Secure Grouping Protocol Using a Deck of Cards

TL;DR

This paper introduces a simple, information-theoretically secure protocol using physical cards for dividing parties into groups without revealing unnecessary information, based on algebraic properties of permutations.

Contribution

It presents a novel, practical protocol for secure grouping using physical cards, with new techniques for manipulating hidden permutations.

Findings

Protocol is secure against information leakage.

Uses algebraic properties of permutations for security.

Applicable to various secure multi-party scenarios.

Abstract

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 information-theoretically 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 non-triviality 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 face-down cards), which would be of independent interest and would have various potential applications.