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dc.contributor.advisorVinod Vaikuntanathan.en_US
dc.contributor.authorLiu, Tianren,Ph. D.Massachusetts Institute of Technology.en_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.date.accessioned2020-03-09T18:58:37Z
dc.date.available2020-03-09T18:58:37Z
dc.date.copyright2019en_US
dc.date.issued2019en_US
dc.identifier.urihttps://hdl.handle.net/1721.1/124114
dc.descriptionThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.en_US
dc.descriptionThesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019en_US
dc.descriptionCataloged from student-submitted PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 50-53).en_US
dc.description.abstractIn this thesis, we study secret sharing schemes for general (non-threshold) access functions. In a secret sharing scheme for n parties associated to a monotone function [mathematical formula], a dealer distributes shares of a secret among n parties. Any subset of parties [mathematical formula] can jointly reconstruct the secret if F(T) = 1, and should have no information about the secret if F(T) = 0. One of the major long-standing questions in information-theoretic cryptography is to determine the minimum size of the shares in a secret-sharing scheme for an access function F. There is an exponential gap between lower and upper bounds for share size: the best known scheme for general monotone functions has shares of size 2[superscript n-o(n)], while the best lower bound is n² / log(n). In this thesis, we improve this more-than-30-year-old upper bound by construct- ing a secret sharing scheme for any access function with shares of size 2[superscript 0.994n] and a linear secret sharing scheme for any access function with shares of size 2[superscript 0.994n]. As a contribution of independent interest, we also construct a secret sharing scheme with shares of size [mathematical formula] for a family of [mathematical formula] monotone access functions, out of a total of [mathematical formula] of them. As an intermediate result, we construct the first conditional disclosure of secrets (CDS) with sub-exponential communication complexity. CDS is a variant of secret sharing, in which a group of parties want to disclose a secret to a referee the parties' respective inputs satisfy some predicate. The key conceptual contribution of this thesis is a novel connection between secret sharing and CDS, and the notion of (2-server, information-theoretic) private information retrieval.en_US
dc.description.statementofresponsibilityby Tianren Liu.en_US
dc.format.extent53 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsMIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectElectrical Engineering and Computer Science.en_US
dc.titleBreaking barriers in secret sharingen_US
dc.typeThesisen_US
dc.description.degreePh. D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.identifier.oclc1142177906en_US
dc.description.collectionPh.D. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Scienceen_US
dspace.imported2020-03-09T18:58:36Zen_US
mit.thesis.degreeDoctoralen_US
mit.thesis.departmentEECSen_US


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