Secret sharing via noisy broadcast channels

Lifeng Lai, Yingbin Liang, Wenliang Du, Shlomo Shamai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

We consider the secret sharing problem, in which a dealer distributes a secret among a set of participants in such a manner that only qualified sets of users can recover the secret by pooling their shares together while non-qualified sets of users will obtain no information about the secret even if they pool their shares together. In contrast to the existing solutions that are mainly based on number theoretic tools, we propose a physical layer approach that exploits the presence of random noise inherent to wireless channels for secret sharing. Two different scenarios are considered. In the first scenario, the classic secret sharing problem with a single secret message is considered, in which qualified sets are specified by a general access structure. A secret sharing scheme is proposed by constructing a secure coding scheme for an equivalent compound wiretap channel. Based on this approach, both lower and upper bounds on the secret sharing capacity are obtained. For some special cases, the secret sharing capacity is fully characterized. In the second scenario, a generalization of the classic secret sharing problem is proposed, in which multiple secret messages are required to be recovered at different qualified sets. A secret sharing scheme is provided by constructing an equivalent broadcast channel with compound eavesdroppers and constructing a secure coding scheme for the equivalent channel.

Original languageEnglish (US)
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages1955-1959
Number of pages5
DOIs
StatePublished - Oct 26 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: Jul 31 2011Aug 5 2011

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8104

Other

Other2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
CountryRussian Federation
CitySt. Petersburg
Period7/31/118/5/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

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  • Cite this

    Lai, L., Liang, Y., Du, W., & Shamai, S. (2011). Secret sharing via noisy broadcast channels. In 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 (pp. 1955-1959). [6033894] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2011.6033894