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Secure Distributed Framework for Achieving -Differential Privacy Dima Alhadidi, Noman Mohammed, Benjamin C. M. Fung, and Mourad Debbabi Concordia Institute for Information Systems Engineering Concordia University, Montreal, Quebec, Canada {dm_alhad,no_moham,fung,debbabi}@encs.concordia.ca
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2 6/24/2012 Outline Motivation Problem Statement Related Work Background Two-Party Differentially Private Data Release Performance Analysis Conclusion
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3 6/24/2012 Outline Motivation Problem Statement Related Work Background Two-Party Differentially Private Data Release Performance Analysis Conclusion
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4 6/24/2012 Motivation IndividualsData PublisherAnonymization Algorithm Data Recipients Centralized Distributed
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5 6/24/2012 Motivation Distributed: Vertically-Partitioned IDJob 1Writer 2Dancer 3Writer 4Dancer 5Engineer 6 7 8Dancer 9Lawyer 10Lawyer IDSexSalary 1M30K 2M25K 3M35K 4F37K 5F65K 6F35K 7M30K 8F44K 9M 10F44K
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6 6/24/2012 Motivation Distributed: Vertically-Partitioned IDJobSexSalary 1WriterM30K 2DancerM25K 3WriterM35K 4DancerF37K 5EngineerF65K 6EngineerF35K 7EngineerM30K 8DancerF44K 9LawyerM44K 10LawyerF44K
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7 6/24/2012 Motivation Distributed: Horizontally-Partitioned IDJobSexAgeSurgery 1JanitorM34Transgender 2LawyerF58Plastic 3MoverM58Urology 4LawyerM24Vascular 5MoverM34Transgender 6JanitorM44Plastic 7DoctorF44Vascular IDJobSexAgeSurgery 8DoctorM58Plastic 9DoctorM24Urology 10JanitorF63Vascular 11MoverF63Plastic
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8 6/24/2012 Motivation Distributed: Horizontally-Partitioned IDJobSexAgeSurgery 1JanitorM34Transgender 2LawyerF58Plastic 3MoverM58Urology 4LawyerM24Vascular 5MoverM34Transgender 6JanitorM44Plastic 7DoctorF44Vascular 8DoctorM58Plastic 9DoctorM24Urology 10JanitorF63Vascular 11MoverF63Plastic
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9 6/24/2012 Motivation Distributed: Horizontally-Partitioned IDJobSexAgeSurgery 1JanitorM34Transgender 2LawyerF58Plastic 3MoverM58Urology 4LawyerM24Vascular 5MoverM34Transgender 6JanitorM44Plastic 7DoctorF44Vascular 8DoctorM58Plastic 9DoctorM24Urology 10JanitorF63Vascular 11MoverF63Plastic
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10 6/24/2012 Motivation Distributed: Horizontally-Partitioned IDJobSexAgeSurgery 1JanitorM34Transgender 2LawyerF58Plastic 3MoverM58Urology 4LawyerM24Vascular 5MoverM34Transgender 6JanitorM44Plastic 7DoctorF44Vascular 8DoctorM58Plastic 9DoctorM24Urology 10JanitorF63Vascular 11MoverF63Plastic
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11 6/24/2012 Motivation Distributed: Horizontally-Partitioned IDJobSexAgeSurgery 1JanitorM34Transgender 2LawyerF58Plastic 3MoverM58Urology 4LawyerM24Vascular 5MoverM34Transgender 6JanitorM44Plastic 7DoctorF44Vascular 8DoctorM58Plastic 9DoctorM24Urology 10JanitorF63Vascular 11MoverF63Plastic
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12 6/24/2012 Outline Motivation Problem Statement Related Work Background Two-Party Differentially Private Data Release Performance Analysis Conclusion
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13 6/24/2012 Problem Statement Desideratum to develop a two-party data publishing algorithm for horizontally-partitioned data which : –achieves differential privacy and –satisfies the security definition of secure multiparty computation (SMC).
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14 6/24/2012 Outline Motivation Problem Statement Related Work Background Two-Party Differentially Private Data Release Performance Analysis Conclusion
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15 6/24/2012 Related Work Algorithms Data OwnerPrivacy Model Centralized Distributed Differential Privacy Partition- based Privacy HorizontallyVertically LeFevre et al., Fung et al., etc Xiao et al., Mohammed et al., etc. Jurczyk and Xiong, Mohammed et al. Jiang and Clifton, Mohammed et al. Our proposal
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16 6/24/2012 Outline Motivation Problem Statement Related Work Background Two-Party Differentially Private Data Release Performance Analysis Conclusion
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17 6/24/2012 k-Anonymity
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18 6/24/2012 k-Anonymity Quasi-identifier (QID)
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19 6/24/2012 k-Anonymity 3-anonymous patient table JobSexAgeDisease ProfessionalMale[36-40]Fever ProfessionalMale[36-40]Fever ProfessionalMale[36-40]Hepatitis ArtistFemale[30-35]Flu ArtistFemale[30-35]Hepatitis ArtistFemale[30-35]Hepatitis ArtistFemale[30-35]Hepatitis
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20 6/24/2012 Differential Privacy D D
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21 6/24/2012 Laplace Mechanism D
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22 6/24/2012 Exponential Mechanism McSherry and Talwar have proposed the exponential mechanism that can choose an output that is close to the optimum with respect to a utility function while preserving differential privacy.
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23 6/24/2012 Outline Motivation Problem Statement Related Work Background Two-Party Differentially Private Data Release Performance Analysis Conclusion
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24 6/24/2012 Two-Party Differentially Private Data Release Generalizing the raw data Adding noisy count
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25 6/24/2012 Generalizing the raw data Distributed Exponential Mechanism (DEM)
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26 6/24/2012 Generalization Distributed Exponential Mechanism (DEM)
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27 6/24/2012 Adding Noisy Count Each party adds a Laplace noise to its count. Each party sends the result to the other party.
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28 6/24/2012 Two-Party Protocol for Exponential Mechanism Input: 1.Two raw data sets by two parties 2.Set of candidates 3.Privacy budget Output : Winner candidate
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29 6/24/2012 Max Utility Function IDClassJobSexAgeSurgery 1NJanitorM34Transgender 2YLawyerF58Plastic 3YMoverM58Urology 4NLawyerM24Vascular 5YMoverM34Transgender 6YJanitorM44Plastic 7YDoctorF44Vascular Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar D1D1
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30 6/24/2012 Max Utility Function Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar D2D2 IDClassJobSexAgeSurgery 8NDoctorM58Plastic 9YDoctorM24Urology 10YJanitorF63Vascular 11YMoverF63Plastic
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31 6/24/2012 Max Utility Function Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar IDClassJobSexAgeSurgery 1NJanitorM34Transgender 2YLawyerF58Plastic 3YMoverM58Urology 4NLawyerM24Vascular 5YMoverM34Transgender 6YJanitorM44Plastic 7YDoctorF44Vascular 8NDoctorM58Plastic 9YDoctorM24Urology 10YJanitorF63Vascular 11YMoverF63Plastic D 1 & D 2
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32 6/24/2012 Computing Max Utility Function Blue-collar Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar
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33 6/24/2012 Computing Max Utility Function max=1 Blue-collar Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar
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34 6/24/2012 Computing Max Utility Function max=1 Blue-collar Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar
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35 6/24/2012 Computing Max Utility Function max=5, sum=5 Blue-collar Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar
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36 6/24/2012 Computing Max Utility Function sum=5 White-collar Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar
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37 6/24/2012 Computing Max Utility Function max=2, sum=5 White-collar Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar
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38 6/24/2012 Computing Max Utility Function max=2, sum=5 White-collar Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar
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39 6/24/2012 Computing Max Utility Function max=3, sum=8 White-collar Max Class JobData Set YN 531Blue-collar D1D1 21White-collar 320Blue-collar D2D2 11White-collar 851Blue-collar Integrated D 1 and D 2 32White-collar Result: Shares 1 and 2
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40 6/24/2012 Computing the Exponential Equation Given the scores of all the candidates, exponential mechanism selects the candidate having score u with the following probability: Shares 1 and 2
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41 6/24/2012 Computing the Exponential Equation = Taylor Series =
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42 6/24/2012 Computing the Exponential Equation Lowest common multiplier of {2!,…,w!}, no fraction Approximating up to a predetermined number s after the decimal point
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43 6/24/2012 Computing the Exponential Equation No fraction
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44 6/24/2012 Computing the Exponential Equation Oblivious Polynomial Evaluation First Party Second Party Result First Party Second Party
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45 6/24/2012 Computing the Exponential Equation Second Party First Party
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46 6/24/2012 Computing the Exponential Equation 01 0.5 0.3 0.20.7 Picking a random number [0,1]
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47 6/24/2012 Computing the Exponential Equation 0 Picking a random number [0, ]
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48 6/24/2012 Picking a Random Number Second Party Random Value Protocol [Bunn and Ostrovsky 2007] First Party Second Party First Party
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49 6/24/2012 Picking a Winner
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50 6/24/2012 Outline Motivation Problem Statement Related Work Background Two-Party Differentially Private Data Release Performance Analysis Conclusion
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51 6/24/2012 Performance Analysis –Adult: is a Census data 6 numerical attributes. 8 categorical attributes. 45,222 census records –Cost Estimates 37.5 minutes of computation 37.3 minutes of communication using T1 line with 1.544 Mbits/second bandwidth.
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52 6/24/2012 Scaling Impact
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53 6/24/2012 Outline Motivation Problem Statement Related Work Background Two-Party Differentially Private Data Release Performance Analysis Conclusion
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54 6/24/2012 Conclusion Data release algorithm –Two-party –Differentially-private –Secure –Horizontally-partitioned –Non-interactive setting
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55 6/24/2012 Future Work Consider different scenarios –Two parties vs. multiple parties –Semi-honest vs. malicious adversary model –Horizontally vs. Vertically partitioned data For all these scenarios, we need efficient algorithms
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