Hypergraphs of multiparty secrets
Hypergraphs of multiparty secrets
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.
Hypergraph, Independence, Information flow, Nondeducibility
79-101
More, Sara Miner
979b2749-1732-4a36-abda-64b4f6899ea9
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0
2011
More, Sara Miner
979b2749-1732-4a36-abda-64b4f6899ea9
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0
More, Sara Miner and Naumov, Pavel
(2011)
Hypergraphs of multiparty secrets.
Annals of Mathematics and Artificial Intelligence, 62 (1-2), .
(doi:10.1007/s10472-011-9252-z).
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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e-pub ahead of print date: 13 July 2011
Published date: 2011
Keywords:
Hypergraph, Independence, Information flow, Nondeducibility
Identifiers
Local EPrints ID: 480220
URI: http://eprints.soton.ac.uk/id/eprint/480220
ISSN: 1012-2443
PURE UUID: 8aba055d-a62d-4378-bf87-447468c25f17
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Date deposited: 01 Aug 2023 17:08
Last modified: 17 Mar 2024 04:10
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Author:
Sara Miner More
Author:
Pavel Naumov
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