A Method for Trust Quantificationin Cloud Computing Environments

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1 A Method for rust Quatificatioi Cloud Computig Eviromets Xiaohui Li,3, Jigsha He 2*,Bi Zhao 2, Jig Fag 2, Yixua Zhag 2, Hogxig Liag 4 College of Computer Sciece ad echology, Beiig Uiversity of echology 2 School of Software Egieerig, Beiig Uiversity of echology Beiig 0024, Chia 3 College of Electrical ad Iformatio Egieerig, Liaoig Uiversity of echology Jizhou, Liaoig200,Chia 4 Jizhou 6563 Force, Jizhou, Liaoig 200, Chia lixiaohui@ s.but.edu.c Abstract Cloud computig ad Iteret of higs (Io) are two emergig techologies that have experieced rapid developmet i the past few years. While cloud computig presets a ew platform over which services are offered to the user more coveietly, Io facilitates the collectio of a large amout of iformatio via itercoected wireless sesors for evet moitorig ad cotrol. I such eviromets, owership ad cotrol over the data may result i potetial coflict betwee the protectio of data ad the provisio of services. As Io techologies become more mature, eve more sesors will be deployed, geeratig more data about users to be stored i the cloud. hus, cloud security has received tremedous attetio i recet years. I this paper, we propose a method for trust quatificatio based o fuzzy comprehesive evaluatio theory for cloud computig eviromet to provide the user with the ability ad flexibility of protectig data through quatifyig the trust of cloud services. he mai cotributios of this paper iclude:()itroducig trust otology for cloud services, (2) defiig user preferece trust values ad (3) proposig a trust quatificatio algorithm. By ehacig the existig trust cocept based o dyamic requiremets, we itroduce some cloud service attributes to study layered service represetatio for trust preferece. We the apply the fuzzy comprehesive evaluatio theory to trust quatificatio i which we propose a method for the distributio of the weights of service trust evaluatio factors ad for quatitative assessmet of trust. Simulatio results show that the proposed method is effective ad ca dyamically perform trust quatificatio to deal with malicious acts of ofaithful services. Keywords: cloud computig, security,trust, fuzziess. Itroductio rust maagemet i a cloud computig eviromet to esure the security of iformatio is a maor challege i the era of cloud computig ad Iteret of higs (Io). Meawhile, trust assessmet is a idispesable part of trust maagemet[-5]. Sice differet techologies ca be used i a cloud computig eviromet, trust assessmet has its ow characteristics ad requiremets. Research i recet years i this area has mostly focused o the evaluatio of trust o the subect, i.e., the service requester,

2 by the obect, i.e., the service provider, as the basis of assigig access permissios for users to access services. I a cloud computig eviromet, however, cloud users ad cloud services may assume dual roles. Whe the cloud service provider is a resource provider, trust ca be used to determie whether it ca accept requests from cloud users for access to cloud services such as computatio or storage, amog may other fuctios. Whe the cloud user becomes a resource provider, trust ca be used to determie whether it ca grat cotrol over the data of the user to the cloud service provider to use the data. As Io techologies become more mature, more ad more wireless sesors will be deployed to form a itercoected etwork amog a vast amout of thigs i additio to regular users for more efficiet moitorig ad cotrol[6-0], geeratig tremedous volumes of data for the cloud. Some of the data are certaily sesitive as far as user privacy is cocered. here thus exists a coflict betwee the protectio of user privacy ad the coveiet use of services. here is thus the requiremet to perform two-way trust assessmet i cloud computig eviromets, i.e., to perform trust evaluatio o behalf of the user i additio to the trust evaluatio traditioally performed by the service provider o the user. hus, trust evaluatio i cloud computig eviromets becomes a two-level hierarchy. Oe is the trust evaluatio o the cloud user to protect cloud services from exteral threats. he other is the trust evaluatio o the cloud computig service provider to allow the user to choose credible cloud services accordig to differet trust values ad may other aspects. I this paper, we focus o the issue of cloud user data protectio i cloud computig ad propose a trust quatificatio method for the evaluatio of cloud services. Our method will use preferece trustbased o cloud computig service attributes to evaluate trust o cloud services. he rest of this paper is orgaized as follows. I Sectio 2, we describe some related work. I Sectio 3, we explai the proposed approach i two parts: oe is the relevat defiitios ad the other is the algorithm descriptio. We also perform some experimet to evaluate our proposed method alog with two scearios for better illustratio. Fially, we coclude this paper i Sectio Related Work I a cloud computig eviromet, evaluatio of trust o cloud services may ivolve various spatial ad temporal factors, which has the characteristics of subectiveess ad fuzziess. herefore, we ca assess ad quatify trust usig fuzzy mathematical theory by followig relevat approaches. Fuzzy comprehesive evaluatio is about the aalysis ad sythesis of fuzzy relatioships that ivolve oe or more factors to deal with vagueess ad subective udgmet of multiple factors accordig to their importace[-3]. rust itself may be subective. hus, dyamic trust quatificatio o cloud services has to ivolve some fuzzy subective iformatio of cloud services to cloud users[4-9].

3 Cosequetly, fuzzy comprehesive evaluatio to quatify the trust of cloud services has practical sigificace. Fuzzy comprehesive evaluatio usually ivolves the followig steps: a) Determie the set of evaluatio factorsu = { u, u2,..., u },where ui (,2,..., ) is the ith evaluatio factor. b) Determie the set of evaluatio levels v { v v v } =, 2,, m,where v ( =,2,..., m) is the ith evaluatio level that correspods to a fuzzy subset. c) Evaluate sigle factor ui through establishig a fuzzy relatioship matrix ad assessig its elemets idividually to quatify compoets of i ad to get the fuzzy relatioship matrix: u so as to establish the fuzzy membership subset ( R u ) R u r r2 r m R u 2 r2 r22 r 2m R = = R u r r 2 rm i I the matrix, elemet ri at the i th row ad the th colum deotes the evaluatio from the perspective of factor ui that correspods to the fuzzy subset = expresses the evaluatio from the perspective of factor u i. v.hus, ( R u ) ( r, r,, r ) i i i2 im e) Determie the weight vector for the evaluatio factors W ( w w w ) =,,, i which elemet i expresses the importace of factor u i i the evaluatio. We propose to apply the maximum etropy method to determie the relative importace of the evaluatio factors. Hece, wi =, 0 w i,, 2,,. f) Derive comprehesive evaluatio results by combiig W with R to get the fuzzy comprehesive evaluatio result vector B : 2 r r2 r m r2 r22 r 2m W R ( w, w2,, w) = = ( b, b2,, bm) = B. r r 2 rm I cloud computig, services are selected based o trust to persoalize the eeds of data protectio i a multi-teat eviromet[20-26]. I this paper, we refer to the specific cotexts i the life cycle of cloud computig as service properties. As aother etity i cloud computig, users may release data that could relate to these service properties. hus, a cloud user ca perform trust evaluatio o services w

4 i accordace with the service properties. Such service properties should be represetative of cloud services, which is ot oly the prerequisite for trust quatificatio, but also the basis for service selectio as well as for cotrollig the graularity of the release of user data durig iteractios. Service properties should also iclude service trust metrics although curret research o trust metrics maily describes the trust of obect o the subect without cosiderig the requiremet for mutual trust i a cloud computig eviromet. his paper aims to propose a method of trust evaluatio from the poit of view of protectig user's data i the cloud. 3. he Proposed rust Quatificatio Method 3. Hierarchical Represetatio of Cloud Service Iformatio o clearly describe cloud services, we eed to cosider service iformatio represetatio. I this sectio, we defie service trust otology through a layered cloud service model. () Cloud Service rust Otology Cloud computig provides ifrastructure, platform or software as a service for the user. Curretly, there are three differet service models defied for the cloud, i.e., IaaS, PaaS ad SaaS that correspod to the above three types of services as show i Figure. he IaaS layer provides the basic services such as databases, file systems ad storage, the PaaS layer provides services are related to the developmet eviromets, ad the SaaS layer provides software as a service to meet user applicatio eeds. Fig. he layered cloud service model

5 I order to accurately describe cloud services, trust evaluatio must cosider how service iformatio ca be expressed. Otology is oe way of describig thigs i a orgaized maer sice it is a philosophical method for describig the ature of thigs. A formal defiitio of otology i the field of iformatio sciece is made by America Kowledge Systems Laboratory at Staford Uiversity which states that otology is a explicit specificatio of a coceptualizatio. Otology is further defied as a cocept specificatio that origiates from the specific eed of uderstadig the ature of kowledge[27-3]. It is used to iterpret cocepts or domais that have reached a cosesus uderstadig. Each domai has a set of covetioal cocepts or words, or a group of closely related meaigs available for selectio. Otology o the trust of cloud service providers ca be described usig the ame of the otology ad a combiatio of a umber of elemets as follows: a) he cloud users who are the service requesters ad who perform trust evaluatio o cloud services. b) he cloud services that are offered by a service provider ad are thus evaluated by the cloud users. c) he type of a cloud service as described by service attributes such as temporal ad spatial factors, user trust factors, historical behavioral factors, etc. d) he evaluatio criteria that are used to measure the trust o each attribute of a service. e) Service backgroud that refers to the ature of a service, such as storage service. Note that each of the above elemets could itself be a composite elemet that cosists of complex data structures such as a collectio of tables. For example, service evaluatio criterio could be a group of elemets. he otology of trust o cloud services is show i Figure 2. rust metrics Cloud users Cloud Services Service backgroud Service Properties Assessmet criteria Fig.2 Otology of trust o cloud services

6 he above characterizatio of cloud services has the followig features. Firstly, the trust metrics are the measuremet of cloud services by cloud users that result from the trust relatioship of the past. It may also iclude direct trust ad recommedatio trust, which affects the selectio of services i the future. Secodly, iformatio about trust is stored i a database that cosists of tuples with each tuple as a row i a database table. o trust a cloud service is a process of obtaiig certai iformatio about service backgroud as well as cloud users i accordace with trust evaluatio criteria for assessig the service attributes. he results are combied with past trust values to quatify the trust o the curret cloud services. he key to evaluatig the trust o cloud services is to defie service evaluatio criteria, which ivolves the followig two issues: oe is that service assessmet criteria should be clearly defied to reflect the properties of cloud services to users ad the other that evaluatio criteria for each service should have differet weights accordig to persoalized service eeds of cloud users. (2) Preferece rust o meet the persoalized service eeds of cloud users ad based o the otology of trust o cloud services, we ca use the otio of preferece trust to evaluate the trust o service providers from the aspects of time, space ad historical behavior, etc. A few related defiitios are as follows: a) Preferece trust results from a iteractive process betwee cloud users ad cloud services, which depeds o oe or more attributes that should cosist of the preferece of idividual users expressed usig temporal, spatial ad other factors such as behavior ad history. Cloud users could the perform trust evaluatio o cloud services. b) Historical behavior is a aspect of evaluatio based o feedback o cloud service providers to give cloud users the iformatio that reflects the itegrity of cloud services. c) Quatificatio of service trust is to establish a quatitative evaluatio system to apply trust evaluatio o cloud services. d) Quatificatio of preferece trust is to perform trust evaluatio usig a give preferece system to quatify the differet factors 0,... ad to apply the various preferece weights W 0, W,... W where 0 Wi = to arrive at a trust value = ( Wi i) Descriptio of the Method Quatificatio of service preferece trust cosists of two steps. he first is to determie the best weight distributio for each factor based o differet trust prefereces. he secod is to establish a method to quatify

7 the factors of trust based o differet trust prefereces to get a comprehesive value for the cloud service preferece trust. Cloud users ca build a trust cloud services quatificatio idex table i accordace with the eeds or the historical behavior iformatio of the services. Cloud users also defie the time iterval accordig to the service eed property. For each time iterval[ t, t ], we eed to establish the appropriate trust quatificatio i- i terval, ] durig which the cloud services are provided at a timet, i.e., ti t t. he, we ca radomly [ i geerate the time factor to quatify the value of trust i, ]. For the time iterval t, t ], if the total [ [ i umber of services is provided times amog which there are m total umber of dishoest services, the the probability of dishoest services durig the period is p = m. If we radomly geerate a time x to quatify the value of trust, ], the the preferece trust value = x ( p). x [ i rust quatificatio based o the time factor ca be show i able : ime factor [, t 0 ) able ime factor trust quatificatio table t t, ) t, )..., t ] [ t 2 [ t 2 3 [ t rust quatificatio Probability of dishoesty, ), ) [ 0 [ [, )..., ] [ p0 p p... p 2 Cloud user trust factor maily refers to trustig cloud users by a cloud service provider. he cloud service provider ca read its ow record to get such iformatio with the default value beig 0.5 if such iformatio is ot available. Cloud user trust quatizatio table ca be established i a similar way as able. History behavioral factor maily refers to the behavior of the service provider. he purpose is to make a dishoest service provider pay a higher price. he service provider record table ca be established for each cloud service ad stored at the cloud service agecy to which cloud users ca access. Cloud users ca the use the historical behavior iformatio records as a importat source for the cofidece o the correspodig services i the future. Cloud service provider record table icludes preferece trust ad service evets which reflect temporal ad spatial factors. Such a table is show i able 2: I able 2, m represets the th factor for the mth cloud service. Here, we oly list the temporal, spatial, user trust, historical behavioral factor ad behavioral feedback a i+ which is the last historical behavior trust value. Whe a cloud service provides services for the first time, the trust value for the history behavioral factor ca be iitialized to be 0.5.

8 able 2 Service record table Cloud services Preferece trust time space User trust Historicalbehavior behavior feedback a a0 a a2 a3 a i+ b b0 b b2 b3 b i+ m m0 m m2 m3 m i+ Aother importat issue is to determie the optimal weights for the differet factors. he approach is to aalyze historical behavior of the services by applyig the maximum etropy aalysis method to determie the weight for each factor through fuzzy comprehesive evaluatio. Based o the records of direct iteractios betwee cloud users ad cloud services, trust evaluatio o the followig attributes are performed: temporal, spatial, user trust ad historical behavior that costitute the evaluatio idex setu = { uuuu, 2, 3, 4}. he evaluatio results ca cosist of four possibilities {complete trust, trust, critical trust, distrust}expressed usig the correspodig decisio set V= { vvvvv, 2, 3, 4, 5}. he maximum etropy method is about the use of iformatio etropy i iformatio theory to determie the weight of each idex i multi-attribute decisio makig. he basic priciple for multi-criteria decisio makig is to select the best from m satisfied solutios based o the amout of iformatio that each idex ca provide as well as the weight of the idex. I this paper, we aalyze the history of the service providers ad apply fuzzy comprehesive evaluatio method ad iformatio etropy theory to determie the best combiatio of weights of various factors i the desig of a preferece trust quatificatio algorithm. We also aalyze the effectiveess of the algorithm. he algorithm is as follows: Step: Check cloud service provider s record to determie the umber of service iteractios that ca be trusted, this value k is set by the cloud user. Step2: If the umber of iteractios with the service is h k, iitialize the weight for preferece trust factor to be 0.25, go to step (8). Step3: Accordig to the time whe a iteractio occurs, select from the cloud service provider record table m records expressed usig X = { x, x2,..., x m } If P, P2,..., P are the properties for each preferece trust, the form a m trust decisio matrix amog which i represets the ith preferece trust ad the th factor.

9 i 2 m m 2 m = Step4: Stadardize each factor i the records X. he calculate = = = for each elemet of X so that [0,]. i m ( i,2,..., m ;,2,..., ) i Step5: Apply the maximum etropy techique to calculate the etropy of each attribute of the preferece trust E k l m = ( =, 2,..., ).Make k / l ( m) i i = to esure that 0. Step6:If the cloud user does t have ay preferece o the properties P, P 2,..., P,the the weight of P /,,2,...,. is w = ( E ) ( E ) ( = ) Step7: If the cloud user has a preferece o the properties (,,..., ) Step 6 to get a ew weight w λ w / λ w =, (, 2,..., ) Step 8: Output the value of the weight for each factor. =. i E λ λ λ2 λ =, the adust the result of Step 9: Apply the fuzzy comprehesive evaluatio method to udge every attribute i order to relate the attribute to a trust level. he, establish the fuzzy relatioship matrix R i which r i is the degree of the service s beig amed v with respect to the property u i, i.e., the degree of u i beig affiliated with v. R r r2 r m r r r r r 2 rm m = Step 0: Sythesize the fuzzy relatioships by selectig the weighted average fuzzy operator b = wr + wr + + wr ad applyig the followig operatio to get the fial evaluatio results z (,, ) = W R= w 2 w r r2 r m r2 r22 r 2m. r r 2 rm

10 3.3Simulatio ad Aalysis o verify the effectiveess of our proposed method for trust quatificatio, we performed some experimet usig the cloud computig simulatio software CloudSim ehaced with org.cloudbus.cloudsim.lists by addig the ServiceDirrustsimulatio etity class to allow us to defie cloud users, cofigure their trust values, ad specify service eeds, service records ad other ecessary parameters. he simulatio experimet would simulate the differet service iteractive eviromets i which our method is applied to respod to the chages of cloud services. For the purpose of illustratio, we radomly geerated three cloud service provider records ad the correspodig quatified values of each factor are show i able 3. able 3 Service record table Cloud Services trust behavior Users Historical ime Space i k p We the stadardized the data i able 3 accordig to Step 4 i our method to get : = Here, we do t assume ay preferece o the weight of each idex. he, by applyig Steps 5-8o the temporal factor of the preferece trust, we get the followig etropy value: E = (0.28 l l l 0.24) = l 3 able4 lists the preferece trust factors weight ad respective etropy values: Preferece trust factor Etropy Weights able 4 he etropy values ad weights of the preferece trust factors ime Space Users trust Historical behavior E w Cosequetly, the quatified value of the service preferece trust is:

11 z = = ( ) [ ] For ease of compariso ad visualizatio with the above assiged weights to the factors, we provide herei the results of a service that has bee provided 30 times durig which the first 9 are provided hoestly but subsequetly becomes dishoest startig from the 0th service. We illustrate the results usig two scearios. I the first sceario, we chaged the history behavioral factors without chagig the weights. he values of the preferece trust of the cloud service are show i Figure rust quatizatio values Fig.3 Preferece trust values with fixed weights I the secod sceario, we chaged both the history behavioral factors ad the weights to the factor. he values of the preferece trust of the cloud service are show i Figure4. Fig.4 Preferece trust values with chagig weights he results i Figures 3& 4 clearly show that whe the cloud service performs hoestly, preferece trust gradually icreases alog with the improvemet of the historical behavior value. However, whe the service

12 provider s behavior becomes dishoest, feedback from cloud users would cause the value of the historical behavior factor to go lower, draggig dow the preferece trust values over the weights of the factors. hus,the proposed trust quatificatio method is effective accordig to the results of the experimet. 4. Coclusio I this paper, we proposed a trust quatificatio method i cloud computig eviromets i which we applied the fuzzy comprehesive evaluatio theory to quatifyig trust o cloud services. First, cosiderig cloud users persoalized service eeds, we defied the cocept of preferece trust which icludes factors that reflect temporal ad spatial properties, cloud user trust ad historical behavior. We the desiged weight distributio for each factor of the preferece trust ad proposed a quatificatio algorithm by applyig iformatio ad fuzzy evaluatio theory. We also performed some simulatio experimet to demostrate that our proposed approach ca help users achieve more beefits ad protect privacy effectively. With trust evaluatio o cloud services providers, cloud users ca choose suitable services with differet trust values alog with other aspects of the services. Our approach ca certaily be used to protect cloud users' data ad cotai services providers malicious behavior. Ackowledgmets he work i this paper has bee supported by Natioal Natural Sciece Foudatio of Chia ( ), Natioal High-tech R&D Program (863 Program) (205AA07204) ad Beiig Natural Sciece Foudatio(442008). Refereces [] Ciriai V, Vimercati S D C D, Foresti S, et al. Combiig Fragmetatio ad Ecryptio to Protect Privacy i Data Storage. Acm ras.if.syst.secur, 200, 3(3): [2] Oliveira D, Ogasawara E, Oca09a K, et al. A adaptive parallel executio strategy for cloud-based scietific workflows. Cocurrecy & Computatio Practice & Experiece, 202, 24(3): [3] Vesyropoulos N, Georgiadis C K, Pimeidis E. Esurig Cloud Security: Curret Cocers ad Research Challeges. Commuicatios i Computer & Iformatio Sciece, 203:3-0. [4] Wag W, Zeg G, Zhag J, et al. Dyamic trust evaluatio ad schedulig framework for cloud computig[j]. Security ad Commuicatio Networks, 202, 5(3):3-38. [5] Marks E A. Bob Lozao Executive s Guide to Cloud computig. Wiley & Sos, 200. [6] Lopez J, Roma R, Agudo I, et al. rust maagemet systems for wireless sesor etworks: Best practices. Computer Commuicatios, 200, 33(9): [7] Abaway J. Establishig rust i Hybrid Cloud Computig Eviromets. rust Security & Privacy i Computig & Commuicatios IEEE Iteratioal, 20:8-25. [8] Joshi L K F A. Movig from Security to Distributed rust i Ubiquitous Computig Eviromets. IEEE Computer, 200. [9] Noor H, Sheg Q Z, Zeadally S, et al. rust maagemet of services i cloud Eviromets: Obstacles ad solutios. ACM Computig Surveys, 203, 46(): [0] Barsoum A, Hasa A. Eablig Dyamic Data ad Idirect Mutual rust for Cloud Computig Storage Systems. IEEE rasactios o Parallel ad Distributed Systems, 203, 24(2):

13 [] Chag E J, Hussai F K, Dillo S. Fuzzy ature of trust ad dyamic trust modelig i service orieted Eviromets. ACM Press, 2005: [2] Jaigaesh M, Aarthi M, Kumar A V A. Fuzzy AR-Based User Behavior rust i Cloud Computig. Advaces i Itelliget Systems & Computig, 205. [3] Kliger R, omaek K. Classical Probabilistic Models ad Coditioal Radom Fields. Algorithm Egieerig Report: R , [4] Li Big,Cao Buqig,We Kumei,et al.rustworthy Assurace of Service Iteroperatio i Cloud Eviromets.Iteratioal Joural of Automatio ad Computig,20: [5] Armbrust M,Fox A,Griffith R,et al. Above the clouds : a berkeley view of cloud computig. Commuicatios of the ACM,200,53(4): [6] Harauz J, Kaufma L M, Potter B. Data security i the world of cloud computig. IEEE Security & Privacy, 2009, 7(4):6-64. [7] Habib S M, Ries S, Mühlh0user M, et al. owards A rust Maagemet System For Cloud Computig Marketplaces: Usig Caiq As A rust Iformatio Source. Security & Commuicatio Networks, 203, 7(): [8] Jøsag A, Ismail R, Boyd C. A survey of trust ad reputatio systems for olie service provisio. Decisio Support Systems, 2007, 43(2): [9] Michael Brock,, Adrze Gosciski. 7. Ehacig Cloud Computig Eviromets Usig a Cluster as a Service. Cloud Computig: Priciples ad Paradigms, 20. [20] Abdelzaher,Shi K G,Bhatti N. Performace Guaratees for Web Server Ed-systems: A Cotroltheoretical Approach. IEEE rasactios o Parallel ad Distributed Systems,2002,3(). [2] Everett C. Cloud computig A questio of trust. Computer Fraud & Security, 2009, 2009:5-7. [22] Walterbusch M, euteberg F. owards a Uderstadig of the Formatio ad Retetio of rust i Cloud Computig: A Research Ageda, Proposed Research Methods ad Prelimiary Results. Lecture Notes i Computer Sciece, 204: [23] Dykstra J, Sherma A. Acquirig foresic evidece from ifrastructure-as-a-service cloud computig: Explorig ad evaluatig tools, trust, ad techiques. Digital Ivestigatio, 202, 9(8):S90-S98. [24] Corporatio H P. A Profile based Network Itrusio Detectio ad Prevetio System for securig Cloud Eviromets. Iteratioal Joural of Distributed Sesor Networks, 203, ():8-0. [25] Hayes B. Cloud Computig. Wiley Iterdiscipliary Reviews Computatioal Statistics, 203, 3(): [26] Hashizume K, Rosado D G, Feradez-Media E, et al. A aalysis of security issues for cloud computig. Joural of Iteret Services & Applicatios, 203, 4:5(). [27] GRUBER R. A traslatio approach to portable otology specificatios. StafordUiversity, ech Rep: Logic-92-, 993. [28] weedie S, Ashburer M, Falls K, et al. FlyBase: ehacig Drosophila Gee Otology aotatios. Nucleic Acids Research, 2009, 37(suppl ):D555-D559. [29] Harris M A, Clark J, Irelad A, et al. he Gee Otology (GO) database ad iformatics resource. Nucleic Acids Research, 2004, 32. [30] Marcela Meia,Nestor Pea,Jose L. Muoz,Oscar Esparza, Marco A. Alzate.A game theoretic trust model for o-lie distributed evolutio of cooperatio i MANEs. Joural of Network ad Computer Applicatios. 200 (). [3] Bowers KD,Juels A,Oprea A. Proofs of retrievability:heory ad implemetatio.new York,USA:Associatio for Computig Machiery,

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