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Card-Based Covert Lottery

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Innovative Security Solutions for Information Technology and Communications (SecITC 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12596))

Abstract

Before starting to play a two-player board game such as Chess and Shogi (namely, Japanese chess), we have to determine who makes the first move. Players’ strategies of Chess and Shogi often rely on whether they will move first or not, and most players have their own preferences. Therefore, it would be nice if we can take their individual requests into account when determining who goes first. To this end, if the two players simply tell their preferable moves to each other, they will notice the other’s strategy. Thus, we want the players to determine the first move according to their requests while hiding any information about them. Note that this problem cannot be solved by a typical way done in Chess, namely, a coin-flipping. In this paper, we formalize this problem in a cryptographic perspective and propose a secure protocol that solves this problem using a deck of physical cards. Moreover, we extend this problem to the multi-player setting: Assume that there is a single prize in a lottery drawing among more than two players, each of who has an individual secret feeling ‘Yes’ or ‘No’ that indicates whether he/she really wants to get the prize or not. If one or more players have ‘Yes,’ we want to randomly and covertly choose a winner among those having ‘Yes.’ If all of them have ‘No,’ we want to randomly pick a winner among all the players. We solve this extended problem, which we call the “covert lottery” problem, by proposing a simple card-based protocol.

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Notes

  1. 1.

    If we make \(X_n\) be two free cards by a random bisection cut before Step 4, the number of cards can be reduced to \(3n+2\) while the number of shuffles becomes \(n+2\). If we apply the AND protocol based on the encode and  [17], we can have a \((3n+1)\)-card n-shuffle protocol or a 3n-card \((n+1)\)-shuffle protocol.

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Acknowledgements

We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper. We thank the anonymous reviewer at some conference who have inspired us to present the protocol shown in Sect. 3. This work was supported in part by JSPS KAKENHI Grant Numbers JP19J21153 and JP20J01192.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Sendai, Japan

    Yuto Shinoda & Daiki Miyahara

  2. The University of Electro-Communications, Tokyo, Japan

    Kazumasa Shinagawa

  3. Cyberscience Center, Tohoku University, Sendai, Japan

    Takaaki Mizuki & Hideaki Sone

  4. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Daiki Miyahara & Kazumasa Shinagawa

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  1. Yuto Shinoda
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Correspondence to Daiki Miyahara .

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Editors and Affiliations

  1. Advanced Technologies Institute, Bucharest, Romania

    Diana Maimut

  2. Advanced Technologies Institute, Bucharest, Romania

    Andrei-George Oprina

  3. Faculté des Sciences et Techniques, University of Limoges, Limoges, France

    Damien Sauveron

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Shinoda, Y., Miyahara, D., Shinagawa, K., Mizuki, T., Sone, H. (2021). Card-Based Covert Lottery. In: Maimut, D., Oprina, AG., Sauveron, D. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2020. Lecture Notes in Computer Science(), vol 12596. Springer, Cham. https://doi.org/10.1007/978-3-030-69255-1_17

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  • DOI: https://doi.org/10.1007/978-3-030-69255-1_17

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