Abstract
The article considers interdependencies between secrets in a multiparty system. Each secret is assumed to be known only to a certain fixed set of parties. These sets can be viewed as edges of a hypergraph whose vertices are the parties of the system. The properties of interdependencies are expressed through a multi-argument relation called independence, which is a generalization of a binary relation also known as nondeducibility. The main result is a complete and decidable logical system that describes interdependencies that may exist on a fixed hypergraph. Additionally, the axioms and inference rules in this system are shown to be independent in the standard logical sense.
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Miner More, S., Naumov, P. Hypergraphs of multiparty secrets. Ann Math Artif Intell 62, 79–101 (2011). https://doi.org/10.1007/s10472-011-9252-z
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DOI: https://doi.org/10.1007/s10472-011-9252-z