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A Linear Construction of Secret Sharing Schemes

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Abstract

In this paper, we will generalize the vector space construction due to Brickell. This generalization, introduced by Bertilsson, leads to 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, and a matrix characterization of the generalized construction is presented. It turns out that the approach of minimal codewords by Massey 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 secret sharing scheme with this information rate.

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Marten van Dijk

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  1. Marten van Dijk
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Dijk, M.v. A Linear Construction of Secret Sharing Schemes. Designs, Codes and Cryptography 12, 161–201 (1997). https://doi.org/10.1023/A:1008259214236

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