Efficient Dynamic Integrity Verification for Big Data Supporting Users Revocability

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1 nformaton Artcle Effcent Dynamc Integrty Verfcaton for Bg Data Supportng Users Revocablty Xnpeng Zhang 1,2, *, Chunxang Xu 1, Xaojun Zhang 1, Tazong Gu 2, Zh Geng 2 and Guopng Lu 2 1 School of Computer Scence and Engneerng, Unversty of Electronc Scence and Technology of Chna, Chengdu , Chna; C.X.; X.Z. 2 Logstc Informaton Center, Jont Logstcs Department, Chengdu Mltary Regon, Chengdu , Chna; T.G.; G.L. * Correspondence: Tel.: Academc Edtor: Gordana Dodg-Crnkovc Receved: 6 February 2016; Accepted: 12 Aprl 2016; Publshed: 27 May 2016 Abstract: Wth the advent of the bg data era, cloud data storage and retreval have become popular for effcent data management n large companes and organzatons, thus they can enjoy the on-demand hgh-qualty cloud storage servce. Meanwhle, for securty reasons, those companes and organzatons would lke to verfy the ntegrty of ther data once storng t n the cloud. To address ths ssue, they need a proper cloud storage audtng scheme whch matches ther actual demands. Current research often focuses on the stuaton where the data manager owns the data; however, the data belongs to the company, rather than the data managers n the real stuaton whch has been overlooked. For example, the current data manager s no longer sutable to manage the data stored n the cloud after a perod and wll be replaced by another one. The successor needs to verfy the ntegrty of the former managed data; ths problem s obvously nevtable n realty. In ths paper, we fll ths gap by gvng a practcal effcent revocable prvacy-preservng publc audtng scheme for cloud storage meetng the audtng requrement of large companes and organzaton s data transfer. The scheme s conceptually smple and s proven to be secure even when the cloud servce provder conspres wth revoked users. Keywords: cloud storage; prvacy-preservng; ntegrty verfcaton; user revocaton 1. Introducton Nowadays, a large amount of data has been gathered and produced by ndvduals, companes and organzatons. Moore s law s broken by the rapd growth of the data scale. The growth of the data scale s far more than the growth of the processng and storage capacty of computer. For companes and organzatons, the volumes of those data are often so tremendous that they cannot process and manage t effectvely by themselves. In fact, some of them even don t have suffcent dsk space to store ther data because t s an enormous burden to purchase such a large number of dsks. Facng ths realty, companes and organzatons have to turn to cloud servce provder CSP for help, e.g., Dropbox, Google Drve and skydrve. As one of the domnate servces n cloud computng, cloud storage allows users to store data on clouds nstead of ther local computng systems. By data outsourcng, ths knd of new storage servce has many advantages such as relevng users burden n terms of data management and mantenance, unversal data access wth ndependent geographcal locatons and avodng captal cost on hardware and software. However, at the meantme, cloud storage also brngs a number of challengng securty problems [1 3] despte ts appealng features. Securty concerns stll deter potental consumers from usng the servce. One of the major securty concerns [1] on the cloud storage servce s whether Informaton 2016, 7, 31; do: /nfo

2 Informaton 2016, 7, 31 2 of 16 the cloud could ensure the ntegrty of the stored data. Integrty challenges of data corrupton are nevtable [4 6], but cloud servce provders may not be fully trusted from the vew of the nterests. Cloud Securty Allance CSA conducted a systematc nvestgaton nto reported vulnerabltes n cloud computng such as outages, downtmes, and data loss. CSA also released a whte paper [7] n 2013 whch revealed that the top three threats were Insecure Interfaces & APIs, Data Loss & Leakage and Hardware Falure. These three threats accounted for 64% of all cloud outage ncdents whle Data Loss & Leakage accounted for 25%. Consequently, guaranteeng the ntegrty of the data, or data audtng, n cloud s a hghly desrable securty demand for secure cloud storage. Many researches have been done on checkng the ntegrty for outsourcng data n the cloud. Despte a number of cloud data audtng schemes [8 15] have been proposed wth dfferent requrements so far, they are all desgned for tradtonal cloud storage envronment wthout consderng the applcatons for user revocable. We notce that almost all of the prevous publc audtng systems are fxed by the user who computes the block tags. In other words, those audtng schemes requre that the user of the cloud storage servce s always the same one durng the entre data perod. However, t s mpractcal. On one hand, the verfcaton nformaton of an audtng system such as the user s publc key may expre after a perod of tme. On the other hand, the user may be a data manager of a company for a tme and may leave for some reasons. For example, the data manager may go to work n another company for a hgher salary. Therefore, for practcal consderatons, an audtng scheme should support effcent user revocaton. Recently, a few publc audtng schemes for cloud storage systems wth user revocaton have been presented, e.g., [16 18]. However those schemes are desgned for audtng shared cloud data rather than for revokng napproprate users when audtng owned cloud data. Moreover, we note that the exstng users revocable publc cloud storage audtng schemes are ether nvolved or less secure. Specfcally, the revocable publc cloud storage audtng schemes n [17] and [18] employ the unweldy dynamc broadcast encrypton [19] and group sgnature [20] technques respectvely. Although the scheme n [16] s more effcent, t can t resst colluson attacks between the cloud and a revoked user. That s, the colluson of the cloud and a revoked user could always deceve an ncumbent user nto belef that the data n the cloud remans ntact even f t s actually not. Thus colluson attack resstance s ndspensable n a revocable publc cloud storage audtng schemes. As a result, t s crucal to desgn effcent and colluson-resstant user revocable publc audtng schemes Related Work Juels et al. proposed an audtng scheme called Proofs Of Retrevablty POR whle the audtng scheme proposed by Atenese et al. s called Provable Data Possesson PDP. Shacham-Waters used BLS sgnature constructed an effcent publc verfable POR scheme [13]. Based on ther research, many cloud storage audtng schemes have been proposed to verfy the data ntegrty wthout needng to retreve entre data [8 13]. However, the prvacy protecton of user s data has not yet been consdered n most of these schemes [11,13]. Ths shortcomng can greatly affect the safety of these schemes. Therefore, the audtng process should not leak the knowledge of the challenged fles to the thrd-party audtor. In 2013, Wang et al. [9] presented a prvacy-preservng publc audtng scheme for cloud storage; t resorts to the homomorphc authentcator technque and random maskng technque to realze prvacy-preservng publc audtng and take advantage of the technque of blnear aggregate sgnature to realze batch audtng. All the audtng schemes mentoned above do not consder the user revocaton problem, thus those schemes can only be appled to statc users. However, user revocaton s an obvously nevtable problem. Recently, a few audtng schemes supportng user revocaton are publshed for realzng mult-user shared cloud storage audt. In 2012 Wang et al. [21] frst ntroduced the shared cloud storage audtng ssue and proposed a prvate audtng scheme wth user revocaton based on group

3 Informaton 2016, 7, 31 3 of 16 sgnature [20]. In 2013, Wang et al. [17] presented a publc audtng scheme wth user revocaton for shared cloud storage, based on the dynamc broadcast encrypton scheme of [19] and the bdrectonal proxy re-sgnature scheme of [21]. Later, usng a group sgnature lke technque, Yuan and Yu proposed a publc verson of the scheme n [18]. As group sgnature and dynamc broadcast encrypton technques are both nvolved, the above revocable audtng schemes are all less effcent n practce. To address ths problem, n 2015 Wang et al. presented an effcent revocable publc audtng scheme n [16] by just usng the bdrectonal proxy re-sgnature scheme of [22]. However, we note that the bdrectonal proxy re-sgnature scheme cannot resst the colluson attack of the cloud and a revoked user snce an ncumbent user s secret key can be recovered from the cloud s update key and a revoked user s secret key. We also notce that all the prevous papers focus on the data ntegrty and securty are under the shared cloud storage model [23,24]. Although these schemes nvolve user revocaton problem, the man research s stll cloud data sharng, where securty problems cannot be gnored. Therefore, we analyze the revocaton need of companes and organzatons cloud storage data users, propose the model of user revocable audtng schemes and desgn an effcent dynamc ntegrty verfcaton scheme for bg data supportng user revocablty. Ths s the major work we are dong n ths paper Our Contrbutons Motvated by above, n ths paper, an effcent dynamc ntegrty verfcaton for bg data supportng users revocablty and thrd-party prvacy-preservng audtng scheme be proposed. To acheve ths, we make the followng contrbutons: we analyze the revocaton need of companes and organzatons cloud storage data users. Based on technque of blnear aggregate sgnature, a specfc revocable publc cloud storage thrd-party audtng scheme be presented. It can help the current user audt the data whch was sent to the cloud by all the prevous users, and can satsfy the user transfer demand of large companes and organzatons. Meanwhle cloud users can delegate a thrd party TPA to perform securty audtng tasks as t s not economcally feasble for them to handle t by themselves. By gven a precse defnton of securty that colluson resstance s mandatory. At last by analyzng the performance of scheme and the results, we demonstrate that our scheme s effcent Paper Organzaton The remander of ths paper s organzed as follows. Prelmnares s descrbed n Secton 2. Secton 3 formalzes the concept of revocable thrd-party prvacy-preservng audtng scheme for cloud storage and also presents our desgn goals. The revocable thrd-party prvacy-preservng audtng scheme for cloud storage s gven n Secton 4. Secton 5 analyzes the scheme securty. Secton 6 analyzes the performance of t. Fnally, Secton 7 concludes ths paper. 2. Prelmnares 2.1. The User Data Stored n the Cloud As llustrated n Fgure 1, a basc cloud storage audtng system nvolves two man enttes: a user and the CSP. The user would be a company or an organzaton more precsely, t s usually a data manager of them who uses the cloud storage servce to store ts superabundant data. The CSP s cloud servce provder who has ample storage space, and could offer economcal and professonal storage servces to users. Specfcally, a cloud storage audtng scheme works as follows. A user frst splts the data M nto n blocks such that each block s m n Z p,.e., M = m 1,..., m n Z p n, M {0, 1, {1,, n, and computes the sgnatures of all blocks usng ts secret key lke σ = σ 1,..., σ n. Here the sgnatures are known as block tags. Then the user sends the data and all tags to the cloud, and deletes them locally. When ther outsourced data needs to be checked, the user pcks a random set of data blocks and sends a correspondng Q = {, v to the cloud, where and v

4 Informaton 2016, 7, 31 4 of 16 ndcate the dentty and random coeffcent of a selected data block respectvely. After recevng Q, the cloud calculates and returns a proof by usng those data blocks as well as the correspondng tags. Fnally, the user verfes the valdty of the proof. If the proof s nvald then the user can confrm that ts data has been damaged. Otherwse, t may be ntact; the user could repeat the challenge verfcaton procedure untl gettng a confrmaton. It obvously shows that the cloud only stored the user data block and the correspondng blocks tags. Fgure 1. The user data stored n the cloud Mult-User Data Stored n the Cloud wth the Revocable System As shown n Fgure 2, cloud storage system supportng revocable user s qute dfferent from the basc cloud storage audtng system, as there are many users who are able to manage the same pece of data. In realty, the data stored n the cloud belongs to the company, not to the data manager. In a specfc perod, there s usually one data manger that s responsble for managng the data, but n a longer tme perod, there mght be many users who are able to managng the data. That s, after some tme, a data manager who s responsble for managng the data s no longer sutable to manage the data, e.g., the data manager leaves the company and work for another company, thus, a successor of the data manager s needed. Fgure 2. Mult-user data stored n the cloud. We assume that there s an ntal user who uploads the company s data to the cloud on behalf of the company, we regard ths ntal user as U 0, then the company recrut a data manger to manage those data stored on the cloud. Clearly the data manager s not tenure. Before leavng, a data manger

5 Informaton 2016, 7, 31 5 of 16 needs to transfer all data he managed to hs successor. The successor also needs to verfy these data to make sure all the data stored on the cloud s ntact. Assume that a company or organzaton only needs one data manager to manage the data n a specfc perod. Then we have U 1, U 2,, U m users n the company or organzaton where m s a postve nteger. So the data management perod s dvded nto T 1, T 2,, T m accordngly. And the user has to transfer the data to the successor at the end of the perod. Note: In the paper the ntal user U 0 can t do anythng except uploads the data to the cloud. Only U 1, U 2,, U m can management the data. The ntal user U 0 frst dvdes all the fles nto n blocks, and calculates ts correspondng tag σ usng hs secret key, then uploads the data and tag to the cloud. U 1 manages the data durng the perod of T 1, then U 1 wll be replaced by ts successor U 2 at the end of T 1, U 2 wll also be replaced by U 3 some tme later, and so on tll the U j replaces U j 1,where j { 0,, m and U j s the current user. As the tag s sgned by the user, f a user has been revoked, the tags computed by the user should be modfed. An obvous approach to update those tags s re-computng the tags of data blocks usng the current user s secret key. However, ths s not a cloud storage audtng scheme supportng user revocaton, as ths method ntroduces large communcaton and computaton overhead. All the data manager can add, modfy and delete the data whch s stored on the cloud. For the current user U j all these operatons can only happen durng the T j perod. For the add operaton, U j dvdes the data nto blocks, computes the tags of each block and sends all the blocks and tags to the cloud. For the modfy operaton, U j frst retreves the data whch needs to be modfed and ts correspondng tags. U j verfes the correctness of the data, and dscards the tags. If the data s ntact, then U j modfes the data and computes the tags for the data usng hs secret key and uploads the data and tags to the cloud. For smplcty, we assume that the cloud server can handle the delete operaton effectvely. e.g., f some deleted data are selected by a challenge, all the data are set to 0, ths wll not affect the alter verfcaton process of the data. In fact, those deleted data wll no longer take any space on the cloud server. Thus for seral number of blocks, ts value wll never decrease. The value of the th of blocks C s related to the perod T and the operaton P. Assume that C 1,, C m are the th of blocks at the end of perod T 1, T 2,, T m, and c 1,, c m are the ncrement of the data block at the end of perod T 1, T 2,, T m, and p j,1, p j,2,, p j,θ are the ncrement of the data block by the operaton P j,1, P j,2,, P j,θ durng the perod T j. Then we get C j = n + l [1,j] c l = C j 1 + c j, where l {1, j, and k [1,θ] p j,k = c j, where p j,k s a postve nteger and k {1, θ. So at the audtng tme the value of the th of blocks s C j, k = C j 1 + p, where p = p j,1 + p j,2 + + p j,k. For a more realstc cloud storage system supportng user revocaton, all the data stored on the cloud ncluded the data m 1,..., m Cm and ts correspondng tags σ 1,..., σ Cm, and ts correspondng perod T 1, T 2,, T m. They are uploaded by the ntal users U 0 and all the other data managers U 1, U 2,, U m. So as shown n Fgure 3, the ntegrty verfcaton of m wll be verfed by σ, C, T. Fgure 3. Each block s attached wth a sgnature, a block d and a current perod. As mentoned above, U j can only add and modfy data at the tme perod of T j, and compete the tags of data blocks usng hs own secret key. In order to dstngush those tags, we use σ j to represent the tags computed by the user U j for data block m. For the current user, he has to not only manage the data blocks m C j 1+1,..., m C and ther correspondng tags, but also manage all the data blocks j,k and tags whch were uploaded to the cloud by all of hs predecessors. Some of the tags mght be

6 Informaton 2016, 7, 31 6 of 16 sgned by dfferent users. For example, n tme perod T 1, user U 1 dd modfy operaton whch gets data block m 2 and tag σ 1 2 ; at the current perod, user U j modfes data block m and computes ts tag σ j The Revocable Scheme Supported Thrd-Party Prvacy-Preservng Audtng Due to reason of the onlne burden whch potentally brought by the perodc storage correctness verfcaton, cloud users tend to delegate a thrd-party audtor TPA to execute securty audtng tasks. Through the TPA automatc executon perodc audtng tasks can save communcaton resources effectvely. Therefore, the thrd-party audtng schemes are more desrable n the real world. As llustrated n Fgure 4, a revocable cloud storage thrd-party audtng scheme works as follows. When the user wants to check ts outsourced data, t sends a verfy request to the TPA. When the TPA receves the request, t pcks a random set of data blocks and sends a correspondng Q = {, v to the cloud, where and v ndcate the dentty and random coeffcent of a selected data block respectvely. After recevng Q, the cloud calculates and returns a proof usng those data blocks as well as the correspondng tags. Then, the user verfes the valdty of the proof. If the proof s nvald then the TPA can confrm that ts data has been damaged. Otherwse, t may be ntact; the TPA could repeat the challenge verfcaton procedure untl gettng a confrmaton. Fnally, the TPA sends the result to the user. It s obvous that the cloud only stored the user s data block and the correspondng blocks tags. Fgure 4. An effcent and securty revocable thrd-party prvacy-preservng audtng scheme for cloud storage. 3. Formalzaton and Defntons Wthout loss of generalty, a revocable thrd-party prvacy-preservng audtng scheme for cloud s assumed as shown n Fgure 4, whch nvolves n m + 1 authorzed users for some m Z > 0 and ther sequence s U 0, U 1, U 2,, U m, correspondng the manager perod T 1, T 2,, T m. Notce that unauthorzed users can be easly recognzed and addtonally they cannot mpar the ntegrty of the outsourced data. Thus t can be assumed that there s no unapproved user n our audtng schemes. Then such an audtng scheme can be defned as below Defnton 1: Revocable Thrd-Party Prvacy-Preservng Audtng Scheme for Cloud Storage A revocable thrd-party prvacy-preservng audtng scheme for cloud storage conssts of sx probablstc polynomal tme PPT algorthms Setup, SgGen, U pdate, Challeng, Proo f Gen, Proo f Ver f y, where:

7 Informaton 2016, 7, 31 7 of 16 Setup: Ths algorthm s to generate each user s publc/secret keys and run by each user U j, where j {0,, m. For the j th user U j, the algorthm takes as nput a securty parameter λ and outputs U j s publc-secret key par pk j, sk j. SgGen: Ths algorthm s to generate the tags of the stored data. It conssts of three chld probablstc polynomal tme algorthmssggen U 0, SgGen U j, SgGen Ul U j. SgGen U 0 : Ths algorthm s to generate the ntal block tags of the stored data n the ntal tme and thus wll be run by the ntal user U 0 The algorthm takes as nput U 0 s secret key sk 0 and block data m 1,..., m n, m {0, 1, {1,, n, and outputs the verfcaton metadata V of m 1,..., m n assocated wth the user U 0. After that, U 0 sends V and m 1,..., m n to the cloud and deletes them locally. SgGen U j : Ths algorthm s to generate the block tags of the stored data n the perod Tj on the operaton p j,k, k {1,, θ, k {1,..., k and thus wll be run by the current user U j. The algorthm takes as nput U j s secret key sk j and block data m Cj,k 1 +1,..., m Cj,k, m {0, 1, where C j,k s a postve nteger. And the output of verfcaton metadata V of m Cj,k 1 +1,..., m Cj,k s assocated wth the user U j. After that, U j sends V and m Cj,k 1 +1,..., m Cj,k to the cloud and then deletes them locally. SgGen U l U j : Ths algorthm s to generate the block tags of the stored data n the perod T j when U j wants to update the data whch the prevous user U l uploaded to the cloud. So t wll be run by the current user U j. The algorthm frst retrevng the data block m and t correspondng tags, then verfed t f nvald turn out, f vald U j replaced the m by m For smple reason we also record t as m too. Later the algorthm takes U j s secret key sk j and block data m as nput and the outputs of verfcaton metadata V of m assocated wth the user U j. After that, U j sends V and m to the cloud and then deletes them locally. Update: Ths s an nteractve algorthm for updatng users. Suppose the user U j needs to be replaced by the user U j+1, then U j+1 wll ntate the algorthm. After the algorthm ends, U j+1 would obtan an update uk j j+1 for the cloud, and fnally sends t to the cloud. Challeng: Ths s an nteractve algorthm for users send checkng order. Assume U j s the current user and wants to check ts outsourced data, t sends a verfy request to the TPA. When TPA receved the request, t pcks a random set of data blocks and sends a correspondng Q = {, v to the cloud, where and v ndcate the dentty and random coeffcent of a selected data block respectvely. Proo f Gen: After recevng Challeng, the cloud would run the algorthm to return a response. To do ths, the algorthm takes as nput the Challeng, the block data m, Q and the verfcaton metadata V of {m Q, and outputs a verfcaton proo f. Proo f Ver f y: Ths algorthm s run by the TPA to verfy the correctness of the proo f. The algorthm takes as nput U j s publc key pk j, the Challeng and the correspondng proo f, and outputs VALID f proo f s vald; INVALID otherwse. Fnally, the TPA sends the result to the U j. For easer understandng, the revocable thrd-party prvacy-preservng audtng scheme for cloud storage ntuton behnd the defnton s gven here. The basc dea of our securty defnton s: f the data n the cloud s ndeed damaged but the cloud cannot admt, even by colludng wth the revoked users, fool the current user nto belevng that the data remans ntact. Let the cloud be an adversary A. To model the colluson between the cloud and revoked users, we permt to query a Corrupt oracle whch takes a revoked user s dentty as nput and outputs the user s secret key. However, accordng to the aforementoned reasons we prohbt A from queryng the Corrupt oracle on the user s dentty. Addtonally, lke other securty models, our securty model also allows A to query SgGen oracle, Update oracle as well as the Proo f Gen oracle for obtanng the ntal block tags, all update keys and vald proofs of any challenges.

8 Informaton 2016, 7, 31 8 of Defnton 2: Securty Model Now we descrbe the securty defnton of revocable thrd-party prvacy-preservng audtng scheme for cloud storage. A revocable thrd-party prvacy-preservng audtng scheme for cloud storage s secure f for any polynomal tme adversary A the probablty wns the followng game played between a challenger C and the adversary A s neglgble. Setup: The challenger C frst runs the algorthm KeyGenλ to generate U j s publc-secret key par { m pk j, sk j for all j {0,, m, and then sends all publc pkj to the adversary A. 0 Query: The adversary A could query the followng oracles adaptvely. SgGen-Oracle: For any data block m {0, 1, f A wants to get the ntal block tags of m, t wll query the oracle on m. After recevng the query, the challenger C frst runs the algorthm SgGensk 0, m to produce a result V 0 and then returnsv 0 as response. Update-Oracle: When A beleves some user s not sutable for audtng, A wll query the oracle on the user s dentty to replace the user wth ts successor. Assume the user to be replaced s U j+1 for j {1,, m 1. The challenger C frst runs the algorthm Update U j+1 to produce a update key uk j j+1 and then sends t to A. After recevng uk j j+1, A could generate the verfcaton metadata V j+1 of a data block m assocated wth the user U j+1 usng the update key uk j j+1, the data block m and the verfcaton metadata V j of m assocated wthu j. Corrupt-Oracle: Suppose all revoked users at present are U 0, U 1,, U d for some d {0,..., m 1, then the adversary A could query the oracle on any of them, wth the excepton of only U 0. When recevng such a query on the user U l for l {1,..., d, the challenger C returns U l s secret key sk l as response. Proof. In order to verfy whether the data block m stored n the cloud s the same as before, the challenger C generates a random challenge Chal and requests the adversary A to return a proof of m assocated wth user U j where j {0,..., m. On nput the challenge Chal, the data block m and the verfcaton metadata U j of M assocated wth U j, the adversary A outputs a proof as response. Forgery. When the above process ends, the adversary A fnally outputs a proof of some challenge Chal on fle M wth respect to user U j, where j {0,..., m. We say A wns the game f the followng condtons hold: 1. Ver f caton pk l, chal, proo f Vald; 2. The data block m s not the orgnal one Desgn Goals To support secure and effcent user revocable and data prvacy preservng n a publc cloud data audtng scheme, we have the followng desgn goals: TPA s allowed to verfy the correctness of the cloud data. It executes data audtng wthout retrevng entre data and ntroduces none addtonal onlne burden to the user. Storage correctness: If the cloud ndeed stores entre data, then t would always output vald proofs. Prvacy-preservng: TPA learns no nformaton of the stored data from nformaton collected durng the audtng process. v Revocablty: If a user s revoked, then ts successor could establsh a new audtng procedure effcently. v Colluson resstance: If the data stored n the cloud s changed, then the audtng scheme should be able to detect t wth hgh probablty even though the cloud colludes wth revoked users. v Effcency: the computaton, communcaton and storage overhead should be as small as possble.

9 Informaton 2016, 7, 31 9 of The Revocable Thrd-Party Prvacy-Preservng Audtng Scheme for Cloud Storage Ths secton gves some prelmnares to be used n ths work, ncludng blnear map and hardness assumptons Blnear Map Let G 1, G 2 and G T be cyclc groups wth the same prme order p. A map e: G 1 G 2 G T s called a blnear map f t satsfes the followng three propertes. 1. Blnearty: For all a, b Z p, and u G 1, v G 2, we have eu a, v b = eu, v ab. 2. Non-degeneracy: eg 1, g 2 = Computablty: There exsts an effcent algorthm to compute the map e. 4. Exchangeablty: eu 1 u 2, v = e u 1, v e u 2, v 4.2. Hardness Assumptons The securty of our constructons wll rest on the Computatonal Dffe-Hellman CDH assumpton and the Dscrete Logarthm DL assumpton. Defnton 3 CDH Assumpton. The CDH assumpton s gven a group of prme order p, a generator g, and two random element g a, g b G t s hard to output g ab. Defnton 4 DL Assumpton. The DL assumpton s gven a group G of prme order p, a generator g, and a random element g c G t s hard to output c Specfcaton In ths secton, the revocable thrd-party prvacy-preservng audtng scheme for cloud storage s proposed. The audtng scheme s llustrated n Fgure 4. Here, a sem-trusted TPA s needed to defne, whch s only responsble for audtng the ntegrty of data blocks honestly. However, t s curous and may try to reveal the user prmtve data blocks based on verfcaton nformaton. In ths paper, the scheme ncludes of the followng sx algorthms: Setup, SgGen, U pdate, Challeng, Proo f Gen, Proo f Ver f y. Let G and G T be two cyclc groups wth the same prme order p, and g be a generator of G.t. Let e : G G G T be a blnear map and H : {0, 1 G, h : {0, 1 G, f k3 : {0, 1 Z p be a hash functon. The audtng scheme s specfed as follows. Setup. On nput a securty parameter λ, each user U j where j {0,, m does the followng steps: 1. Select a random x j Z p. 2. Compute ts publc key g x j. 3. Output pk j = g x j and sk j = x j. SgGen. Ths algorthm s to generate the tags of the stored data. It conssts of three chld algorthms SgGen U 0, SgGen U j, SgGen Ul U j. SgGen U 0. When the companes and organzatons delegate a trust user U 0 upload the ntal data at the ntal tme perod. 1. The ntal user U 0 encodes all the fles and then splts them nto n block such that each block s n Z p,.e., m 1,..., m n Z p n. 2. For all {m, {1,, n compute the tag of th data block m as σ = H W u m x 0, t = W Sg ssk W, where u s a publc parameter chosen randomly from G, W = T j and j {1,, m. 3. Send the ntal verfcaton metadata V = {σ, t 1 n and the data blocks {m 1 n to the cloud and then deletes them locally.

10 Informaton 2016, 7, of 16 SgGen U j. Ths algorthm s to generate the block tags of the stored data n the perod Tj on the operaton p j,k, k {1,, θ, k {1,..., k. 1. The data blocks s processed as {m Cj,k 1 C j,k by current user U j, where C j,k s a postve nteger. The ncrement of the data block by the operatons denoted by p j,k, whch user U j wll add these data to the cloud n the perod T j. 2. For all {m Cj,k 1 +1 C j,k, U j compute the tag of th data block m as σ = H W u m x j, t = W Sg ssk W, where u s a publc parameter chosen randomly from G, W = T j and j {1,, m. Send the verfcaton metadata V = {σ, t Cj,k 1 +1 C and data blocks j,k {m Cj,k 1 +1 C j,k to the cloud and then deletes them locally. SgGen U l U j. Ths algorthm s to generate the block tags of the stored data n the perod T j. If the current user U j wants to update the data of prevous user U l do. 1. When the current user U j wants to update the data m n the prevous T l perod for some reason, the m and V = {σ, t, C l should be retreved frstly. 2. Then the user U j verfed the t = W Sg ssk W wth the prevous user publc key. If wrong the audtng scheme ends, f rght the user U j deals wth the data block as m and replaced the tag σ l = H W u m x l by σ j = H W u m x j At the same tme the user U j replaced the t = T l Sg sskul T l by t = T j SgsskUj Tj. 3. At last the user U j sends verfcaton metadata V = {σ, t and the block m to the cloud and then deletes them locally. Update. If the user U j+1 would take the place of the user U j, then U j+1 computes the update key 1 uk j j+1 as uk j j+1 = g x x j x j+1 j+1 = g, and sends t to the cloud. The cloud does the followng steps: x j 1. Set α j = pk j, β j+1 = uk j j For any j {0,, m 1, let the verfcaton metadata of block data m assocated wth user U j be V = σ, t, α 1,..., α j, β 1,..., β j. For the sake of clarty, we lst some used sgnals n Table 1. The protocol s llustrated n Fgure 5. Table 1. Sgnal and ts explanaton. Sg. Represson n T 1, T 2,, T m the number of the ntal data block; the perod of data manager s management; T j the current perod s correspondence the current user U j ; C the number of the total data blocks at the audtng tme: C j, k = C j 1 + p where p = p j,1 + p j,2 + + p j,k ; C 1,, C m the th of blocks at the end of perod T 1, T 2,, T m ; c 1,, c m the ncrement of the data block at the end of perod T 1, T 2,, T m ; p j,1, p j,2,, p j,θ the ncrement of the data block by the operaton P j,1, P j,2,, P j,θ durng the perod T j ; σ j the tag s generated by the U j and data block m ; Q the set of ndex-coeffcent pars,.e., Q = {, v ; t t used to verfy f the block -th match the data block; V the response for the challenge Q;

11 Informaton 2016, 7, of 16 TPA 1 Retreve fle tag, verfy ts sgnature, and qut f fal; 2 Generate a challenge message challenge: Q = {, v, {1,..., C j,k ; 6 Compute: r = f k3 challenge Z p ; verfy PK Ul Sg sskul W = T l, then verfy µ, σ, t, α, β va the verfcaton equaton. Q = {, v µ, σ, t, α, β The cloud server 3 Splt ths Q to {Q T0,..., Q Tl,..., Q Tj ; 4 Compute µ = Q v m, σ = Q σ v G 1 ; 5 compute r = f k3 challenge Z p, R = u r G 1, µ = µ + rhr Z p, and t = {t Q ; Fgure 5. Revocable thrd-party prvacy-preservng audtng protocol. Challeng. When the U j wants to verfy the ntegrty of the data block stored n the cloud n the perod of T j U j s perod, t would send a verty request to the TPA. Proo f Gen. When the TPA receves the request of user, t would ssue a random set Q = {, v and a communcaton key k 3 to the cloud as a Challeng, where {1,, C j,k and v Z p. After recevng Challeng, the cloud can splt ths Q to {Q T0,..., Q Tl,..., Q Tj then computes and returns µ, σ, t, α, β as a proo f, where r = f k3 challenge Z p, R = u r G 1, µ = Q v m, µ = µ + rhr Z p, σ = Q σ v G 1, and t = {t Q. Proo f Ver f y. When the TPA receves the proo f, nput the publc key pk l of user U l, the Challeng, Q = {, v, k 3 and the proo f, µ, σ, t, α, β, the algorthm outputs VALID to the U j as the Result f the followng equaltes smultaneously hold. Frst for each t verfes PK Ul Sg sskul W = T l. Second verfes the data block and tags e σ, g = l [0,j] e α l, u µ R hr QTl HW v. Thrd verfes the user e α j 1, g = e pk j, β j e αl, g = e α l+1, β l f orl {0,..., j 2. Remark 1. The update process of the revocable thrd-party prvacy-preservng audtng scheme s smple and s also effcent n terms of both computaton and communcaton costs because t only needs to compute and send one update key uk l l+1. Remark 2. There s only one publc key,.e., the current user s publc key, n the revocable thrd-party prvacy-preservng audtng scheme for any perod of tme. All publc keys of revoked users are not certfed any more, and thus a malcous cloud could modfy them dscretonarly.

12 Informaton 2016, 7, of Analyss of the Proposed Audtng Scheme 5.1. Correctness Now we prove the correctness and securty of our revocable thrd-party prvacy-preservng audtng scheme. Theorem 1. The audtng scheme satsfes correctness. Proof. Accordng to the above constructon, that for any challenge Q = {, u, ths challenge can be splt to Q = {Q T0,..., Q Tl,..., Q Tj, l {0,..., j, have e σ, g = e Q σ v, g = l [0,j] e QTl σ v, g = l [0,j] e QTl H W u m v, g x l = l [0,j] e α l, u µ rhr QTl HW v = l [0,j] e α l, u µ R hr QTl HW v Also, for any user U j where j {1,, m, we know that e α j 1, g = e g x j 1, g = e g x j, g x j 1 x j = e pk j, β j and for all l {0,, j 2 have e α l, g = e g x l, g = e g x x l x l+1, g l+1 = e α l+1, β l Therefore, the audtng scheme s correct Securty Analyss Theorem 2. The audtng scheme s secure n the random oracle model under the CDH assumpton. Proof. Accordng to Defnton 2, f there exsts a polynomal tme adversary A who breaks the scheme wth non-neglgble probablty ɛ, we construct an algorthm B that uses the adversary A as a subroutne to solve a hard CDH problem wth probablty ɛ too. Algorthm B does so by nteractng wth A as follows. Setup. Gven a securty parameter λ, the algorthm B frst randomly pcks a generator g of G, g α G and a hash functon H : {0, 1 G that wll be modeled as a random oracle n the proof. B also chooses random g x 0 from G for an unknown x 0 as U 0 s publc key and computes U j s publc key g x j for all j {0,, m, where x j s pcked from Z q. Then B sets u = g α and sends the system parameters g, u and all users publc keys {g x j m 0 to the adversary A. Query. The adversary A can query the followng types of oracles adaptvely. It s assumed that for any data block m, A wll frst make a H-Oracle query on the block before others. H-Oracle. When A queres the oracle on a data block m, B looks up m n H-lst, an ntal empty lst wth the tuples m, s, H W. If B fnds a matched tuple, t outputs H W as response. Otherwse B frst pcks a random value s Z p and then computes H W = g s /u m, stores m, s, H W n H-lst and fnally outputs H W as response. SgnGen-Oracle. To get the tags of data blocks {m [1,Cj,k ], A queres the oracle on the fle. Upon recevng the query, for all {1,, C j,k, j {1,, m, l {0,, j, B looks up

13 Informaton 2016, 7, of 16 m n H-lst, fnds a matched tuple m, s, H W, computes σ = g x l s and fnally outputs the set V = σ 1,..., σ Cj,k as response. Snce σ = HW u m x l, pluggng H W = g s /u m nto the equalty, we can see that σ = g x l s for all {1,, C j,k. Update-Oracle. If A wants to replace the user U j wth ts successor U j+1 for some j {1,, m 1, A wll query the oracle on U j. Upon recevng the query, B frst computes the update key uk j j+1 = g xj/x j+1 usng U j+1 s secret key x j+1 and sends the result to A. Then A sets α j = g x j and β j+1 = uk j j+1, and adds them nto U, j s verfcaton metadata. Let V j = µ, σ, t, α 1,..., α j 1, β 1,..., β j be, Uj s verfcaton metadata, then we know that U j+1 s verfcaton metadata s V j+1 = µ, σ, t, α 1,..., α j, β 1,..., β j+1. Corrupt-Oracle. Let all revoked users at present be U 1,..., U d for some d {1,, m 1. If the adversary A queres the oracle on the user U j where j {1,, d, then B returns U, j s secret key x j as response. Proof. If B wants to verfy whether the data block m stored n the cloud remans ntact or not, t wll ssue a random challenge Challeng Q, k 3, Q = {, v to A, where {1,, C j,k and v Z p. Let m 1,..., m Cj,k n Z p and the current user be Uj. Upon recevng ChallengQ, k 3, A computes r = f k3 challenge Z p, R = u r G 1, µ = Q v m, µ = µ + rhr Z p, σ = Q σ v, t = {t Q, and returns a vald proof V j = µ, σ, t, α 1,..., α j 1, β 1,..., β j to B. Forgery. A wth non-neglgble probablty ɛ outputs a vald proof µ, σ, t, α 1,..., α j 1, β 1,..., β j of a Challeng Q, k 3 on a damaged fle {m [1,Cj,k ] wth respect to user U j, where j {1,, m. Let the proof of the Challeng Q, k 3 on the unbroken data blocks {m [1,Cj,k] wth respect to user U j be µ, σ, then we know µ = µ. Let µ = µ µ Snce e σ, g = l [0,j] e α l, u µ R hr QTl HW v and e σ, g = l [0,j] e α 0, u µ R hr QTl HW v, by Defnton 2, we have eσ σ 1, g = e g x 0, u µ. As a result, we know u x 0 = g ax 0 = σ σ 1 1 µ. That s, B wth probablty ɛ solves a CDH problem: gven g, g a, g x l G,output g ax Performance Analyss In ths secton, we analyze the communcaton and computaton complextes of revocable thrd-party prvacy-preservng audtng scheme for cloud storage. Partcularly, we are only nterested n the communcaton and computaton costs of ts frequent actvtes, and gnore the costs of the ntal system setup that s the same as other conventonal publc audtng schemes. NOTATION. Let Par denote one parng operaton, Exp denote one exponentaton operaton n G, and MZ and MG respectvely denote one multplcaton operaton n Z p and G. We denote the bt sze of the element n {1,, C j,k, {1,, n, Z p and G by C, n, p and G respectvely. The number of the data blocks selected by a challenge user s assumed to be a constant c Communcaton Cost We can see that the communcaton overhead of our scheme depends on the communcaton complexty of algorthm Proof. Accordng to the Proof algorthm, the user U j n one audtng process would frst send a challenge Q = {, v wth sze c C + p to the cloud and then the cloud would send a proof µ, σ, t, α 1,..., α j 1, β 1,..., β j wth sze p + 2j G + c C + G to the user U j f t s the user U j, s frst audtng query; otherwse the cloud would just send µ, σ, t wth sze p + G + c C to the user U j. Therefore, the total communcaton cost of one audt process n our scheme s p + G + c 2 C + p bts.

14 Informaton 2016, 7, of Computaton Cost The computaton cost ncludes update tme and audt tme. To update a user U j, the Update algorthm only needs to compute g x j 1/x j. Hence the update tme of our scheme s Exp. To complete one audt, the cloud should output a proof and the audtng user should verfy ts correctness. We know that the audt tme of our scheme for user U j depends on the generaton and verfcaton costs of µ, σ, t. Therefore, the audt tme for user U j s c + 2j MZ + jmg + 2c + j Exp + j + 1 Par here we gnore the smple addton and hash operatons. Addtonal Comparson. We also gve a comparson between our scheme and the revsed scheme of [16] for audtng owned cloud storage. Table 2 shows the detals of the comparson. We know that the audtng scheme n [16] s nsecure under colluson attacks but t s the most effcent revocable publc cloud storage audtng scheme n the lterature. When a user U j executes the Proof algorthm of [16], t would send a challenge Q = {, v wth sze c n + q to the cloud and the cloud would send a proof { α, β, {d l, s l l L wth sze j p + G + c d to the user Uj. Therefore, the total communcaton cost of one audt process n that scheme s j p + G + c d + n + p bts. As the Update algorthm of [16] needs to recalculate all the tags of ndata blocks, we know the update tme of [16] s nexp. To complete one audt, the scheme n [16] frst requests the cloud to output a proof nexp and then nstructs the audtng user to verfy ts correctness. Therefore, we know that the audt tme of [16] for any user s c + 2j MZ + jmg + c + j Exp + j + 1 Par here the smple addton and hash operatons are also gnored. From Table 2, we can see that the communcaton cost of our scheme wll has superor effcency than the [16] n some cases. And audt tme of our scheme s almost the same as those of [16], whle the update tme of [16] s larger than that of our scheme. Therefore we know our scheme s more computatonally effcent than the scheme n [16]. Table 2. The comparson of two revocable publc cloud storage audtng schemes. Scheme Communcaton Cost Computaton Cost Colluson Update Tme Audt Tme Resstance [16] j p + G + c d + n + p nexp c + 2j MZ + jmg + c + j Exp + j + 1 Par NO Our scheme p + G + c 2 C + p Exp c + 2j MZ + jmg + 2c + j Exp + j + 1 Par YES 6.3. Expermental Results As we know, the comparson of computaton cost s obvous. Our Update tme s Exp, t s much lower than the update tme of [16]: nexp. Our audtng tme s approxmately equal the scheme n [16], t s only a dfference of cexp. So we only need compare the communcaton cost of our audtng scheme wth the work of [16] n experments. Our experments are mplemented on a wndows 7 system wth an Intel Core 2 5 CPU runnng at 2.53 GHz, 2 GB DDR 3 of RAM 1.74 GB avalable. All algorthms are mplemented by C language, and our code uses the MIRACL lbrary verson The ellptc curve we use s an MNT curve, the base feld sze s 159 bts and the embeddng degree s 6. The securty level s chosen to be 80 bt, and p = q = 160. For smplcty, we also set k = 20, c = 300. All the results of experments are represented as the average of 30 trals. As descrbed n Fgure 6, the expermental results show that, compared wth the audtng scheme n [16], the communcaton cost of our audtng scheme are much lght-weght than the scheme n [16].

15 Informaton 2016, 7, of Communcaton cost KB Wang's scheme Our scheme Number of challenge block c Fgure 6. Comparson on the communcaton cost between our scheme and the scheme n [16]. 7. Conclusons In ths paper, we have nvestgated the effcent user revocaton problem n publc cloud storage audtng systems and have proposed a dynamc revocable thrd-party prvacy-preservng audtng scheme for cloud storage. We have proved that our scheme s secure aganst colluson attacks and have also demonstrated ts effectveness. In the lght of the smplcty and extensblty of revocable thrd-party prvacy-preservng audtng scheme for cloud storage, we beleve the scheme would be much applcable n real-world cloud storage audtng systems. Acknowledgments: Ths work s supported by the Natonal Natural Scence Foundaton of Chna No and the Scence and Technology on Communcaton Securty Laboratory FoundatonGrant No. 9140C C1103. Author Contrbutons: Theory: Xnpeng Zhang and Chunxang Xu; Math analyss: Xnpeng Zhang and Xaojun Zhang; Smulatons: Xnpeng Zhang; Interpretaton: Xnpeng Zhang and Xaojun Zhang; Wrtng: Xnpeng Zhang, Tazong Gu, Zh Geng and Guopng Lu. All authors have read and approved the fnal manuscrpt. Conflcts of Interest: The authors declare no conflct of nterest. References 1. 9 worst cloud securty threats. Avalable onlne: tructure-as-a-servce/9-worst-cloud-securty-threats/d/d-d/ accessed on 25 May Cloud Securty Allance. Top Hreats to Cloud Computng. Avalable onlne: allance.org accessed on 25 May Kncad, J. Medamax/Helnkup Close Its Doors. Avalable onlne: medamaxthelnkup-closes-ts-doors/ accessed on 25 May Cloud Computng Users Are Losng Data, Symantec Fnds. Avalable onlne: technology/ cloud-computng-data-loss-hgh-n-symantec-study.htm accessed on 25 May Kher, V.; Km, Y. Securng dstrbuted storage: Challenges, technques, and systems. In Proceedngs of the 2005 ACM Workshop on Storage Securty and Survvablty, Farfax, VA, USA, 11 November 2005; pp Schroeder, B.; Gbson, G.A. Dsk falures n the real world: What does an mttf of 1, 000, 000 hours mean to you? In Proceedngs of the FAST 07: 5th USENIX Conference on Fle and Storage Technologes, San Jose, CA, USA, Februery 2007; Volume 7, pp Cloud Securty Allance. Cloud computng vulnerablty ncdents: a statstcal overvew. Avalable onlne: lty-incdents. pdf/?mod=ajperes accessed on 25 May 2016.

16 Informaton 2016, 7, of Yu, S.; Wang, C.; Ren, K.; Lou, W. Achevng secure, scalable, and fne-graned data access control n cloud computng. In Proceedngs of the 2010 Proceedngs IEEE INFOCOM, San Dego, CA, USA, March 2010; pp Wang, C.; Chow, S.S.M.; Wang, Q.; Ren, K.; Lou, W. Prvacy-preservng publc audtng for secure cloud storage. IEEE Trans. Comput. 2013, 62, Wang, Q.; Wang, C.; L, J.; Ren, K.; Lou, W. Enablng publc verfablty and data dynamcs for storage securty n cloud computng. In Computer Securty ESORICS 2009; Sprnger: Medford, MA, USA, 2009; pp Atenese, G.; Burns, R.; Curtmola, R.; Herrng, J.; Kssner, L.; Peterson, Z.; Song, D. Provable data possesson at untrusted stores. In Proceedngs of the 14th ACM Conference on Computer and Communcatons Securty, Alexandra, VA, USA, 29 October 2 November 2007; pp Juels, A.; Kalsk, B.S., Jr. Pors: Proofs of retrevablty for large fles. In Proceedngs of the 14th ACM Conference on Computer and Communcatons Securty, Alexandra, VA, USA, 29 October 2 November 2007; pp Shacham, H.; Waters, B. Compact proofs of retrevablty. In Advances n Cryptology-ASIACRYPT 2008; Sprnger: Medford, MA, USA, 2008; pp L, M.; Yu, S.; Ren, K.; Lou, W. Securng personal health records n cloud computng: Patent-centrc and fne-graned data access control n mult-owner settngs. In Securty and Prvacy n Communcaton Networks; Sprnger: Medford, MA, USA, 2010; pp Zhang, X.; Xu, C.; Zhang, X. Effcent parng-free prvacy-preservng audtng scheme for cloud storage n dstrbuted sensor networks. Int. J. Dstrb. Sens. Netw. 2015, 501, , 16. Wang, B.; L, B.; L, H. Panda: Publc audtng for shared data wth effcent user revocaton n the cloud. IEEE Trans. Serv. Comput. 2015, 8, Wang, B.; L, H.; L, M. Prvacy-preservng publc audtng for shared cloud data supportng group dynamcs. In Proceedngs of the 2013 IEEE Internatonal Conference on Communcatons ICC, Budapest, Hungary, 9 13 June 2013; pp Yuan, J.; Yu, S. Effcent publc ntegrty checkng for cloud data sharng wth mult-user modfcaton. In Proceedngs of the IEEE Conference on Computer Communcatons INFOCOM, Toronto, ON, Canada, 27 Aprl 2 May 2014; pp Delerablée, C.; Paller, P.; Pontcheval, D. Fully colluson secure dynamc broadcast encrypton wth constant-sze cphertexts or decrypton keys. In Parng-Based Cryptography Parng 2007; Sprnger: Medford, MA, USA, 2007; pp Chaum, D.; Van Heyst, E. Group sgnatures. In Advances n Cryptology EUROCRYPT 91; Sprnger: Medford, MA, USA, 1991; pp Wang, B.; L, B.; L, H. Knox: Prvacy-preservng audtng for shared data wth large groups n the cloud. In Appled Cryptography and Network Securty; Sprnger: Medford, MA, USA, 2012; pp Atenese, G.; Hohenberger, S. Proxy re-sgnatures: New defntons, algorthms, and applcatons. In Proceedngs of the 12th ACM conference on Computer and Communcatons Securty, Alexandra, VA, USA, 7 10 November 2005; pp Lu, Q.; Wang, G.; Wu, J. Effcent sharng of secure cloud storage servces. In Proceedngs of the 2010 IEEE 10th Internatonal Conference on Computer and Informaton Technology CIT, Bradford, UK, 29 June 1 July 2010; pp Lu, Q.; Wang, G.; Wu, J. Tme-based proxy re-encrypton scheme for secure data sharng n a cloud envronment. Inf. Sc. 2014, 258, c 2016 by the authors; lcensee MDPI, Basel, Swtzerland. Ths artcle s an open access artcle dstrbuted under the terms and condtons of the Creatve Commons by Attrbuton CC-BY lcense

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