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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Suken BINGO and Its Secure Variants Using Card-Based Cryptography

Ren IGARI, Yuichi Komano, Takaaki Mizuki

Published Jan 1, 2026• 0 citations
Publisher

Abstract

BINGO is a classic game where players compete to complete a line on a 5 × 5 grid, and it is fun and popular. However, since it typically requires a specialized bingo machine, spontaneous games of BINGO are challenging. To address this, we introduce Suken BINGO, a new board game that allows players to declare integers instead of using a bingo machine, making it more accessible. Specifically, players verbally call out integers in a manner similar to the Japanese hand game Suken. This removes the need for a dedicated bingo machine.

DOI
10.1587/transfun.2026cip0022

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BINGO is a classic game where players compete to complete a line on a 5 × 5 grid, and it is fun and popular. However, since it typically requires a specialized bingo machine, spontaneous games of BINGO are challenging. To address this, we introduce Suken BINGO, a new board game that allows players to declare integers instead of using a bingo machine, making it more accessible. Specifically, players verbally call out integers in a manner similar to the Japanese hand game Suken. This removes the need for a dedicated bingo machine.
Mental card games are played without a trusted party and without cards. It is well known that the problem of mental card games can be solved in principle. But the schemes known so far are too messy to be used in practice. Only for the mental poker game a suitable solution is known [Cr'ep 87] that achieves security against player coalition and complete confidentiality of a player's strategy. Here, we present a general-purpose scheme that may be used as basic toolbox for straight-forward implementations of card games. We present a data structure for cards and decks that is secure against player coalitions and enables standard operations like picking up a card, opening it, and (re-)mixing stacks. Futhermore, we introduce tools for special operations like inserting a card into the deck, splitting the deck, parting the game. The correctness of all operations is testified by zeroknowledge proofs. Finally, we discuss security problems that are typical for mental card games and suggest solutio...
Research in secure multi-party computation using a deck of playing cards, often called card-based cryptography, dates back to 1989 when Den Boer introduced the five-card trick to compute the logical AND function. Since then, many protocols to compute different functions have been developed. In this paper, we propose a new encoding scheme using five cards to encode each integer in Z/6Z\mathbb{Z}/6\mathbb{Z}Z/6Z. Using this encoding scheme, we develop protocols that can copy a commitment with 13 cards, add two integers with 10 cards, and multiply two integers with 16 cards. All of our protocols are the currently best known protocols in terms of the required number of cards. Our encoding scheme can also be generalized to encode integers in Z/nZ\mathbb{Z}/n\mathbb{Z}Z/nZ for other values of nnn as well.
Sudoku is a popular pencil puzzle where a player fills in the empty cells with numbers on an n × n board so that each row, column, and -block must contain all the numbers from 1 to n; a typical puzzle size is n = 9. In 2007, Gradwohl, Naor, Pinkas, and Rothblum proposed a physical zero-knowledge proof protocol for Sudoku using a physical deck of cards; their card-based protocol requires 3nℓ shuffles, where ℓ is a security parameter to eliminate the soundness error. Since the invention of this seminal protocol, several soundness-error-free protocols were constructed to reduce the number of required shuffles; the state-of-the-art one was designed in 2023, which uses shuffles. In this paper, we show that only three or two shuffles are sufficient to construct a zero-knowledge proof protocol for Sudoku, no matter how large n is, i.e., we propose two card-based protocols using constant numbers (namely, 3 and 2) of shuffles. Our proposed protocols are simple and efficient enough for people to execute for a 9 × 9 Sudoku puzzle in reality.
Quantum technologies enable new ways to distribute and process information. The enormous progress over the recent decades has led to an urgent need for new educational programs to train professionals to work in this field. Here, we present a card game that teaches students the building blocks of quantum computing through strategic gameplay. Participants start from the lowest quantum state and play cards that change their state and/or their opponents' state, aiming to build an algorithm that achieves the highest possible quantum state. Players can utilize several different strategies that rely on quantum features such as randomness, superposition, interference, and entanglement. Our game expands on the existing Q|Cards⟩ game, originally developed using traditional qubits (with 2-level states), by including an option to play with qutrits (with 3-level states), and by developing cooperative and single player modes in addition to the existing competitive mode. The presented game contributes to the ongoing efforts on gamifying quantum physics education with a particular focus on the counter-intuitive features that make quantum computing powerful.
We introduce a new board game based on the ancient Chinese game of Go (Weiqi, Igo, Baduk). The key difference from the original game is that players no longer alternatively play single stones on the board but instead they take turns placing pairs of entangled go stones. A phenomenon of quantum-like collapse occurs when one of the stones in an entangled pair is directly in contact with at least one other stone. The player to whom the entangled pair belongs must then remove one of the stones in the pair from the board. The aim of the game is still to surround more territory than the opponent and as the number of stones increases, all the entangled pairs of stones eventually reduce to single stones. Quantum Go provides an interesting and tangible illustration of quantum concepts such as superposition, entanglement and collapse.
Abstract Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm shift in computing, with a steep learning gradient. The creation of games is a way to ease the transition for beginners. We present a game similar to the Poker variant Texas hold ’em with the intention to serve as an engaging pedagogical tool to learn the basics rules of quantum computing. The concepts of quantum states, quantum operations and measurement can be learned in a playful manner. The difference to the classical variant is that the community cards are replaced by a quantum register that is “randomly” initialized, and the cards for each player are replaced by quantum gates, randomly drawn from a set of available gates. Each player can create a quantum circuit with their cards, with the aim to maximize the number of 1’s that are measured in the computational basis. The basic concepts of superposition, entanglement and quantum gates are employed. We provide a proof-of-concept implementation using Qiskit (Aleksandrowicz et al. in An open-source framework for quantum computing, 2019). A comparison of the results for the created circuits using a simulator and IBM machines is conducted, showing that error rates on contemporary quantum computers are still very high. For the success of noisy intermediate scale quantum (NISQ) computers, improvements on the error rates and error mitigation techniques are necessary, even for simple circuits. We show that quantum error mitigation (QEM) techniques can be used to improve expectation values of observables on real quantum devices.