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Ideal hierarchical secret sharing and lattice path matroids

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Abstract

By a fundamental result by Brickell and Davenport (J Cryptol 4:123–134, 1991), the access structures of ideal secret sharing schemes are matroid ports. Farràs and Padró (IEEE Trans Inf Theory 58(5):3273–3286, 2012) presented a characterization of ideal hierarchical access structures. In this paper, we provide a different characterization. Specifically, we show that an access structure is ideal and hierarchical if and only if it is a port of a lattice path matroid at some specific points.

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Notes

  1. Taking a cue from the concept of Isbel’s desirability relation [30] in game theory.

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Acknowledgements

This research is supported by a PhD scholarship from The University of Auckland. The author thanks Prof Arkadii Slinko for his advice and the reviewers for their useful suggestions.

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  1. Department of Mathematics, The University of Auckland, Auckland, New Zealand

    Songbao Mo

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Communicated by C. Padro.

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Mo, S. Ideal hierarchical secret sharing and lattice path matroids. Des. Codes Cryptogr. 91, 1335–1349 (2023). https://doi.org/10.1007/s10623-022-01154-9

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