Abstract
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.
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Keywords
- Access Structure
- Information Rate
- Secret Sharing Scheme
- Parity Check Matrix
- Information Theoretic Approach
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© 1995 Springer-Verlag Berlin Heidelberg
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van Dijk, M. (1995). A linear construction of perfect secret sharing schemes. In: De Santis, A. (eds) Advances in Cryptology — EUROCRYPT'94. EUROCRYPT 1994. Lecture Notes in Computer Science, vol 950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053421
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DOI: https://doi.org/10.1007/BFb0053421
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