# Secure Computations Through Checking Suits of Playing Cards

Daiki Miyahara, Takaaki Mizuki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

## Abstract

Card-based cryptography started with the “five-card trick” designed by Den Boer (EUROCRYPT 1989); it enables Alice and Bob to securely evaluate the AND value of their private bits using a physical deck of five cards. It was then shown that the same task can be done with only four cards, i.e., Mizuki et al. proposed a four-card AND protocol (ASIACRYPT 2012). These two AND protocols are simple and easy even for non-experts, such as high school students, to execute. Their only common drawback is the need to prepare a customized deck consisting of red and black cards such that all cards of the same color must be identical. Fortunately, several existing protocols are based on a standard deck of playing cards (commercially available). Among them, the state-of-the-art AND protocol was constructed by Koch et al. (ASIACRYPT 2019); it uses four playing cards (such as ‘A, J, Q, K’) to securely evaluate the AND value. The protocol is elaborate, while its possible drawback is the need to repeat a shuffling operation six times (in expectation), which makes it less practical. This paper aims to provide the first practical protocol working on a standard deck of playing cards. We present an extremely simple AND protocol that terminates after only one shuffle using only four cards; our proposed protocol relies on a new operation, called the “half-open” action, whereby players can check only the suit of a face-down card without revealing the number on it. We believe that this new operation is easy-to-implement, and hence, our four-card AND protocol working on a standard deck is practical. We formalize the half-open action to present a formal description of our proposed protocol. Moreover, we discuss what is theoretically implied by introducing the half-open action and show that it can be applied to efficiently solving Yao’s Millionaires’ problem with a standard deck of cards.

Original language English Frontiers of Algorithmic Wisdom - International Joint Conference, IJTCS-FAW 2022, Revised Selected Papers Minming Li, Xiaoming Sun Springer Science and Business Media Deutschland GmbH 110-128 19 9783031207952 https://doi.org/10.1007/978-3-031-20796-9_9 Published - 2022 International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom, IJTCS-FAW 2022 - Hong Kong, ChinaDuration: 2022 Aug 15 → 2022 Aug 19

### Publication series

Name Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 13461 LNCS 0302-9743 1611-3349

### Conference

Conference International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom, IJTCS-FAW 2022 China Hong Kong 22/8/15 → 22/8/19

## Keywords

• Card-based cryptography
• Real-life hands-on cryptography
• Secure computation

## ASJC Scopus subject areas

• Theoretical Computer Science
• Computer Science(all)

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