Secret-sharing for NP

Ilan Komargodski*, Moni Naor, Eylon Yogev

*Corresponding author for this work

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

18 Scopus citations

Abstract

A computational secret-sharing scheme is a method that enables a dealer, that has a secret, to distribute this secret among a set of parties such that a “qualified” subset of parties can efficiently reconstruct the secret while any “unqualified” subset of parties cannot efficiently learn anything about the secret. The collection of “qualified” subsets is defined by a monotone Boolean function.It has been a major open problem to understand which (monotone) functions can be realized by a computational secret-sharing scheme. Yao suggested a method for secret-sharing for any function that has a polynomial-size monotone circuit (a class which is strictly smaller than the class of monotone functions in P). Around 1990 Rudich raised the possibility of obtaining secret-sharing for all monotone functions in NP: In order to reconstruct the secret a set of parties must be “qualified” and provide a witness attesting to this fact.Recently, Garg et al. [14] put forward the concept of witness encryption, where the goal is to encrypt a message relative to a statement x ∈ L for a language L ∈ NP such that anyone holding a witness to the statement can decrypt the message, however, if x ∉ L, then it is computationally hard to decrypt. Garg et al. showed how to construct several cryptographic primitives from witness encryption and gave a candidate construction.One can show that computational secret-sharing implies witness encryption for the same language. Our main result is the converse: we give a construction of a computational secret-sharing scheme for any monotone function in NP assuming witness encryption for NP and one-way functions. As a consequence we get a completeness theorem for secret- sharing: computational secret-sharing scheme for any single monotone NP-complete function implies a computational secret-sharing scheme for every monotone function in NP.

Original languageAmerican English
Title of host publicationAdvances in Cryptology - ASIACRYPT 2014 - 20th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings, Part II
EditorsPalash Sarkar, Tetsu Iwata
PublisherSpringer Verlag
Pages254-273
Number of pages20
ISBN (Electronic)9783662456071
DOIs
StatePublished - 2014
Externally publishedYes
Event20th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2014 - Kaoshiung, Taiwan, Province of China
Duration: 7 Dec 201411 Dec 2014

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8874
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2014
Country/TerritoryTaiwan, Province of China
CityKaoshiung
Period7/12/1411/12/14

Bibliographical note

Publisher Copyright:
© International Association for Cryptologic Research 2014.

Fingerprint

Dive into the research topics of 'Secret-sharing for NP'. Together they form a unique fingerprint.

Cite this