research-article

Efficient Card-Based Majority Voting Protocols

Authors:

Kazuo OhtaAuthors Info & Claims

New Generation Computing, Volume 40, Issue 1

Pages 173 - 198

https://doi.org/10.1007/s00354-022-00161-7

Published: 01 April 2022 Publication History

Abstract

Card-based cryptography is a variety of secure multiparty computation (MPC). Recently, a new technique called private operations was introduced because the protocol can be implemented with fewer cards than that by using the conventional technique called the shuffle. For example, Nakai et al. showed that if the private operations are available, secure computations of AND and OR operations for two inputs can be realized simultaneously by using four cards, and the protocol is applied to a four-card majority voting protocol with three inputs. This paper shows that only three cards are sufficient to construct a majority voting protocol with three inputs. Specifically, we propose two constructions of three-input majority voting protocols. One is a protocol assuming that players can announce their output, and the other is not allowed. Compared to Nakai et al.’s protocol, the protocol with the announcement is realized without any additional private operations and communications. On the other hand, the second construction requires two more private operations and communications because it removes the assumption on the announcement from the first construction. More importantly, the idea of the second protocol can be extended to an n-input majority voting protocol with n cards, which is the main result of this paper.

References

[1]

den Boer, B.: More efficient match-making and satisfiability: the five card trick. In: J. Quisquater, J. Vandewalle (eds.) Proceedings, Lecture Notes in Computer Science, Advances in Cryptology-EUROCRYPT ’89, Workshop on the Theory and Application of of Cryptographic Techniques, Houthalen, Belgium, April 10–13, vol. 434, pp. 208–217. Springer (1989).

Crossref

Google Scholar

[2]

Koch, A., Walzer, S., Härtel, K.: Card-based cryptographic protocols using a minimal number of cards. In: T. Iwata, J.H. Cheon (eds.) Proceedings, Part I. Lecture Notes in Computer Science, Advances in Cryptology-ASIACRYPT 2015–21st International Conference on the Theory and Application of Cryptology and Information Security, Auckland, New Zealand, November 29–December 3, 2015, vol. 9452, pp. 783–807. Springer (2015).

Crossref

Google Scholar

[3]

Manabe, Y., Ono, H.: Secure card-based cryptographic protocols using private operations against malicious players. In: D. Maimut, A. Oprina, D. Sauveron (eds.) Revised Selected Papers, Lecture Notes in Computer Science, Innovative Security Solutions for Information Technology and Communications-13th International Conference, SecITC 2020, Bucharest, Romania, November 19–20, 2020, vol. 12596, pp. 55–70. Springer (2020).

Crossref

Google Scholar

[4]

Marcedone, A., Wen, Z., Shi, E.: Secure dating with four or fewer cards. IACR Cryptol. ePrint Arch. 2015, 1031 (2015). http://eprint.iacr.org/2015/1031

Google Scholar

[5]

Mizuki, T., Asiedu, I.K., Sone, H.: Voting with a logarithmic number of cards. In: G. Mauri, A. Dennunzio, L. Manzoni, A.E. Porreca (eds.) Proceedings, Lecture Notes in Computer Science, Unconventional Computation and Natural Computation-12th International Conference, UCNC 2013, Milan, Italy, July 1–5, 2013. vol. 7956, pp. 162–173. Springer (2013).

Crossref

Google Scholar

[6]

Mizuki, T., Sone, H.: Six-card secure AND and four-card secure XOR. In: X. Deng, J.E. Hopcroft, J. Xue (eds.) Proceedings, Lecture Notes in Computer Science, Frontiers in Algorithmic, Third International Workshop, FAW 2009, Hefei, China, June 20–23, 2009, vol. 5598, pp. 358–369. Springer (2009).

Crossref

Google Scholar

[7]

Nakai, T., Shirouchi, S., Iwamoto, M., Ohta, K.: Four cards are sufficient for a card-based three-input voting protocol utilizing private permutations. In: J. Shikata (ed.) Proceedings, Lecture Notes in Computer Science, Information Theoretic Security-10th International Conference, ICITS 2017, Hong Kong, China, November 29–December 2, 2017, vol. 10681, pp. 153–165. Springer (2017).

Crossref

Google Scholar

[8]

Nakai, T., Tokushige, Y., Misawa, Y., Iwamoto, M., Ohta, K.: Efficient card-based cryptographic protocols for millionaires’ problem utilizing private permutations. In: S. Foresti, G. Persiano (eds.) Proceedings, Lecture Notes in Computer Science, Cryptology and Network Security-15th International Conference, CANS 2016, Milan, Italy, November 14–16, 2016, vol. 10052, pp. 500–517 (2016).

Crossref

Google Scholar

[9]

Nishida, T., Mizuki, T., Sone, H.: Securely computing the three-input majority function with eight cards. In: A. Dediu, C. Martín-Vide, B. Truthe, M.A. Vega-Rodríguez (eds.) Proceedings, Lecture Notes in Computer Science, Theory and Practice of Natural Computing-Second International Conference, TPNC 2013, Cáceres, Spain, December 3–5, 2013, vol. 8273, pp. 193–204. Springer (2013).

Crossref

Google Scholar

[10]

Ono H and Manabe Y Card-based cryptographic logical computations using private operations New Gener. Comput. 2021 39 1 19-40

Crossref

Google Scholar

[11]

Watanabe, Y., Kuroki, Y., Suzuki, S., Koga, Y., Iwamoto, M., Ohta, K.: Card-based majority voting protocols with three inputs using three cards. In: International Symposium on Information Theory and Its Applications, ISITA 2018, Singapore, October 28–31, 2018, pp. 218–222. IEEE (2018).

Crossref

Google Scholar

[12]

Yao, A.C.: Protocols for secure computations (extended abstract). In: 23rd Annual Symposium on Foundations of Computer Science, Chicago, Illinois, USA, 3–5 November 1982, pp. 160–164. IEEE Computer Society (1982).

Crossref

Google Scholar

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Index Terms

Efficient Card-Based Majority Voting Protocols
1. Security and privacy
  1. Cryptography
2. Theory of computation
  1. Computational complexity and cryptography

Index terms have been assigned to the content through auto-classification.

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New Generation Computing Volume 40, Issue 1

Apr 2022

388 pages

ISSN:0288-3635

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Ohmsha

Japan

Publication History

Published: 01 April 2022

Accepted: 08 February 2022

Received: 03 September 2021

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Tamura YSuzuki AMizuki T(2024)Card-Based Zero-Knowledge Proof Protocols for the 15-Puzzle and the Token Swapping ProblemProceedings of the 11th ACM Asia Public-Key Cryptography Workshop10.1145/3659467.3659905(11-22)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1145/3659467.3659905
Takahashi YShinagawa KShikata HMizuki T(2024)Efficient Card-Based Protocols for Symmetric Functions Using Four-Colored DecksProceedings of the 11th ACM Asia Public-Key Cryptography Workshop10.1145/3659467.3659902(1-10)Online publication date: 1-Jul-2024
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