Secure Distributed Framework for Achieving ϵ -Differential Privacy

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Secure Distributed Framework for Achieving ϵ -Differential Privacy. Dima Alhadidi , Noman Mohammed, Benjamin C. M. Fung, and Mourad Debbabi Concordia Institute for Information Systems Engineering Concordia University, Montreal, Quebec, Canada - PowerPoint PPT Presentation

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Secure Distributed Framework for Achieving -Differential Privacy

Secure Distributed Framework for Achieving -Differential PrivacyDima Alhadidi, Noman Mohammed, Benjamin C. M. Fung, and Mourad DebbabiConcordia Institute for Information Systems EngineeringConcordia University, Montreal, Quebec, Canada{dm_alhad,no_moham,fung,debbabi}@encs.concordia.ca1OutlineMotivationProblem StatementRelated WorkBackgroundTwo-Party Differentially Private Data ReleasePerformance AnalysisConclusion

#6/24/20122OutlineMotivationProblem StatementRelated WorkBackgroundTwo-Party Differentially Private Data ReleasePerformance AnalysisConclusion

#6/24/20123Motivation

IndividualsData PublisherAnonymization AlgorithmData RecipientsCentralized

Distributed

#6/24/20124MotivationDistributed: Vertically-Partitioned

IDJob1Writer2Dancer3Writer4Dancer5Engineer6Engineer7Engineer8Dancer9Lawyer10LawyerIDSexSalary1M30K2M25K3M35K4F37K5F65K6F35K7M30K8F44K9M44K10F44K#6/24/2012MotivationDistributed: Vertically-Partitioned

IDJobSexSalary1WriterM30K2DancerM25K3WriterM35K4DancerF37K5EngineerF65K6EngineerF35K7EngineerM30K8DancerF44K9LawyerM44K10LawyerF44K#6/24/2012MotivationDistributed: Horizontally-Partitioned

IDJobSexAgeSurgery1JanitorM34Transgender2LawyerF58Plastic3MoverM58Urology4LawyerM24Vascular5MoverM34Transgender6JanitorM44Plastic7DoctorF44VascularIDJobSexAgeSurgery8DoctorM58Plastic9DoctorM24Urology10JanitorF63Vascular11MoverF63Plastic#6/24/2012MotivationDistributed: Horizontally-Partitioned

IDJobSexAgeSurgery1JanitorM34Transgender2LawyerF58Plastic3MoverM58Urology4LawyerM24Vascular5MoverM34Transgender6JanitorM44Plastic7DoctorF44Vascular8DoctorM58Plastic9DoctorM24Urology10JanitorF63Vascular11MoverF63Plastic#6/24/2012MotivationDistributed: Horizontally-Partitioned

IDJobSexAgeSurgery1JanitorM34Transgender2LawyerF58Plastic3MoverM58Urology4LawyerM24Vascular5MoverM34Transgender6JanitorM44Plastic7DoctorF44Vascular8DoctorM58Plastic9DoctorM24Urology10JanitorF63Vascular11MoverF63Plastic#6/24/2012MotivationDistributed: Horizontally-Partitioned

IDJobSexAgeSurgery1JanitorM34Transgender2LawyerF58Plastic3MoverM58Urology4LawyerM24Vascular5MoverM34Transgender6JanitorM44Plastic7DoctorF44Vascular8DoctorM58Plastic9DoctorM24Urology10JanitorF63Vascular11MoverF63Plastic#6/24/2012MotivationDistributed: Horizontally-Partitioned

IDJobSexAgeSurgery1JanitorM34Transgender2LawyerF58Plastic3MoverM58Urology4LawyerM24Vascular5MoverM34Transgender6JanitorM44Plastic7DoctorF44Vascular8DoctorM58Plastic9DoctorM24Urology10JanitorF63Vascular11MoverF63Plastic#6/24/2012OutlineMotivationProblem StatementRelated WorkBackgroundTwo-Party Differentially Private Data ReleasePerformance AnalysisConclusion

#6/24/201212Problem StatementDesideratum 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).

#6/24/2012OutlineMotivationProblem StatementRelated WorkBackgroundTwo-Party Differentially Private Data ReleasePerformance AnalysisConclusion

#6/24/201214Related WorkAlgorithmsData OwnerPrivacy ModelCentralizedDistributedDifferential PrivacyPartition-based PrivacyHorizontallyVerticallyLeFevre et al., Fung et al., etcXiao et al. , Mohammed et al. , etc.Jurczyk and Xiong, Mohammed et al. Jiang and Clifton, Mohammed et al. Our proposal #6/24/201215OutlineMotivationProblem StatementRelated WorkBackgroundTwo-Party Differentially Private Data ReleasePerformance AnalysisConclusion

#6/24/201216k-AnonymityRaw patient tableJobSexAgeDiseaseEngineerMale35FeverEngineerMale38FeverLawyerMale38HepatitisMusicianFemale30FluMusicianFemale30HepatitisDancerFemale30HepatitisDancerFemale30Hepatitis#6/24/201217k-AnonymityRaw patient tableJobSexAgeDiseaseEngineerMale35FeverEngineerMale38FeverLawyerMale38HepatitisMusicianFemale30FluMusicianFemale30HepatitisDancerFemale30HepatitisDancerFemale30HepatitisQuasi-identifier (QID)#6/24/201218k-Anonymity3-anonymous patient tableJobSexAgeDiseaseProfessionalMale[36-40]FeverProfessionalMale[36-40]FeverProfessionalMale[36-40]HepatitisArtistFemale[30-35]FluArtistFemale[30-35]HepatitisArtistFemale[30-35]HepatitisArtistFemale[30-35]HepatitisRaw patient tableJobSexAgeDiseaseEngineerMale35FeverEngineerMale38FeverLawyerMale38HepatitisMusicianFemale30FluMusicianFemale30HepatitisDancerFemale30HepatitisDancerFemale30Hepatitis#6/24/201219Differential Privacy

DD

#6/24/201220Laplace Mechanism

D#6/24/2012Exponential MechanismMcSherry 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.#6/24/201222OutlineMotivationProblem StatementRelated WorkBackgroundTwo-Party Differentially Private Data ReleasePerformance AnalysisConclusion

#6/24/201223Two-Party Differentially Private Data ReleaseGeneralizing the raw dataAdding noisy count#6/24/201224Generalizing the raw data

Distributed Exponential Mechanism(DEM)#6/24/2012Generalization

Distributed Exponential Mechanism(DEM)#6/24/2012Adding Noisy CountEach party adds a Laplace noise to its count .Each party sends the result to the other party.#6/24/2012Two-Party Protocol for Exponential MechanismInput:Two raw data sets by two partiesSet of candidatesPrivacy budgetOutput : Winner candidate

#6/24/201228Max Utility FunctionIDClassJobSexAgeSurgery1NJanitorM34Transgender2YLawyerF58Plastic3YMoverM58Urology4NLawyerM24Vascular5YMoverM34Transgender6YJanitorM44Plastic7YDoctorF44VascularMaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collarD1#6/24/201229Max Utility FunctionMaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collarD2IDClassJobSexAgeSurgery8NDoctorM58Plastic9YDoctorM24Urology10YJanitorF63Vascular11YMoverF63Plastic#6/24/201230Max Utility FunctionMaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collarIDClassJobSexAgeSurgery1NJanitorM34Transgender2YLawyerF58Plastic3YMoverM58Urology4NLawyerM24Vascular5YMoverM34Transgender6YJanitorM44Plastic7YDoctorF44Vascular8NDoctorM58Plastic9YDoctorM24Urology10YJanitorF63Vascular11YMoverF63PlasticD1 & D2#6/24/201231Computing Max Utility FunctionBlue-collar

MaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collar#6/24/2012Computing Max Utility Functionmax=1 Blue-collar

MaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collar#6/24/2012Computing Max Utility Functionmax=1 Blue-collar

MaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collar#6/24/2012Computing Max Utility Functionmax=5, sum=5 Blue-collar

MaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collar#6/24/2012Computing Max Utility Functionsum=5 White-collar

MaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collar#6/24/2012Computing Max Utility Functionmax=2, sum=5 White-collar

MaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collar#6/24/2012Computing Max Utility Functionmax=2, sum=5 White-collar

MaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collar#6/24/201238Computing Max Utility Functionmax=3, sum=8 White-collar

MaxClassJobData SetYN531Blue-collarD121White-collar320Blue-collarD2

11White-collar851Blue-collarIntegrated D1 and D232White-collarResult: Shares 1 and 2 #6/24/2012Computing the Exponential EquationGiven the scores of all the candidates, exponential mechanism selects the candidate having score u with the following probability:

Shares 1 and 2 #6/24/2012Computing the Exponential Equation

=

Taylor Series

=

#6/24/2012Computing the Exponential Equation

Lowest common multiplier of {2!,,w!}, no fractionApproximating up to a predetermined number s after the decimal point

#6/24/2012Computing the Exponential Equation

No fraction

#6/24/201243Computing the Exponential Equation

Oblivious Polynomial EvaluationFirst PartySecond Party

ResultFirst Party Second Party

#6/24/201244Computing the Exponential Equation

Second PartyFirst Party#6/24/201245Computing the Exponential Equation

010.50.30.20.7Picking a random number[0,1]#6/24/201246Computing the Exponential Equation

0

Picking a random number[0, ]

#6/24/201247Picking a Random NumberSecond PartyRandom Value Protocol[Bunn and Ostrovsky 2007]

First PartySecond Party

First Party#6/24/2012Picking a Winner

#6/24/2012OutlineMotivationProblem StatementRelated WorkBackgroundTwo-Party Differentially Private Data ReleasePerformance AnalysisConclusion

#6/24/201250Performance AnalysisAdult: is a Census data6 numerical attributes.8 categorical attributes.45,222 census recordsCost Estimates37.5 minutes of computation37.3 minutes of communication using T1 line with 1.544 Mbits/second bandwidth.

#6/24/2012Scaling Impact

#6/24/2012OutlineMotivationProblem StatementRelated WorkBackgroundTwo-Party Differentially Private Data ReleasePerformance AnalysisConclusion

#6/24/201253ConclusionData release algorith