N. Vadya, Expermental performance comparson of byzantne fault-tolerant protocols for data centers, Proceedngs of 3st IEEE Internatonal Conference on Computer Communcatons (INFOCOM), (202) March 25-30, Orlando, FL, USA. [0] S. Neumayer, G. Zussman, R. Chen and E. Modano, Assessng the mpact of geographcally correlated network falures, Proceedngs of IEEE Mltary Communcatons Conference (MILCOM), (2008) November 6-9, San Dego, CA, USA. [] P. Agarwal, A. Efrat, S. Gangunte, D. Hay, S. Sankararaman and G. Zussman, Network vulnerablty to sngle, multple, and probablstc physcal attacks, Proceedngs of IEEE Mltary Communcatons Conference (MILCOM), (200) October 3-November 3, San Jose, CA, USA. [2] S. Baneree, S. Sshrazpourazad and A. Sen, On-regon-based fault fault tolerant desgn of dstrbuted fle storage n networks, Proceedngs of 3st IEEE Internatonal Conference on Computer Communcatons (INFOCOM), (202) March 25-30, Orlando, FL, USA. [3] S. Neumayer and E. Modan, Network relablty wth geographcally correlated falures, Proceedngs of 29st IEEE Internatonal Conference on Computer Communcatons (INFOCOM), (200) March 5-9, San Dego, CA, USA. [4] D. Leong, A. G. Dmaks and T. Ho, Dstrbuted storage allocatons, IEEE Transactons on Informaton Theory, vol. 58, no. 7, (202). [5] A. Jang and J. Bruck, Network fle storage wth graceful performance degradaton, ACM Transactons on Storage, vol., no. 2, (2005). [6] M. Sardar, R. Restrepo, F. Fekr and E. Solann, Memory allocaton n dstrbuted storage networks, Proceedngs of IEEE Internatonal Symposum on Informaton Theory (ISIT), (200) June 3-8, Austn, TX, USA. [7] T. K. Moon, Error correcton codng: mathematcal methods and algorthms, John Wley & Sons Corporaton, New Jersey, (2005). Authors Zhqang Ruan, s a lecturer at the unversty of Mnang Unversty, Chna. He receved the B.S. degree n Computer Scence from Fuan Normal Unversty, Chna, n 2006, the M.S. and Ph.D n Computng Scence from Hunan Unversty of Informaton and Engneerng, Chna, n 2009 and 202, respectvely. Hs research nterests nclude network and nformaton securty, dstrbuted algorthms, Byzantne fault tolerance, and ad hoc wreless networks. Zh L, receved the Ph.D. degree from the Graduate Unversty of Chnese Academy of Scence, Beng, Chna, n 203. He s currently an Assstant Researcher wth the Insttute of Informaton Engneerng, Chna Academy of Scence, Beng, Chna. Hs research nterests nclude moble computng, delay tolerant networks, wreless sensor networks, wreless securty, and cloud computng. 26 Copyrght c 205 SERSC