TY - GEN
T1 - Card-Based Zero-Knowledge Proof Protocols for Graph Problems and Their Computational Model
AU - Miyahara, Daiki
AU - Haneda, Hiromichi
AU - Mizuki, Takaaki
N1 - Funding Information:
We thank the anonymous referees, whose comments have helped us improve the presentation of the paper. We would like to thank Hideaki Sone for his cooperation in preparing a Japanese draft version at an earlier stage of this work. We would also like to thank Kazumasa Shinagawa for his idea improving a protocol for the 3-coloring problem. The second author is grateful to Haruka Mizuta for helpful discussions at the beginning of this work. This work was supported in part by JSPS KAKENHI Grant Numbers JP19J21153 and JP21K11881.
Funding Information:
Acknowledgements. We thank the anonymous referees, whose comments have helped us improve the presentation of the paper. We would like to thank Hideaki Sone for his cooperation in preparing a Japanese draft version at an earlier stage of this work. We would also like to thank Kazumasa Shinagawa for his idea improving a protocol for the 3-coloring problem. The second author is grateful to Haruka Mizuta for helpful discussions at the beginning of this work. This work was supported in part by JSPS KAKENHI Grant Numbers JP19J21153 and JP21K11881.
Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - Zero-Knowledge Proof (ZKP) is a cryptographic technique that enables a prover to convince a verifier that a given statement is true without revealing any information other than its truth. It is known that ZKP can be realized by physical objects such as a deck of cards; recently, many such “card-based” ZKP protocols for pencil puzzles (such as Sudoku and Numberlink) have been devised. In this paper, we shift our attention to graph theory problems from pencil puzzles: We propose card-based ZKP protocols for the graph 3-coloring problem and the graph isomorphism problem. Similar to most of the existing card-based ZKP protocols, our two protocols have no soundness error. The proposed protocols can be implemented without any technical knowledge, and the principle of zero-knowledge proof is easy to understand. In particular, our protocol for the graph isomorphism problem requires only three shuffles regardless of the sizes of a pair of given graphs. In addition, to deal with our proposed protocols more rigorously, we present a formal framework for card-based ZKP protocols which are non-interactive and have no soundness error.
AB - Zero-Knowledge Proof (ZKP) is a cryptographic technique that enables a prover to convince a verifier that a given statement is true without revealing any information other than its truth. It is known that ZKP can be realized by physical objects such as a deck of cards; recently, many such “card-based” ZKP protocols for pencil puzzles (such as Sudoku and Numberlink) have been devised. In this paper, we shift our attention to graph theory problems from pencil puzzles: We propose card-based ZKP protocols for the graph 3-coloring problem and the graph isomorphism problem. Similar to most of the existing card-based ZKP protocols, our two protocols have no soundness error. The proposed protocols can be implemented without any technical knowledge, and the principle of zero-knowledge proof is easy to understand. In particular, our protocol for the graph isomorphism problem requires only three shuffles regardless of the sizes of a pair of given graphs. In addition, to deal with our proposed protocols more rigorously, we present a formal framework for card-based ZKP protocols which are non-interactive and have no soundness error.
KW - Card-based cryptography
KW - Graph 3-coloring problem
KW - Graph isomorphism problem
KW - Physical zero-knowledge proof
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U2 - 10.1007/978-3-030-90402-9_8
DO - 10.1007/978-3-030-90402-9_8
M3 - Conference contribution
AN - SCOPUS:85119853845
SN - 9783030904012
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 136
EP - 152
BT - Provable and Practical Security - 15th International Conference, ProvSec 2021, Proceedings
A2 - Huang, Qiong
A2 - Yu, Yu
PB - Springer Science and Business Media Deutschland GmbH
T2 - 15th International Conference on Provable Security, ProvSec 2021
Y2 - 5 November 2021 through 8 November 2021
ER -