On statistically secure obfuscation with approximate correctness

Zvika Brakerski, Christina Brzuska, Nils Fleischhacker

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

Abstract

Goldwasser and Rothblum (TCC’07) prove that statistical indistinguishability obfuscation (iO) cannot exist if the obfuscator must maintain perfect correctness (under a widely believed complexity theoretic assumption: NP ⊈ SZK ⊆ AM∩ coAM). However, for many applications of iO, such as constructing public-key encryption from oneway functions (one of the main open problems in theoretical cryptography), approximate correctness is sufficient. It had been unknown thus far whether statistical approximate iO (saiO) can exist. We show that saiO does not exist, even for a minimal correctness requirement, if NP ⊈ AM∩ coAM, and if one-way functions exist. A simple complementary observation shows that if one-way functions do not exist, then average-case saiO exists. Technically, previous approaches utilized the behavior of the obfuscator on evasive functions, for which saiO always exists. We overcome this barrier by using a PRF as a “baseline” for the obfuscated program. We broaden our study and consider relaxed notions of security for iO. We introduce the notion of correlation obfuscation, where the obfuscations of equivalent circuits only need to be mildly correlated (rather than statistically indistinguishable). Perhaps surprisingly, we show that correlation obfuscators exist via a trivial construction for some parameter regimes, whereas our impossibility result extends to other regimes. Interestingly, within the gap between the parameters regimes that we show possible and impossible, there is a small fraction of parameters that still allow to build public-key encryption from one-way functions and thus deserve further investigation.

Original languageEnglish
Title of host publicationAdvances in Cryptology
Subtitle of host publication36th Annual International Cryptology Conference, CRYPTO 2016, Proceedings
EditorsMatthew Robshaw, Jonathan Katz
PublisherSpringer Verlag
Pages551-578
Number of pages28
ISBN (Print)9783662530078
DOIs
StatePublished - 21 Jul 2016
Event36th Annual International Cryptology Conference, CRYPTO 2016 - Santa Barbara, United States
Duration: 14 Aug 201618 Aug 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9815

Conference

Conference36th Annual International Cryptology Conference, CRYPTO 2016
Country/TerritoryUnited States
CitySanta Barbara
Period14/08/1618/08/16

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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