On removing graded encodings from functional encryption

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

Abstract

Functional encryption (FE) has emerged as an outstanding concept. By now, we know that beyond the immediate application to computation over encrypted data, variants with succinct ciphertexts are so powerful that they yield the full might of indistinguishability obfuscation (IO). Understanding how, and under which assumptions, such succinct schemes can be constructed has become a grand challenge of current research in cryptography. Whereas the first schemes were based themselves on IO, recent progress has produced constructions based on constant-degree graded encodings. Still, our comprehension of such graded encodings remains limited, as the instantiations given so far have exhibited different vulnerabilities. Our main result is that, assuming LWE, black-box constructions of sufficiently succinct FE schemes from constant-degree graded encodings can be transformed to rely on a much better-understood object — bilinear groups. In particular, under an über assumption on bilinear groups, such constructions imply IO in the plain model. The result demonstrates that the exact level of ciphertext succinctness of FE schemes is of major importance. In particular, we draw a fine line between known FE constructions from constant-degree graded encodings, which just fall short of the required succinctness, and the holy grail of basing IO on better understood assumptions. In the heart of our result, are new techniques for removing ideal graded encoding oracles from FE constructions. Complementing the result, for weaker ideal models, namely the generic group model and the random oracle model, we show a transformation from collusion-resistant FE in either of the two models directly to FE (and IO) in the plain model, without assuming bilinear groups.

Original languageEnglish
Title of host publicationAdvances in Cryptology – EUROCRYPT 2017 - 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
EditorsJean-Sebastien Coron, Jesper Buus Nielsen
PublisherSpringer Verlag
Pages3-29
Number of pages27
ISBN (Print)9783319566139
DOIs
StatePublished - 2017
Externally publishedYes
Event36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2017 - Paris, France
Duration: 30 Apr 20174 May 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10211 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2017
Country/TerritoryFrance
City Paris
Period30/04/174/05/17

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