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How To Simulate It – A Tutorial on the Simulation Proof ...

HowToSimulateIt ATutorialontheSimulationProofTechnique ThistutorialappearedinthebookTutorialson theFoundationsofCryptography,publishedin honorofOdedGoldreich SemanticSecurity44 SecureComputation ObliviousTransfer499 TheCommonReferenceStringModel , realworld towhathappensinan idealworld , , , (thisisan idealworld thatissecurebydefinition),thisimpliestha tintherealworld,wheretheadversaryreceive stheciphertext, , snotatallclearhowtoformalizethenotiontha t nothingislearned .Ifwetrytosaythatanadversarywhoreceivesa ciphertextcannotoutputanyinformationabou ttheplaintext,thenwhathappensiftheadvers aryalreadyhasinformationabouttheplaintex t?Forexample, , (oroutputbytheadversary) , Simulation ; (firstinSection3).Fornow,itsufficestosay thatsecurityproofsfordefinitionsformulat edinthiswayworkbyconstructingasimulatort hatresidesinthealternativeworldthatissec urebydefinition, ,aswewillshow, ; ; , , ,wewilldemonstratethesimulationparadigmi nanumberofdifferentsettings, , ,inSection4,weshowhowtosimulatesecurecom putationprotocolsforthecaseofsemi-honest adversaries(whofollowtheprotocolspecific ation,buttrytolearnmorethanallowedbyinsp ectingtheprotocol2transcript).

Organization. In this tutorial, we will demonstrate the simulation paradigm in a number of different settings, together with explanations about what is required from the simulator and proof. We demonstrate the aforementioned three different tasks of the simulator in simulation-based proofs via a gradual progression.

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