A study of efficient secret sharing

We show a general connection between various types of statistical zero-knowledge (SZK) proof systems and (unconditionally secure) secret sharing schemes. Viewed through the SZK lens, we obtain several new results on secret-sharing: " Characterizations: We obtain an almost-characterization of access structures for which there are secret-sharing schemes with an efficient sharing algorithm (but not necessarily efficient reconstruction). In particular, we show that for every language L [set membership] SZKL (the class of languages that have statistical zero knowledge proofs with log-space verifiers and simulators), a (monotonized) access structure associated with L has such a secret-sharing scheme. Conversely, we show that such secret-sharing schemes can only exist for languages in SZK. " Constructions: We show new constructions of secret-sharing schemes with efficient sharing and reconstruction for access structures that are in P, but are not known to be in NC, namely Bounded-Degree Graph Isomorphism and constant-dimensional lattice problems. In particular, this gives us the first combinatorial access structure that is conjectured to be outside NC but has an efficient secret-sharing scheme. Previous such constructions (Beimel and Ishai; CCC 2001) were algebraic and number-theoretic in nature. " Limitations: We show that universally-efficient secret-sharing schemes, where the complexity of computing the shares is a polynomial independent of the complexity of deciding the access structure, cannot exist for all (monotone languages in) P, unless there is a polynomial q such that P [subset] DSPACE(q(n)).

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Vasudevan, Prashant Nalini

Advisor dc:contributor.advisor

• Vinod Vaikuntanathan.

• Electrical Engineering and Computer Science.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/101590

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/101590