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Secure Grouping Protocol Using a Deck of Cards
Yuji HASHIMOTO Kazumasa SHINAGAWA Koji NUIDA Masaki INAMURA Goichiro HANAOKA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E101A
No.9
pp.15121524 Publication Date: 2018/09/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E101.A.1512
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications) Category: Keyword: cardbased protocol, permutation,
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Summary:
We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about how the remaining parties are divided (except for certain public predetermined constraints, such as the number of parties in each group). In this paper, we construct an informationtheoretically secure protocol using a deck of physical cards to solve the problem, which is jointly executable by the parties themselves without a trusted third party. Despite the nontriviality and the potential usefulness of the secure grouping, our proposed protocol is fairly simple to describe and execute. Our protocol is based on algebraic properties of conjugate permutations. A key ingredient of our protocol is our new techniques to apply multiplication and inverse operations to hidden permutations (i.e., those encoded by using facedown cards), which would be of independent interest and would have various potential applications.

