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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.9 pp.1512-1524

- Publication Date
- 2018/09/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E101.A.1512

- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

- Category

Yuji HASHIMOTO

Tokyo Denki University,the National Institute of Advanced Industrial Science and Technology

Kazumasa SHINAGAWA

the National Institute of Advanced Industrial Science and Technology,Tokyo Institute of Technology

Koji NUIDA

the National Institute of Advanced Industrial Science and Technology

Masaki INAMURA

Tokyo Denki University

Goichiro HANAOKA

the National Institute of Advanced Industrial Science and Technology

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Yuji HASHIMOTO, Kazumasa SHINAGAWA, Koji NUIDA, Masaki INAMURA, Goichiro HANAOKA, "Secure Grouping Protocol Using a Deck of Cards" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 9, pp. 1512-1524, September 2018, doi: 10.1587/transfun.E101.A.1512.

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.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1512/_p

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@ARTICLE{e101-a_9_1512,

author={Yuji HASHIMOTO, Kazumasa SHINAGAWA, Koji NUIDA, Masaki INAMURA, Goichiro HANAOKA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Secure Grouping Protocol Using a Deck of Cards},

year={2018},

volume={E101-A},

number={9},

pages={1512-1524},

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.},

keywords={},

doi={10.1587/transfun.E101.A.1512},

ISSN={1745-1337},

month={September},}

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TY - JOUR

TI - Secure Grouping Protocol Using a Deck of Cards

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1512

EP - 1524

AU - Yuji HASHIMOTO

AU - Kazumasa SHINAGAWA

AU - Koji NUIDA

AU - Masaki INAMURA

AU - Goichiro HANAOKA

PY - 2018

DO - 10.1587/transfun.E101.A.1512

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E101-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2018

AB - 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.

ER -