On virtual grey box obfuscation for general circuits

Nir Bitansky, Ran Canetti, Yael Tauman Kalai, Omer Paneth

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

Abstract

An obfuscator O is Virtual Grey Box (VGB) for a class C of circuits if, for any C ∈ C and any predicate π, deducing π(C) given O(C) is tantamount to deducing π(C) given unbounded computational resources and polynomially many oracle queries to C. VGB obfuscation is often significantly more meaningful than indistinguishability obfuscation (IO). In fact, for some circuit families of interest VGB is equivalent to full-fledged Virtual Black Box obfuscation. We investigate the feasibility of obtaining VGB obfuscation for general circuits. We first formulate a natural strengthening of IO, called strong IO (SIO). Essentially, O is SIO for class C if O(C) ≈ O(C′) whenever the pair (C,C′) is taken from a distribution over C where, for all x, C(x) ≠ C′(x) only with negligible probability. We then show that an obfuscator is VGB for a class C if and only if it is SIO for C. This result is unconditional and holds for any C. We also show that for some circuit collections, SIO implies virtual black-box obfuscation. Finally, we formulate a slightly stronger variant of the semantic security property of graded encoding schemes [Pass-Seth-Telang Crypto 14], and show that existing obfuscators such as the obfuscator of Barak et. al [Eurocrypt 14] are SIO for all circuits in NC1, assuming that the underlying graded encoding scheme satisfies our variant of semantic security. Put together, we obtain VGB obfuscation for all NC1 circuits under assumptions that are almost the same as those used by Pass et. al to obtain IO for NC1 circuits. We also show that semantic security is in essence necessary for showing VGB obfuscation.

Original languageEnglish
Title of host publicationAdvances in Cryptology, CRYPTO 2014 - 34th Annual Cryptology Conference, Proceedings
PublisherSpringer Verlag
Pages108-125
Number of pages18
EditionPART 2
ISBN (Print)9783662443804
DOIs
StatePublished - 2014
Event34rd Annual International Cryptology Conference, CRYPTO 2014 - Santa Barbara, CA, United States
Duration: 17 Aug 201421 Aug 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume8617 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference34rd Annual International Cryptology Conference, CRYPTO 2014
Country/TerritoryUnited States
CitySanta Barbara, CA
Period17/08/1421/08/14

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