Release time:2025-03-31

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DOI number:10.1007/s12095-013-0092-z

Journal:Cryptography and Communications-Discrete-Structures Boolean Functions and Sequences

Key Words:Secret sharing;Linear code;Matroid;Graph

Abstract:We study the access structure and multiplicativity of linear secret sharing schemes based on codes from complete graphs. First, we describe the access structure of the schemes based on cut-set and cycle codes. Second, we show that the class of access structures based on odd cycles cannot be realized by ideal multiplicative linear secret sharing schemes over any finite field. This can be seen as a contribution to the characterization of access structures of ideal multiplicative schemes. The access structure based on odd cycles corresponds to the scheme based on the dual of the extended cycle code. Finally, we show that we can obtain ideal multiplicative linear secret sharing scheme based on the dual of an augmented extended cycle code.

Co-author:Romar dela Cruz

First Author:Ying Gao

Indexed by:Journal paper

Correspondence Author:Ying Gao

Volume:6

Issue:2

Page Number:137-155

ISSN No.:1936-2447

Translation or Not:no

Date of Publication:2013-10-19