Obfuscation for evasive functions

Boaz Barak, Nir Bitansky, Ran Canetti, Yael Tauman Kalai, Omer Paneth, Amit Sahai

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

Abstract

An evasive circuit family is a collection of circuits such that for every input x, a random circuit from outputs 0 on x with overwhelming probability. We provide a combination of definitional, constructive, and impossibility results regarding obfuscation for evasive functions: 1 The (average case variants of the) notions of virtual black box obfuscation (Barak et al, CRYPTO '01) and virtual gray box obfuscation (Bitansky and Canetti, CRYPTO '10) coincide for evasive function families. We also define the notion of input-hiding obfuscation for evasive function families, stipulating that for a random it is hard to find, given, a value outside the preimage of 0. Interestingly, this natural definition, also motivated by applications, is likely not implied by the seemingly stronger notion of average-case virtual black-box obfuscation. 2 If there exist average-case virtual gray box obfuscators for all evasive function families, then there exist (quantitatively weaker) average-case virtual gray obfuscators for all function families. 3 There does not exist a worst-case virtual black box obfuscator even for evasive circuits, nor is there an average-case virtual gray box obfuscator for evasive Turing machine families. 4 Let be an evasive circuit family consisting of functions that test if a low-degree polynomial (represented by an efficient arithmetic circuit) evaluates to zero modulo some large prime p. Then under a natural analog of the discrete logarithm assumption in a group supporting multilinear maps, there exists an input-hiding obfuscator for. Under a new perfectly-hiding multilinear encoding assumption, there is an average-case virtual black box obfuscator for the family.

Original languageEnglish
Title of host publicationTheory of Cryptography - 11th Theory of Cryptography Conference, TCC 2014, Proceedings
PublisherSpringer Verlag
Pages26-51
Number of pages26
ISBN (Print)9783642542411
DOIs
StatePublished - 2014
Event11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014 - San Diego, CA, United States
Duration: 24 Feb 201426 Feb 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8349 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference11th Theory of Cryptography Conference on Theory of Cryptography, TCC 2014
Country/TerritoryUnited States
CitySan Diego, CA
Period24/02/1426/02/14

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