Geodesic
Access structures for finding characteristic-dependent linear rank inequalities
Kybernetika, Tome 59 (2023) no. 2, pp. 198-208.

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Determining information ratios of access structures is an important problem in secret sharing. Information inequalities and linear rank inequalities play an important role for proving bounds on these ratios. Characteristic-dependent linear rank inequalities are rank inequalities which are true over vector spaces with specific field characteristic. In this paper, using ideas of secret sharing, we show a theorem that produces characteristic-dependent linear rank inequalities. These inequalities are then used for getting lower bounds on information ratios of some access structures in linear secret sharing.
DOI : 10.14736/kyb-2023-2-0198
Classification : 68P30, 94A15
Keywords: secret sharing; cryptography; access structures; matroids; complementary spaces; linear rank inequalities; entropy 
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Peña-Macias, Victor. Access structures for finding characteristic-dependent linear rank inequalities. Kybernetika, Tome 59 (2023) no. 2, pp. 198-208. doi : 10.14736/kyb-2023-2-0198. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2023-2-0198/

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