Function secret sharing

Elette Boyle, Niv Gilboa, Yuval Ishai

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

89 Scopus citations

Abstract

Motivated by the goal of securely searching and updating distributed data, we introduce and study the notion of function secret sharing (FSS). This new notion is a natural generalization of distributed point functions (DPF), a primitive that was recently introduced by Gilboa and Ishai (Eurocrypt 2014). Given a positive integer p ≥ 2 and a class F of functions f: {0, 1}n → (image found), where (image found) is an Abelian group, a p-party FSS scheme for F allows one to split each f ∈ F into p succinctly described functions fi: {0, 1}n →(image found), 1 ≤ i ≤ p, such that: (1) ∑p i=1 fi = f, and (2) any strict subset of the fi hides f. Thus, an FSS for F can be thought of as method for succinctly performing an “additive secret sharing” of functions from F. The original definition of DPF coincides with a twoparty FSS for the class of point functions, namely the class of functions that have a nonzero output on at most one input. We present two types of results. First, we obtain efficiency improvements and extensions of the original DPF construction. Then, we initiate a systematic study of general FSS, providing some constructions and establishing relations with other cryptographic primitives. More concretely, we obtain the following main results: – Improved DPF. We present an improved (two-party) DPF construction from a pseudorandom generator (PRG), reducing the length of the key describing each fi from O(λ ・ nlog2 3) to O(λn), where λ is the PRG seed length. – Multi-party DPF. We present the first nontrivial construction of a p-party DPF for p ≥ 3, obtaining a near-quadratic improvement over a naive construction that additively shares the truth-table of f. This constrcution too can be based on any PRG. – FSS for simple functions. We present efficient PRG-based FSS constructions for natural function classes that extend point functions, including interval functions and partial matching functions. – A study of general FSS. We show several relations between general FSS and other cryptographic primitives. These include a construction of general FSS via obfuscation, an indication for the implausibility of constructing general FSS from weak cryptographic assumptions such as the existence of one-way functions, a completeness result, and a relation with pseudorandom functions.

Original languageEnglish
Title of host publicationAdvances in Cryptology - 34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2015, Proceedings
EditorsMarc Fischlin, Elisabeth Oswald
PublisherSpringer Verlag
Pages337-367
Number of pages31
ISBN (Print)9783662468029
DOIs
StatePublished - 1 Jan 2015
Event34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2015 - Sofia, Bulgaria
Duration: 26 Apr 201530 Apr 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9057
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference34th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Eurocrypt 2015
Country/TerritoryBulgaria
CitySofia
Period26/04/1530/04/15

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