On Increasing the Number of Users in (t, n) Threshold Secret Sharing Schemes

Todorka ALEXANDROVA  Hiroyoshi MORITA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.8   pp.2138-2150
Publication Date: 2008/08/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.8.2138
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Cryptography and Information Security
threshold secret sharing systems,  recursive construction algorithm,  bounds on number of users,  information rate,  

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Constructing ideal (t,n) threshold secret sharing schemes leads to some limitations on the maximum number of users, that are able to join the secret sharing scheme. We aim to remove these limitations by reducing the information rate of the constructed threshold secret sharing schemes. In this paper we propose recursive construction algorithms of (t,n) threshold secret sharing schemes, based on the generalized vector space construction. Using these algorithms we are able to construct a (t,n) threshold secret sharing scheme for any arbitrary n.