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1、OptimalGeo-IndistinguishableMechanismsforLocationPrivacyNicolásE.Bordenabe1;3,KonstantinosChatzikokolakis2;3,andCatusciaPalamidessi1;31INRIA2CNRS3LIX,EcolePolytechniqueAbstract.Withlocation-basedservicesbecomingincreasinglymorepop-ular,seriousconcernsarebeingraisedaboutthepotentialprivacybreaches
2、thatthedisclosureoflocationinformationmayinduce.Weconsidertwoapproachesthathavebeenproposedtolimitandcontroltheprivacyloss:oneisthegeo-indistinguishabilitynotionofAndrésetal.,whichisinspiredbydifferentialprivacy,andlikethelatteritisindependentfromthesideknowledgeoftheadversary,androbustwithrespect
3、tocompo-sitionofattacks.TheotheroneisthemechanismofShokrietal.,whichoffersanoptimaltrade-offbetweenthelossofqualityofserviceandtheprivacyprotectionwithrespecttoagivenBayesianadversary.Weshowthatitispossibletocombinetheadvantagesofthetwoapproaches:givenaminimumthresholdforthedegreeofgeo-indistinguis
4、hability,weconstructamechanismthatoffersthemaximalutility,asthesolutionofalinearprogram.Thankstothefactthatgeo-indistinguishabilityisinsensitivetotheremappingofaBayesianadversary,themechanismsoconstructedisoptimalalsointhesenseofShokrietal.Furthermoreweproposeamethodtoreducethenumberofconstraintso
5、fthelinearpro-gramfromcubictoquadratic(withrespecttothenumberoflocations),maintainingtheprivacyguaranteeswithoutaffectingsignificantlytheutilityofthegeneratedmechanism.Thislowersconsiderablythetimerequiredtosolvethelinearprogram,thusenlargingsignificantlythesizeoflocationsetsforwhichtheoptimaltrade-
6、offmechanismscanstillbecomputed.arXiv:1402.5029v1[cs.CR]20Feb20141IntroductionWhilelocation-basedsystems(LBSs)havedemonstratedtoprovideenormousbenefitstoindividualsandsociety,thesebenefitscomeatthecostofusers’pri-vacy:asdiscussedin[1,2,3],locationdatacanbeeasilylinkedtoavarietyofotherinformationabou
7、tanindividual,andexposesensitiveaspectsofherprivatelifesuchasherhomeaddress,herpoliticalviews,herreligiouspractices,etc..Thereis,therefore,agrowinginterestinthedevelopmentoflocation-privacyprotectionmechanisms(LPPMs),t
