Abstract
A secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret, but any non-qualified subset has absolutely no information on the secret.
In this paper we consider the problem of designing efficient secret sharing schemes having the additional feature that qualified minorities can forbid any other set of participants from reconstructing the secret key. This problem was first considered by Beutelspacher [2] who gave an algorithm, based on protective geometries, to construct threshold schemes in which qualified minorities have this “veto” capability. We show that well known tools from Error Correcting Coding Theory allow to modify the classical Shamir secret sharing algorithm [22] to handle this more general problem.
Partially supported by Italian Ministry of University and Research (M.U.R.S.T.) and by National Council for Research (C.N.R.) under grant 91.02326.CT12.
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Blundo, C., De Santis, A., Gargano, L., Vaccaro, U. (1994). Secret sharing schemes with veto capabilities. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_11
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