Secret Sharing, Rank Inequalities, and Information Inequalities
نویسندگان
چکیده
منابع مشابه
Linear Secret Sharing and the Automatic Search of Linear Rank Inequalities
We study the problem of computing linear rank inequalities, and the related problem of computing lower bounds on the linear share complexity of access structures. We prove that if one knows a generating set for the cone of linear rank inequalities on n + 1 variables, then he can use this generating set and linear programming (or semi-infinite programming) to compute the exact linear optimal inf...
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Though algebraic geometry over C is often used to describe the closure of the tensors of a given size and complex rank, this variety includes tensors of both smaller and larger rank. Here we focus on the n × n × n tensors of rank n over C, which has as a dense subset the orbit of a single tensor under a natural group action. We construct polynomial invariants under this group action whose non-v...
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Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the secret. Thus, secret sharing schemes are systems of variables in which it is very clearly specified which subsets have information about the secret. As such, the...
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A simple relaxation of two rows of a simplex tableau is a mixed integer set consisting of two equations with two free integer variables and non-negative continuous variables. Recently Andersen et al. [3] and Cornuéjols and Margot [17] showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. Throug...
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We construct non-linear information inequalities from Matúš’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they ...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2016
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2015.2500232