One-way functions and (im)perfect obfuscation

Ilan Komargodski, Tal Moran, Moni Naor, Rafael Pass, Alon Rosen, Eylon Yogev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A program obfuscator takes a program and outputs a 'scrambled' version of it, where the goal is that the obfuscated program will not reveal much about its structure beyond what is apparent from executing it. There are several ways of formalizing this goal. Specifically, in indistinguishability obfuscation, first defined by Barak et al. (CRYPTO 2001), the requirement is that the results of obfuscating any two functionally equivalent programs (circuits) will be computationally indistinguishable. Recently, a fascinating candidate construction for indistinguishability obfuscation was proposed by Garg et al. (FOCS 2013). This has led to a flurry of discovery of intriguing constructions of primitives and protocols whose existence was not previously known (for instance, fully deniable encryption by Sahai and Waters, STOC 2014). Most of them explicitly rely on additional hardness assumptions, such as one-way functions. Our goal is to get rid of this extra assumption. We cannot argue that indistinguishability obfuscation of all polynomial-time circuits implies the existence of one-way functions, since if P = NP, then program obfuscation (under the indistinguishability notion) is possible. Instead, the ultimate goal is to argue that if P ≠ NP and program obfuscation is possible, then one-way functions exist. Our main result is that if NP ioBPP and there is an efficient (even imperfect) indistinguishability obfuscator, then there are one-way functions. In addition, we show that the existence of an indistinguishability obfuscator implies (unconditionally) the existence of SZK-arguments for NP. This, in turn, provides an alternative version of our main result, based on the assumption of hard-on-the average NP problems. To get some of our results we need obfuscators for simple programs such as 3CNF formulas.

Original languageEnglish
Title of host publicationProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
PublisherIEEE Computer Society
Pages374-383
Number of pages10
ISBN (Electronic)9781479965175
DOIs
StatePublished - 7 Dec 2014
Externally publishedYes
Event55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014 - Philadelphia, United States
Duration: 18 Oct 201421 Oct 2014

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference55th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2014
Country/TerritoryUnited States
CityPhiladelphia
Period18/10/1421/10/14

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