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Keywords:
secret sharing; cryptography; access structures; matroids; complementary spaces; linear rank inequalities; entropy
secret sharing; cryptography; access structures; matroids; complementary spaces; linear rank inequalities; entropy
Summary:
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.
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