IEICE TRANSACTIONS on Fundamentals
Automorphism Shuffles for Graphs and Hypergraphs and Its Applications
Summary :
In card-based cryptography, a deck of physical cards is used to achieve secure computation. A shuffle, which randomly permutes a card-sequence along with some probability distribution, ensures the security of a card-based protocol. The authors proposed a new class of shuffles called graph shuffles, which randomly permutes a card-sequence by an automorphism of a directed graph (New Generation Computing 2022). For a directed graph G with n vertices and m edges, such a shuffle could be implemented with pile-scramble shuffles with 2(n + m) cards. In this paper, we study graph shuffles and give an implementation, an application, and a slight generalization. First, we propose a new protocol for graph shuffles with 2n + m cards. Second, as a new application of graph shuffles, we show that any cyclic group shuffle, which is a shuffle over a cyclic group, is a graph shuffle associated with some graph. Third, we define a hypergraph shuffle, which is a shuffle by an automorphism of a hypergraph, and show that any hypergraph shuffle can also be implemented with pile-scramble shuffles.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.3 pp.306-314
- Publication Date
- 2023/03/01
- Publicized
- 2022/09/12
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022CIP0020
- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)
- Category
Authors
Kazumasa SHINAGAWA
Ibaraki University,National Institute of Advanced Industrial Science and Technology (AIST)
Kengo MIYAMOTO
Ibaraki University
Keyword
Latest Issue
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Kazumasa SHINAGAWA, Kengo MIYAMOTO, "Automorphism Shuffles for Graphs and Hypergraphs and Its Applications" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 3, pp. 306-314, March 2023, doi: 10.1587/transfun.2022CIP0020.
Abstract: In card-based cryptography, a deck of physical cards is used to achieve secure computation. A shuffle, which randomly permutes a card-sequence along with some probability distribution, ensures the security of a card-based protocol. The authors proposed a new class of shuffles called graph shuffles, which randomly permutes a card-sequence by an automorphism of a directed graph (New Generation Computing 2022). For a directed graph G with n vertices and m edges, such a shuffle could be implemented with pile-scramble shuffles with 2(n + m) cards. In this paper, we study graph shuffles and give an implementation, an application, and a slight generalization. First, we propose a new protocol for graph shuffles with 2n + m cards. Second, as a new application of graph shuffles, we show that any cyclic group shuffle, which is a shuffle over a cyclic group, is a graph shuffle associated with some graph. Third, we define a hypergraph shuffle, which is a shuffle by an automorphism of a hypergraph, and show that any hypergraph shuffle can also be implemented with pile-scramble shuffles.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022CIP0020/_p
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@ARTICLE{e106-a_3_306,
author={Kazumasa SHINAGAWA, Kengo MIYAMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Automorphism Shuffles for Graphs and Hypergraphs and Its Applications},
year={2023},
volume={E106-A},
number={3},
pages={306-314},
abstract={In card-based cryptography, a deck of physical cards is used to achieve secure computation. A shuffle, which randomly permutes a card-sequence along with some probability distribution, ensures the security of a card-based protocol. The authors proposed a new class of shuffles called graph shuffles, which randomly permutes a card-sequence by an automorphism of a directed graph (New Generation Computing 2022). For a directed graph G with n vertices and m edges, such a shuffle could be implemented with pile-scramble shuffles with 2(n + m) cards. In this paper, we study graph shuffles and give an implementation, an application, and a slight generalization. First, we propose a new protocol for graph shuffles with 2n + m cards. Second, as a new application of graph shuffles, we show that any cyclic group shuffle, which is a shuffle over a cyclic group, is a graph shuffle associated with some graph. Third, we define a hypergraph shuffle, which is a shuffle by an automorphism of a hypergraph, and show that any hypergraph shuffle can also be implemented with pile-scramble shuffles.},
keywords={},
doi={10.1587/transfun.2022CIP0020},
ISSN={1745-1337},
month={March},}
Copy
TY - JOUR
TI - Automorphism Shuffles for Graphs and Hypergraphs and Its Applications
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 306
EP - 314
AU - Kazumasa SHINAGAWA
AU - Kengo MIYAMOTO
PY - 2023
DO - 10.1587/transfun.2022CIP0020
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2023
AB - In card-based cryptography, a deck of physical cards is used to achieve secure computation. A shuffle, which randomly permutes a card-sequence along with some probability distribution, ensures the security of a card-based protocol. The authors proposed a new class of shuffles called graph shuffles, which randomly permutes a card-sequence by an automorphism of a directed graph (New Generation Computing 2022). For a directed graph G with n vertices and m edges, such a shuffle could be implemented with pile-scramble shuffles with 2(n + m) cards. In this paper, we study graph shuffles and give an implementation, an application, and a slight generalization. First, we propose a new protocol for graph shuffles with 2n + m cards. Second, as a new application of graph shuffles, we show that any cyclic group shuffle, which is a shuffle over a cyclic group, is a graph shuffle associated with some graph. Third, we define a hypergraph shuffle, which is a shuffle by an automorphism of a hypergraph, and show that any hypergraph shuffle can also be implemented with pile-scramble shuffles.
ER -
English
