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.
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

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