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  1. 1. Ensuring Data Storage Security in Cloud Computing Cong Wang, Qian Wang, and Kui Ren Wenjing Lou Department of ECE Department of ECE Illinois Institute of Technology Worcester Polytechnic Institute Email: {cwang, qwang, kren} Email: Abstract—Cloud Computing has been envisioned as the next- number of reasons. Firstly, traditional cryptographic primitivesgeneration architecture of IT Enterprise. In contrast to tradi- for the purpose of data security protection can not be directlytional solutions, where the IT services are under proper physical, adopted due to the users’ loss control of data under Cloudlogical and personnel controls, Cloud Computing moves theapplication software and databases to the large data centers, Computing. Therefore, verification of correct data storagewhere the management of the data and services may not be in the cloud must be conducted without explicit knowledgefully trustworthy. This unique attribute, however, poses many of the whole data. Considering various kinds of data fornew security challenges which have not been well understood. each user stored in the cloud and the demand of long termIn this article, we focus on cloud data storage security, which continuous assurance of their data safety, the problem ofhas always been an important aspect of quality of service. Toensure the correctness of users’ data in the cloud, we propose an verifying correctness of data storage in the cloud becomeseffective and flexible distributed scheme with two salient features, even more challenging. Secondly, Cloud Computing is not justopposing to its predecessors. By utilizing the homomorphic token a third party data warehouse. The data stored in the cloudwith distributed verification of erasure-coded data, our scheme may be frequently updated by the users, including insertion,achieves the integration of storage correctness insurance and data deletion, modification, appending, reordering, etc. To ensureerror localization, i.e., the identification of misbehaving server(s).Unlike most prior works, the new scheme further supports secure storage correctness under dynamic data update is hence ofand efficient dynamic operations on data blocks, including: data paramount importance. However, this dynamic feature alsoupdate, delete and append. Extensive security and performance makes traditional integrity insurance techniques futile andanalysis shows that the proposed scheme is highly efficient and entails new solutions. Last but not the least, the deploymentresilient against Byzantine failure, malicious data modification of Cloud Computing is powered by data centers running inattack, and even server colluding attacks. a simultaneous, cooperated and distributed manner. Individual I. I NTRODUCTION user’s data is redundantly stored in multiple physical loca- Several trends are opening up the era of Cloud Computing, tions to further reduce the data integrity threats. Therefore,which is an Internet-based development and use of computer distributed protocols for storage correctness assurance will betechnology. The ever cheaper and more powerful processors, of most importance in achieving a robust and secure cloud datatogether with the software as a service (SaaS) computing archi- storage system in the real world. However, such important areatecture, are transforming data centers into pools of computing remains to be fully explored in the literature.service on a huge scale. The increasing network bandwidth and Recently, the importance of ensuring the remote datareliable yet flexible network connections make it even possible integrity has been highlighted by the following researchthat users can now subscribe high quality services from data works [3]–[7]. These techniques, while can be useful to ensureand software that reside solely on remote data centers. the storage correctness without having users possessing data, Moving data into the cloud offers great convenience to can not address all the security threats in cloud data storage,users since they don’t have to care about the complexities since they are all focusing on single server scenario andof direct hardware management. The pioneer of Cloud Com- most of them do not consider dynamic data operations. Asputing vendors, Amazon Simple Storage Service (S3) and an complementary approach, researchers have also proposedAmazon Elastic Compute Cloud (EC2) [1] are both well distributed protocols [8]–[10] for ensuring storage correct-known examples. While these internet-based online services ness across multiple servers or peers. Again, none of thesedo provide huge amounts of storage space and customizable distributed schemes is aware of dynamic data operations.computing resources, this computing platform shift, however, As a result, their applicability in cloud data storage can beis eliminating the responsibility of local machines for data drastically limited.maintenance at the same time. As a result, users are at the In this paper, we propose an effective and flexible distributedmercy of their cloud service providers for the availability and scheme with explicit dynamic data support to ensure theintegrity of their data. Recent downtime of Amazon’s S3 is correctness of users’ data in the cloud. We rely on erasure-such an example [2]. correcting code in the file distribution preparation to provide From the perspective of data security, which has always redundancies and guarantee the data dependability. This con-been an important aspect of quality of service, Cloud Com- struction drastically reduces the communication and storageputing inevitably poses new challenging security threats for overhead as compared to the traditional replication-based file
  2. 2. distribution techniques. By utilizing the homomorphic token S Me s e cu rity sag ewith distributed verification of erasure-coded data, our scheme rit y low cu F F low Se ageachieves the storage correctness insurance as well as data Mes s Optional Third Party Auditor Cloud Storageerror localization: whenever data corruption has been detected Serversduring the storage correctness verification, our scheme can Data Flowalmost guarantee the simultaneous localization of data errors, Usersi.e., the identification of the misbehaving server(s). essage Flow Security M Our work is among the first few ones in this field to consider Cloud Service Providerdistributed data storage in Cloud Computing. Our contributioncan be summarized as the following three aspects: Fig. 1: Cloud data storage architecture1) Compared to many of its predecessors, which only providebinary results about the storage state across the distributedservers, the challenge-response protocol in our work further these operations we are considering are block update, delete,provides the localization of data error. insert and append.2) Unlike most prior works for ensuring remote data integrity, As users no longer possess their data locally, it is of criticalthe new scheme supports secure and efficient dynamic opera- importance to assure users that their data are being correctlytions on data blocks, including: update, delete and append. stored and maintained. That is, users should be equipped with security means so that they can make continuous correctness3) Extensive security and performance analysis shows that assurance of their stored data even without the existence ofthe proposed scheme is highly efficient and resilient against local copies. In case that users do not necessarily have theByzantine failure, malicious data modification attack, and even time, feasibility or resources to monitor their data, they canserver colluding attacks. delegate the tasks to an optional trusted TPA of their respective The rest of the paper is organized as follows. Section II choices. In our model, we assume that the point-to-pointintroduces the system model, adversary model, our design goal communication channels between each cloud server and theand notations. Then we provide the detailed description of our user is authenticated and reliable, which can be achieved inscheme in Section III and IV. Section V gives the security practice with little overhead. Note that we don’t address theanalysis and performance evaluations, followed by Section VI issue of data privacy in this paper, as in Cloud Computing,which overviews the related work. Finally, Section VII gives data privacy is orthogonal to the problem we study here.the concluding remark of the whole paper. B. Adversary Model II. P ROBLEM S TATEMENT Security threats faced by cloud data storage can comeA. System Model from two different sources. On the one hand, a CSP can A representative network architecture for cloud data storage be self-interested, untrusted and possibly malicious. Not onlyis illustrated in Figure 1. Three different network entities can does it desire to move data that has not been or is rarelybe identified as follows: accessed to a lower tier of storage than agreed for monetary • User: users, who have data to be stored in the cloud and reasons, but it may also attempt to hide a data loss incident rely on the cloud for data computation, consist of both due to management errors, Byzantine failures and so on. individual consumers and organizations. On the other hand, there may also exist an economically- • Cloud Service Provider (CSP): a CSP, who has signif- motivated adversary, who has the capability to compromise icant resources and expertise in building and managing a number of cloud data storage servers in different time distributed cloud storage servers, owns and operates live intervals and subsequently is able to modify or delete users’ Cloud Computing systems. data while remaining undetected by CSPs for a certain period. • Third Party Auditor (TPA): an optional TPA, who has Specifically, we consider two types of adversary with different expertise and capabilities that users may not have, is levels of capability in this paper: trusted to assess and expose risk of cloud storage services Weak Adversary: The adversary is interested in corrupting the on behalf of the users upon request. user’s data files stored on individual servers. Once a server is In cloud data storage, a user stores his data through a CSP comprised, an adversary can pollute the original data files byinto a set of cloud servers, which are running in a simulta- modifying or introducing its own fraudulent data to preventneous, cooperated and distributed manner. Data redundancy the original data from being retrieved by the user.can be employed with technique of erasure-correcting code Strong Adversary: This is the worst case scenario, in whichto further tolerate faults or server crash as user’s data grows we assume that the adversary can compromise all the storagein size and importance. Thereafter, for application purposes, servers so that he can intentionally modify the data files asthe user interacts with the cloud servers via CSP to access or long as they are internally consistent. In fact, this is equivalentretrieve his data. In some cases, the user may need to perform to the case where all servers are colluding together to hide ablock level operations on his data. The most general forms of data loss or corruption incident.
  3. 3. C. Design Goals integrated with the verification of erasure-coded data [8] [12]. To ensure the security and dependability for cloud data Subsequently, it is also shown how to derive a challenge-storage under the aforementioned adversary model, we aim response protocol for verifying the storage correctness as wellto design efficient mechanisms for dynamic data verification as identifying misbehaving servers. Finally, the procedure forand operation and achieve the following goals: (1) Storage file retrieval and error recovery based on erasure-correctingcorrectness: to ensure users that their data are indeed stored code is outlined.appropriately and kept intact all the time in the cloud. (2) A. File Distribution PreparationFast localization of data error: to effectively locate the mal-functioning server when data corruption has been detected. (3) It is well known that erasure-correcting code may be usedDynamic data support: to maintain the same level of storage to tolerate multiple failures in distributed storage systems. Incorrectness assurance even if users modify, delete or append cloud data storage, we rely on this technique to disperse thetheir data files in the cloud. (4) Dependability: to enhance data data file F redundantly across a set of n = m + k distributedavailability against Byzantine failures, malicious data modifi- servers. A (m + k, k) Reed-Solomon erasure-correcting codecation and server colluding attacks, i.e. minimizing the effect is used to create k redundancy parity vectors from m databrought by data errors or server failures. (5) Lightweight: vectors in such a way that the original m data vectors can beto enable users to perform storage correctness checks with reconstructed from any m out of the m + k data and parityminimum overhead. vectors. By placing each of the m + k vectors on a different server, the original data file can survive the failure of any k ofD. Notation and Preliminaries the m+k servers without any data loss, with a space overhead • F – the data file to be stored. We assume that F can be of k/m. For support of efficient sequential I/O to the original denoted as a matrix of m equal-sized data vectors, each file, our file layout is systematic, i.e., the unmodified m data consisting of l blocks. Data blocks are all well represented file vectors together with k parity vectors is distributed across as elements in Galois Field GF (2p ) for p = 8 or 16. m + k different servers. • A – The dispersal matrix used for Reed-Solomon coding. Let F = (F1 , F2 , . . . , Fm ) and Fi = (f1i , f2i , . . . , fli )T • G – The encoded file matrix, which includes a set of (i ∈ {1, . . . , m}), where l ≤ 2p − 1. Note all these blocks n = m + k vectors, each consisting of l blocks. are elements of GF (2p ). The systematic layout with parity • fkey (·) – pseudorandom function (PRF), which is defined vectors is achieved with the information dispersal matrix A, as f : {0, 1}∗ × key → GF (2p ). derived from an m × (m + k) Vandermonde matrix [13]: • φkey (·) – pseudorandom permutation (PRP), which is   1 1 ... 1 1 ... 1 defined as φ : {0, 1}log2 (l) × key → {0, 1}log2 (l) .  β1  β2 ... βm βm+1 . . . βn   • ver – a version number bound with the index for individ-  , . . . . .. . . . . .. . . ual blocks, which records the times the block has been  . . . . . . .  modified. Initially we assume ver is 0 for all data blocks. m−1 m−1 m−1 m−1 m−1 β1 β2 . . . βm βm+1 . . . βn • sver – the seed for PRF, which depends on the file name, ij block index i, the server position j as well as the optional where βj (j ∈ {1, . . . , n}) are distinct elements randomly block version number ver. picked from GF (2p ). After a sequence of elementary row transformations, the III. E NSURING C LOUD DATA S TORAGE desired matrix A can be written as In cloud data storage system, users store their data in   1 0 . . . 0 p11 p12 . . . p1kthe cloud and no longer possess the data locally. Thus, the  0 1 . . . 0 p21 p22 . . . p2k   correctness and availability of the data files being stored on the A = (I|P) =  . . . . . . .. . ,distributed cloud servers must be guaranteed. One of the key  . . . . .. .. . . . . . .  .issues is to effectively detect any unauthorized data modifica- 0 0 . . . 1 pm1 pm2 . . . pmktion and corruption, possibly due to server compromise and/or where I is a m × m identity matrix and P is the secret parityrandom Byzantine failures. Besides, in the distributed case generation matrix with size m × k. Note that A is derivedwhen such inconsistencies are successfully detected, to find from a Vandermonde matrix, thus it has the property that anywhich server the data error lies in is also of great significance, m out of the m + k columns form an invertible matrix.since it can be the first step to fast recover the storage errors. By multiplying F by A, the user obtains the encoded file: To address these problems, our main scheme for ensuringcloud data storage is presented in this section. The first part of G= F·A = (G(1) , G(2) , . . . , G(m) , G(m+1) , . . . , G(n) )the section is devoted to a review of basic tools from coding = (F1 , F2 , . . . , Fm , G(m+1) , . . . , G(n) ),theory that are needed in our scheme for file distribution across (j) (j) (j)cloud servers. Then, the homomorphic token is introduced. where G(j) = (g1 , g2 , . . . , gl )T (j ∈ {1, . . . , n}). AsThe token computation function we are considering belongs noticed, the multiplication reproduces the original data fileto a family of universal hash function [11], chosen to pre- vectors of F and the remaining part (G(m+1) , . . . , G(n) ) areserve the homomorphic properties, which can be perfectly k parity vectors generated based on F.
  4. 4. Algorithm 1 Token Pre-computation Algorithm 2 Correctness Verification and Error Localization 1: procedure 1: procedure C HALLENGE (i) (i) 2: Choose parameters l, n and function f, φ; 2: Recompute αi = fkchal (i) and kprp from KP RP ; (i) 3: Choose the number t of tokens; 3: Send {αi , kprp } to all the cloud servers; 4: Choose the number r of indices per verification; 4: Receive from servers: (j) 5: Generate master key Kprp and challenge kchal ; {Ri = r αq ∗ G(j) [φk(i) (q)]|1 ≤ j ≤ n} q=1 i for vector G(j) , j ← 1, n do prp 6: 5: for (j ← m + 1, n) do 7: for round i← 1, t do 6: R(j) ← R(j) − r fkj (sIq ,j )·αq , Iq = φk(i) (q) (i) q=1 i prp 8: Derive αi = fkchal (i) and kprp from KP RP . 7: end for (j) r 9: Compute vi = q=1 αq ∗ G(j) [φk(i) (q)] i 8: (1) (m) if ((Ri , . . . , Ri ) · P==(Ri (m+1) (n) , . . . , Ri )) then prp10: end for 9: Accept and ready for the next challenge.11: end for 10: else12: Store all the vi s locally. 11: for (j ← 1, n) do13: end procedure (j) (j) 12: if (Ri ! =vi ) then 13: return server j is misbehaving. 14: end ifB. Challenge Token Precomputation 15: end for In order to achieve assurance of data storage correctness 16: end if 17: end procedureand data error localization simultaneously, our scheme entirelyrelies on the pre-computed verification tokens. The main ideais as follows: before file distribution the user pre-computes acertain number of short verification tokens on individual vector user stores them locally to obviate the need for encryptionG(j) (j ∈ {1, . . . , n}), each token covering a random subset and lower the bandwidth overhead during dynamic data op-of data blocks. Later, when the user wants to make sure the eration which will be discussed shortly. The details of tokenstorage correctness for the data in the cloud, he challenges generation are shown in Algorithm 1. Once all tokens are computed, the final step beforethe cloud servers with a set of randomly generated block (j)indices. Upon receiving challenge, each cloud server computes file distribution is to blind each parity block gi ina short “signature” over the specified blocks and returns them (G(m+1) , . . . , G(n) ) byto the user. The values of these signatures should match the (j) (j) gi ← gi + fkj (sij ), i ∈ {1, . . . , l},corresponding tokens pre-computed by the user. Meanwhile,as all servers operate over the same subset of the indices, the where kj is the secret key for parity vector G(j) (j ∈ {m +requested response values for integrity check must also be a 1, . . . , n}). This is for protection of the secret matrix P. Wevalid codeword determined by secret matrix P. will discuss the necessity of using blinded parities in detail Suppose the user wants to challenge the cloud servers t in Section V. After blinding the parity information, the usertimes to ensure the correctness of data storage. Then, he disperses all the n encoded vectors G(j) (j ∈ {1, . . . , n})must pre-compute t verification tokens for each G(j) (j ∈ across the cloud servers S1 , S2 , . . . , Sn .{1, . . . , n}), using a PRF f (·), a PRP φ(·), a challenge key C. Correctness Verification and Error Localizationkchal and a master permutation key KP RP . To generate the Error localization is a key prerequisite for eliminating errorsith token for server j, the user acts as follows: in storage systems. However, many previous schemes do not 1) Derive a random challenge value αi of GF (2p ) by αi = explicitly consider the problem of data error localization, (i) fkchal (i) and a permutation key kprp based on KP RP . thus only provide binary results for the storage verification. 2) Compute the set of r randomly-chosen indices: Our scheme outperforms those by integrating the correctness verification and error localization in our challenge-response {Iq ∈ [1, ..., l]|1 ≤ q ≤ r}, where Iq = φk(i) (q). prp protocol: the response values from servers for each challenge 3) Calculate the token as: not only determine the correctness of the distributed storage, r but also contain information to locate potential data error(s). (j) (j) Specifically, the procedure of the i-th challenge-response for vi = αq ∗ G(j) [Iq ], where G(j) [Iq ] = gIq . i q=1 a cross-check over the n servers is described as follows: 1) The user reveals the αi as well as the i-th permutation (j) (i)Note that vi , which is an element of GF (2p ) with small key kprp to each servers.size, is the response the user expects to receive from server j 2) The server storing vector G(j) aggregates those r rows (i)when he challenges it on the specified data blocks. specified by index kprp into a linear combination After token generation, the user has the choice of either r (j)keeping the pre-computed tokens locally or storing them in Ri = αq ∗ G(j) [φk(i) (q)]. i prpencrypted form on the cloud servers. In our case here, the q=1
  5. 5. (j) Algorithm 3 Error Recovery 3) Upon receiving Ri s from all the servers, the user takes away blind values in R(j) (j ∈ {m + 1, . . . , n}) by 1: procedure r % Assume the block corruptions have been detected (j) (j) among Ri ← Ri − fkj (sIq ,j ) · αq , where Iq = φk(i) (q). i q=1 prp % the specified r rows; % Assume s ≤ k servers have been identified misbehaving 4) Then the user verifies whether the received values re- 2: Download r rows of blocks from servers; main a valid codeword determined by secret matrix P: 3: Treat s servers as erasures and recover the blocks. (1) (m) ? (m+1) (n) 4: Resend the recovered blocks to corresponding servers. (Ri , . . . , Ri ) · P = (Ri , . . . , Ri ). 5: end procedure Because all the servers operate over the same subset ofindices, the linear aggregation of these r specified rows (1) (n)(Ri , . . . , Ri ) has to be a codeword in the encoded file operations of update, delete and append to modify the data filematrix. If the above equation holds, the challenge is passed. while maintaining the storage correctness assurance.Otherwise, it indicates that among those specified rows, there The straightforward and trivial way to support these opera-exist file block corruptions. tions is for user to download all the data from the cloud servers Once the inconsistency among the storage has been success- and re-compute the whole parity blocks as well as verificationfully detected, we can rely on the pre-computed verification tokens. This would clearly be highly inefficient. In this section,tokens to further determine where the potential data error(s) we will show how our scheme can explicitly and efficiently (j)lies in. Note that each response Ri is computed exactly in the handle dynamic data operations for cloud data storage. (j)same way as token vi , thus the user can simply find whichserver is misbehaving by verifying the following n equations: A. Update Operation (j) ? (j) In cloud data storage, sometimes the user may need to Ri = vi , j ∈ {1, . . . , n}. modify some data block(s) stored in the cloud, from itsAlgorithm 2 gives the details of correctness verification and current value fij to a new one, fij + ∆fij . We refer thiserror localization. operation as data update. Due to the linear property of Reed- Solomon code, a user can perform the update operation andD. File Retrieval and Error Recovery generate the updated parity blocks by using ∆fij only, without Since our layout of file matrix is systematic, the user can involving any other unchanged blocks. Specifically, the userreconstruct the original file by downloading the data vectors can construct a general update matrix ∆F asfrom the first m servers, assuming that they return the correct   ∆f11 ∆f12 . . . ∆f1mresponse values. Notice that our verification scheme is based  ∆f21 ∆f22 . . . ∆f2m   on random spot-checking, so the storage correctness assurance ∆F =  . . .. . is a probabilistic one. However, by choosing system param-  . . . . . . . eters (e.g., r, l, t) appropriately and conducting enough times ∆fl1 ∆fl2 . . . ∆flmof verification, we can guarantee the successful file retrieval = (∆F1 , ∆F2 , . . . , ∆Fm ).with high probability. On the other hand, whenever the data Note that we use zero elements in ∆F to denote the unchangedcorruption is detected, the comparison of pre-computed tokens blocks. To maintain the corresponding parity vectors as well asand received response values can guarantee the identification be consistent with the original file layout, the user can multiplyof misbehaving server(s), again with high probability, which ∆F by A and thus generate the update information for bothwill be discussed shortly. Therefore, the user can always the data vectors and parity vectors as follows:ask servers to send back blocks of the r rows specified inthe challenge and regenerate the correct blocks by erasure ∆F · A = (∆G(1) , . . . , ∆G(m) , ∆G(m+1) , . . . , ∆G(n) )correction, shown in Algorithm 3, as long as there are at most = (∆F1 , . . . , ∆Fm , ∆G(m+1) , . . . , ∆G(n) ),k misbehaving servers are identified. The newly recoveredblocks can then be redistributed to the misbehaving servers where ∆G(j) (j ∈ {m + 1, . . . , n}) denotes the updateto maintain the correctness of storage. information for the parity vector G(j) . Because the data update operation inevitably affects some IV. P ROVIDING DYNAMIC DATA O PERATION S UPPORT or all of the remaining verification tokens, after preparation of So far, we assumed that F represents static or archived update information, the user has to amend those unused tokensdata. This model may fit some application scenarios, such for each vector G(j) to maintain the same storage correctnessas libraries and scientific datasets. However, in cloud data assurance. In other words, for all the unused tokens, the userstorage, there are many potential scenarios where data stored needs to exclude every occurrence of the old data block andin the cloud is dynamic, like electronic documents, photos, or replace it with the new one. Thanks to the homomorphiclog files etc. Therefore, it is crucial to consider the dynamic construction of our verification token, the user can performcase, where a user may wish to perform various block-level the token update efficiently. To give more details, suppose a
  6. 6. (j)block G(j) [Is ], which is covered by the specific token vi , has To support block append operation, we need a slight modi-been changed to G(j) [Is ] + ∆G(j) [Is ], where Is = φk(i) (s). fication to our token pre-computation. Specifically, we require prp (j)To maintain the usability of token vi , it is not hard to verify the user to expect the maximum size in blocks, denoted asthat the user can simply update it by lmax , for each of his data vector. The idea of supporting block append, which is similar as adopted in [7], relies on (j) (j) vi ← vi + αs ∗ ∆G(j) [Is ], i the initial budget for the maximum anticipated data size lmax in each encoded data vector as well as the system parameterwithout retrieving any other r − 1 blocks required in the pre- (j) rmax = ⌈r ∗ (lmax /l)⌉ for each pre-computed challenge-computation of vi . response token. The pre-computation of the i-th token on After the amendment to the affected tokens1 , the user needs (j) server j is modified as follows:to blind the update information ∆gi for each parity block in rmax(∆G(m+1) , . . . , ∆G(n) ) to hide the secret matrix P by vi = αq ∗ G(j) [Iq ], i (j) (j) ∆gi ← ∆gi + fkj (sver ), i ij ∈ {1, . . . , l}. q=1Here we use a new seed sver for the PRF. The version number where ijver functions like a counter which helps the user to keep G(j) [φk(i) (q)] , [φk(i) (q)] ≤ ltrack of the blind information on the specific parity blocks. G(j) [Iq ] = prp prpAfter blinding, the user sends update information to the cloud 0 , [φk(i) (q)] > l prpservers, which perform the update operation as This formula guarantees that on average, there will be r indices G (j) ←G (j) + ∆G (j) , (j ∈ {1, . . . , n}). falling into the range of existing l blocks. Because the cloud servers and the user have the agreement on the number ofB. Delete Operation existing blocks in each vector G(j) , servers will follow exactly Sometimes, after being stored in the cloud, certain data the above procedure when re-computing the token values uponblocks may need to be deleted. The delete operation we are receiving user’s challenge request.considering is a general one, in which user replaces the data Now when the user is ready to append new blocks, i.e.,block with zero or some special reserved data symbol. From both the file blocks and the corresponding parity blocks arethis point of view, the delete operation is actually a special case generated, the total length of each vector G(j) will be increasedof the data update operation, where the original data blocks and fall into the range [l, lmax ]. Therefore, the user will updatecan be replaced with zeros or some predetermined special those affected tokens by adding αs ∗ G(j) [Is ] to the old vi iblocks. Therefore, we can rely on the update procedure to whenever G(j) [Is ] = 0 for Is > l, where Is = φk(i) (s). The prpsupport delete operation, i.e., by setting ∆fij in ∆F to be parity blinding is similar as introduced in update operation,−∆fij . Also, all the affected tokens have to be modified and thus is omitted here.the updated parity information has to be blinded using thesame method specified in update operation. D. Insert Operation An insert operation to the data file refers to an appendC. Append Operation operation at the desired index position while maintaining the In some cases, the user may want to increase the size of same data block structure for the whole data file, i.e., insertinghis stored data by adding blocks at the end of the data file, a block F [j] corresponds to shifting all blocks starting withwhich we refer as data append. We anticipate that the most index j + 1 by one slot. An insert operation may affect manyfrequent append operation in cloud data storage is bulk append, rows in the logical data file matrix F, and a substantial numberin which the user needs to upload a large number of blocks of computations are required to renumber all the subsequent(not a single block) at one time. blocks as well as re-compute the challenge-response tokens. Given the file matrix F illustrated in file distribution prepa- Therefore, an efficient insert operation is difficult to supportration, appending blocks towards the end of a data file is and thus we leave it for our future work.equivalent to concatenate corresponding rows at the bottomof the matrix layout for file F. In the beginning, there are V. S ECURITY A NALYSIS AND P ERFORMANCE E VALUATIONonly l rows in the file matrix. To simplify the presentation, In this section, we analyze our proposed scheme in termswe suppose the user wants to append m blocks at the end of of security and efficiency. Our security analysis focuses onfile F, denoted as (fl+1,1 , fl+1,2 , ..., fl+1,m ) (We can always the adversary model defined in Section II. We also evaluateuse zero-padding to make a row of m elements.). With the the efficiency of our scheme via implementation of both filesecret matrix P, the user can directly calculate the append distribution preparation and verification token precomputation.blocks for each parity server as (m+1) (n) A. Security Strength Against Weak Adversary (fl+1,1 , ..., fl+1,m ) · P = (gl+1 , ..., gl+1 ). 1) Detection Probability against data modification: In our 1 In practice, it is possible that only a fraction of tokens need amendment, scheme, servers are required to operate on specified rows insince the updated blocks may not be covered by all the tokens. each correctness verification for the calculation of requested