From cryptomania to obfustopia through secret-key functional encryption

Nir Bitansky, Ryo Nishimaki, Alain Passelègue, Daniel Wichs

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

Abstract

Functional encryption lies at the frontiers of current research in cryptography; some variants have been shown sufficiently powerful to yield indistinguishability obfuscation (IO) while other variants have been constructed from standard assumptions such as LWE. Indeed, most variants have been classified as belonging to either the former or the latter category. However, one mystery that has remained is the case of secretkey functional encryption with an unbounded number of keys and ciphertexts. On the one hand, this primitive is not known to imply anything outside of minicrypt, the land of secret-key crypto, but on the other hand, we do no know how to construct it without the heavy hammers in obfustopia. In this work, we show that (subexponentially secure) secret-key functional encryption is powerful enough to construct indistinguishability obfuscation if we additionally assume the existence of (subexponentially secure) plain public-key encryption. In other words, secret-key functional encryption provides a bridge from cryptomania to obfustopia. On the technical side, our result relies on two main components. As our first contribution, we show how to use secret key functional encryption to get “exponentially-efficient indistinguishability obfuscation” (XIO), a notion recently introduced by Lin et al. (PKC ’16) as a relaxation of IO. Lin et al. show how to use XIO and the LWE assumption to build IO. As our second contribution, we improve on this result by replacing its reliance on the LWE assumption with any plain publickey encryption scheme. Lastly, we ask whether secret-key functional encryption can be used to construct public-key encryption itself and therefore take us all the way from minicrypt to obfustopia. A result of Asharov and Segev (FOCS '15) shows that this is not the case under black-box constructions, even for exponentially secure functional encryption. We show, through a non-black box construction, that subexponentially secure-key functional encryption indeed leads to public-key encryption. The resulting publickey encryption scheme, however, is at most quasi-polynomially secure, which is insufficient to take us to obfustopia.

Original languageEnglish
Title of host publicationTheory of Cryptography - 14th International Conference, TCC 2016-B, Proceedings
EditorsAdam Smith, Martin Hirt
PublisherSpringer Verlag
Pages391-418
Number of pages28
ISBN (Print)9783662536438
DOIs
StatePublished - 2016
Externally publishedYes
Event14th International Conference on Theory of Cryptography, TCC 2016-B - Beijing, China
Duration: 31 Oct 20163 Nov 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9986 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Conference on Theory of Cryptography, TCC 2016-B
Country/TerritoryChina
CityBeijing
Period31/10/163/11/16

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