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Playing President with Virtual Players: How to Play Multiple Cards of a Kind

Authors Daiki Miyahara , Pascal Lafourcade , Takaaki Mizuki , Kazumasa Shinagawa

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Subject Classification

ACM Subject Classification
  • Security and privacy → Cryptography
Keywords
  • Card-Based Cryptography
  • Player-Simulation Problem
  • President

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Abstract

President is a popular card game in which players may play one to four cards of the same rank. Since it is less enjoyable with too few human players, to address this, we study the player-simulation problem for President: realizing the moves of a virtual player while keeping its hand hidden. We propose a selection protocol, which selects multiple cards of the same rank uniformly at random from a hidden virtual player’s hand, whose rank exceeds the latest played cards. Our construction reduces the task to secure sorting, so the overall efficiency is dominated by the underlying sorting protocol. To address this bottleneck, we design an efficient sorting protocol, which reduces the number of steps from O(m log m) to O(m), compared to the existing sorting protocols.

Cite As Get BibTex

Daiki Miyahara, Pascal Lafourcade, Takaaki Mizuki, and Kazumasa Shinagawa. Playing President with Virtual Players: How to Play Multiple Cards of a Kind. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 34:1-34:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FUN.2026.34

Author Details

Daiki Miyahara
  • The University of Electro-Communications, Tokyo, Japan
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
Pascal Lafourcade
  • Université Clermont Auvergne, CNRS, Clermont Auvergne INP, LIMOS, 63000 Clermont-Ferrand, France
Takaaki Mizuki
  • Cyberscience Center, Tohoku University, Sendai, Japan
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
Kazumasa Shinagawa
  • University of Tsukuba, Tsukuba, Japan
  • Kyushu University, Fukuoka, Japan
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

Funding

This work was supported in part by ANR PROJECT PRIVA-SIQ ANR-23-CE39-0008, JSPS KAKENHI Grant Numbers JP21K17702, JP23H00479, JP24K02938, JP26K21162, and JP26K21164, JST CREST Grant Number JPMJCR22M1, JSPS Bilateral Joint Research Projects JPJSBP120253206, and JST K Program Grant Number JPMJKP24U2, Japan.

Acknowledgements

We thank the anonymous reviewers, whose comments have helped us improve the presentation of the paper. We thank Hayato Shikata and Yuto Shinoda for helpful discussions on the sorting protocol presented in Section 3 at the early stages of this work.

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