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1、One-RoundSecureComputationandSecureAutonomousMobileAgents(ExtendedAbstract)ChristianCachin1,JanCamenisch1,JoeKilian2,andJoyM•uller1Abstract.Thispaperinvestigatesone-roundsecurecomputationbe-tweentwodistrustingparties:AliceandBobeachhaveprivateinputstoac
2、ommonfunction,butonlyAlice,actingasthereceiver,istolearntheoutput;theprotocolislimitedtoonemessagefromAlicetoBobfollowedbyonemessagefromBobtoAlice.AmodelinwhichBobmaybecompu-tationallyunboundedisinvestigated,whichcorrespondstoinformation-theoreticsecuri
3、tyforAlice.Itisshownthat1.forhonest-but-curiousbehaviorandunboundedBob,anyfunctioncomputablebyapolynomial-sizecircuitcanbecomputedsecurelyassumingthehardnessofthedecisionalDie-Hellmanproblem;2.formaliciousbehaviorbyboth(bounded)parties,anyfunctioncom-p
4、utablebyapolynomial-sizecircuitcanbecomputedsecurely,inapublic-keyframework,assumingthehardnessofthedecisionalDie-Hellmanproblem.Theresultsareappliedtosecureautonomousmobileagents,whichmi-gratebetweenseveraldistrustinghostsbeforereturningtotheirorigina
5、-tor.Aschemeispresentedforprotectingtheagent'ssecretssuchthatonlytheoriginatorlearnstheoutputofthecomputation.1IntroductionSupposeAlicehasasecretinputx,Bobhasasecretinputy,andtheywishtocomputeg(x;y)securelyusingoneroundofinteraction:Aliceshouldlearng(x;
6、y)butnothingelseaboutyandBobshouldlearnnothingatall.Commu-nicationisrestrictedtoonemessagefromAlicetoBobfollowedbyonemessagefromBobtoAlice.Withouttherestrictiononthenumberofrounds,thisistheproblemofsecurefunctionevaluationintroducedbyYao[26]andGoldreich
7、etal.[17].Itisknownthatundercryptographicassumptions,everyfunctioncanbecomputedsecurelyandusinga(small)constantnumberofrounds.Theproblemiscloselyrelatedtothequestionofcomputingwithencrypteddata"[22]:Aliceholdssomeinputx,Bobholdsafunctionf,andAliceshoul
8、dlearnf(x)inaone-roundprotocol,whereAlicesendstoBobanencryption"ofx,Bobcomputesfontheencrypted"dataxandsendstheresulttoAlice,whodecrypts"thistof(x).Thedualofthisiscomputingwithencryptedfunctions,"whereAliceholdsafunctionf,Bob
