Two matrices for Blakley's secret sharing scheme

Xiali Hei, Xiaojiang Du, Binheng Song

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

7 Scopus citations

Abstract

The secret sharing scheme was invented by Adi Shamir and George Blakley independently in 1979. In a (k, n)-threshold linear secret sharing scheme, any k-out-of-n participants could recover the shared secret, and any less than k participants could not recover the secret. Shamir's secret sharing scheme is more popular than Blakley's even though the former is more complex than the latter. The reason is that Blakley's scheme lacks determined, general and suitable matrices. In this paper, we present two matrices that can be used for Blakley's secret sharing system. Compared with the Vandermonde matrix used by Shamir's scheme, the elements in these matrices increase slowly. Furthermore, we formulate the optimal matrix problem and find the lower bound of the minimal maximized element for k=2 and upper bound of the minimal maximized element of matrix for given k.

Original languageEnglish
Title of host publication2012 IEEE International Conference on Communications, ICC 2012
Pages810-814
Number of pages5
DOIs
StatePublished - 2012
Event2012 IEEE International Conference on Communications, ICC 2012 - Ottawa, ON, Canada
Duration: 10 Jun 201215 Jun 2012

Publication series

NameIEEE International Conference on Communications
ISSN (Print)1550-3607

Conference

Conference2012 IEEE International Conference on Communications, ICC 2012
Country/TerritoryCanada
CityOttawa, ON
Period10/06/1215/06/12

Keywords

  • Pascal matrix
  • linear secret sharing
  • linear threshold cryptography

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