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.
CITATION STYLE
Van Dijk, M. (1995). A linear construction of perfect secret sharing schemes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 950, pp. 23–34). Springer Verlag. https://doi.org/10.1007/bfb0053421
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