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Card-Based Protocols Imply PSM Protocols

Authors Kazumasa Shinagawa , Koji Nuida

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Subject Classification

ACM Subject Classification
  • Security and privacy → Information-theoretic techniques
Keywords
  • Card-based cryptography
  • private simultaneous messages

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Abstract

Card-based cryptography is the art of cryptography using a deck of physical cards. While this area is known as a research area of recreational cryptography and is recently paid attention in educational purposes, there is no systematic study of the relationship between card-based cryptography and the other "conventional" cryptography. This paper establishes the first generic conversion from card-based protocols to private simultaneous messages (PSM) protocols, a special kind of secure multiparty computation. Our compiler supports "simple" card-based protocols, which is a natural subclass of finite-runtime protocols. The communication complexity of the resulting PSM protocol depends on how many cards are opened in total in all possible branches of the original card-based protocol. This result shows theoretical importance of such "opening complexity" of card-based protocols, which had not been focused in this area. As a consequence, lower bounds for PSM protocols imply those for simple card-based protocols. In particular, if there exists no PSM protocol with subexponential communication complexity for a function f, then there exists no simple card-based protocol with subexponential opening complexity for the same f.

Cite As Get BibTex

Kazumasa Shinagawa and Koji Nuida. Card-Based Protocols Imply PSM Protocols. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 72:1-72:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.72

Author Details

Kazumasa Shinagawa
  • Ibaraki University, Ibaraki, Japan
  • National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan
Koji Nuida
  • Institute of Mathematics for Industry (IMI), Kyushu University, Fukuoka, Japan
  • National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

Funding

This work was supported by Institute of Mathematics for Industry, Joint Usage/Research Center in Kyushu University: FY2022 Short-term Visiting Researcher "On Minimal Construction of Private Simultaneous Messages Protocols" (2022a006), FY2023 Short-term Visiting Researcher "On the Relationship between Physical and Non-physical Secure Computation Protocols" (2023a009), and FY2024 Short-term Visiting Researcher "Private Simultaneous Messages and Card-Based Cryptography" (2024a015).
  • Shinagawa, Kazumasa: This work was supported in part by JSPS KAKENHI Grant Numbers 21K17702 and 23H00479, and JST CREST Grant Number MJCR22M1.
  • Nuida, Koji: This work was supported in part by JSPS KAKENHI Grant Number JP22K11906.

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