Optimal complexity of secret sharing schemes with four minimal qualified subsets |
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Authors: | Jaume Martí-Farré Carles Padró Leonor Vázquez |
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Institution: | 1.Technical University of Catalonia,Barcelona,Spain;2.Nanyang Technological University,Singapore,Singapore;3.Instituto Politécnico Nacional, ESCOM - IPN,México D. F.,Mexico |
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Abstract: | The complexity of a secret sharing scheme is defined as the ratio between the maximum length of the shares and the length
of the secret. This paper deals with the open problem of optimizing this parameter for secret sharing schemes with general
access structures. Specifically, our objective is to determine the optimal complexity of the access structures with exactly
four minimal qualified subsets. Lower bounds on the optimal complexity are obtained by using the known polymatroid technique
in combination with linear programming. Upper bounds are derived from decomposition constructions of linear secret sharing
schemes. In this way, the exact value of the optimal complexity is determined for several access structures in that family.
For the other ones, we present the best known lower and upper bounds. |
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Keywords: | |
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