On constructing one-way permutations from indistinguishability obfuscation

Gilad Asharov*, Gil Segev

*Corresponding author for this work

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

14 Scopus citations

Abstract

We prove that there is no black-box construction of a oneway permutation family from a one-way function and an indistinguishability obfuscator for the class of all oracle-aided circuits, where the construction is “domain invariant” (i.e., where each permutation may have its own domain, but these domains are independent of the underlying building blocks). Following the framework of Asharov and Segev (FOCS’15), by considering indistinguishability obfuscation for oracle-aided circuits we capture the common techniques that have been used so far in constructions based on indistinguishability obfuscation. These include, in particular, non-black-box techniques such as the punctured programming approach of Sahai and Waters (STOC’14) and its variants, as well as sub-exponential security assumptions. For example, we fully capture the construction of a trapdoor permutation family from a one-way function and an indistinguishability obfuscator due to Bitansky, Paneth and Wichs (TCC’16). Their construction is not domain invariant and our result shows that this, somewhat undesirable property, is unavoidable using the common techniques. In fact, we observe that constructions which are not domain invariant circumvent all known negative results for constructing one-way permutations based on one-way functions, starting with Rudich’s seminal work (PhD thesis’88). We revisit this classic and fundamental problem, and resolve this somewhat surprising gap by ruling out all such black-box constructions – even those that are not domain invariant.

Original languageAmerican English
Title of host publicationTheory of Cryptography - 3th International Conference, TCC 2016-A, Proceedings
EditorsEyal Kushilevitz, Tal Malkin
PublisherSpringer Verlag
Pages512-541
Number of pages30
ISBN (Print)9783662490983
DOIs
StatePublished - 2016
Event13th International Conference on Theory of Cryptography, TCC 2016 - Tel Aviv, Israel
Duration: 10 Jan 201613 Jan 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9563
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference on Theory of Cryptography, TCC 2016
Country/TerritoryIsrael
CityTel Aviv
Period10/01/1613/01/16

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2016.

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