Zero knowledge LTCs and their applications

Yuval Ishai, Amit Sahai, Michael Viderman, Mor Weiss

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

5 Scopus citations

Abstract

Locally testable codes (LTCs) are error-correcting codes for which membership in the code can be tested by probing few symbols of a purported codeword. Motivated by applications in cryptography, we initiate the study of zero knowledge locally testable codes (ZK-LTCs). ZK-LTCs are LTCs which admit a randomized encoding function, such that even a malicious tester which reads a large number of codeword symbols learns essentially nothing about the encoded message. We obtain ZK-LTCs with good parameters by applying general transformations to standard LTCs. We also obtain LTCs and ZK-LTCs which are stable in the sense that they limit the influence of adaptively corrupted symbols on the output of the testing procedure. Finally, we apply stable ZK-LTCs for obtaining protocols for verifiable secret sharing (VSS) in which the communication complexity required for verifying a shared secret is sublinear in the secrecy threshold. We also obtain the first statistically secure VSS protocols and distributed coin-flipping protocols which use n servers, tolerate a constant fraction of corrupted servers, and have error that vanishes almost exponentially with n using only O(n) bits of communication. These improve over previous VSS and coin-flipping protocols from the literature, which require nearly quadratic communication to achieve similar guarantees.

Original languageEnglish
Title of host publicationApproximation, Randomization, and Combinatorial Optimization
Subtitle of host publicationAlgorithms and Techniques - 16th International Workshop, APPROX 2013 and 17th International Workshop, RANDOM 2013, Proceedings
Pages607-622
Number of pages16
DOIs
StatePublished - 2013
Externally publishedYes
Event16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013 and the 17th International Workshop on Randomization and Computation, RANDOM 2013 - Berkeley, CA, United States
Duration: 21 Aug 201323 Aug 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8096 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013 and the 17th International Workshop on Randomization and Computation, RANDOM 2013
Country/TerritoryUnited States
CityBerkeley, CA
Period21/08/1323/08/13

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