A linear construction of perfect secret sharing schemes

M. Dijk, van

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

20 Citations (Scopus)


In this paper, we generalize the vector space construction due to Brickell [5]. This generalization, introduced by Bertilsson [1], leads to perfect secret sharing schemes with rational information rates in which the secret can be computed efficiently by each qualified group. A one to one correspondence between the generalized construction and linear block codes is stated. It turns out that the approach of minimal codewords by Massey [15] is a special case of this construction. For general access structures we present an outline of an algorithm for determining whether a rational number can be realized as information rate by means of the generalized vector space construction. If so, the algorithm produces a perfect secret sharing scheme with this information rate. As a side-result we show a correspondence between the duality of access structures and the duality of codes.
Original languageEnglish
Title of host publicationAdvances in Cryptology - EUROCRYPT'94 (Proceedings Workshop on the Theory and Application of Cryptographic Techniques, Perugia, Italy, May 9-12, 1994)
EditorsA. Santis, De
Place of PublicationBerlin
ISBN (Print)3-540-60176-7
Publication statusPublished - 1995

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743


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