Card-Based Protocols Using Regular Polygon Cards

Shinagawa, Kazumasa; Mizuki, Takaaki; Schuldt, Jacob C. N.; Nuida, Koji; Kanayama, Naoki; Nishide, Takashi; Hanaoka, Goichiro; Okamoto, Eiji

doi:10.1587/transfun.e100.a.1900

Cited by 41 publications

(12 citation statements)

References 15 publications

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“…Intriguing future work involves applying our new criteria to other existing protocols using different types of cards (e.g., [21,22]) or those using private operations (e.g., [14,[17][18][19]). Table 5 The experimental result of measuring the execution time of adding, turning over, and permuting cards, which was mainly conducted by the second author, who is familiar with playing cards.…”

Section: Resultsmentioning

confidence: 99%

Evaluating card-based protocols in terms of execution time

Miyahara

Ueda

Hayashi

et al. 2020

Int. J. Inf. Secur.

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Card-based cryptography is an attractive and unconventional computation model; it provides secure computing methods using a deck of physical cards. It is noteworthy that a card-based protocol can be easily executed by non-experts such as high school students without the use of any electric device. One of the main goals in this discipline is to develop efficient protocols. The efficiency has been evaluated by the number of required cards, the number of colors, and the average number of protocol trials. Although these evaluation metrics are simple and reasonable, it is difficult to estimate the total number of operations or execution time of protocols based only on these three metrics. Therefore, in this paper, we consider adding other metrics to estimate the execution time of protocols more precisely. Furthermore, we actually evaluate some of the important existing protocols using our new criteria.

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Section: Resultsmentioning

confidence: 99%

Evaluating card-based protocols in terms of execution time

Miyahara

Ueda

Hayashi

et al. 2020

Int. J. Inf. Secur.

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“…We construct an efficient protocol for computing interesting predicates: a carry of addition " x + y ≥ n ", equality with zero " x = 0 ", equality " x = y ", and greater than " x ≥ y ". Table 1 shows a comparison between our protocols and the previous protocols [15] with regular polygon cards (RPC). Somewhat surprisingly, our protocols with dihedral cards (DC) for these predicates requires only two cards while all existing RPC-based protocols for the same predicates requires a large number of cards depending on the modulus n.…”

Section: Our Contributionmentioning

confidence: 99%

“…It captures a wide class of protocols not only our dihedral cards but also other type of cards. For example, our model also captures regular polygon cards [14,15]. See Appendix for the definition of regular polygon cards in our model.…”

Section: Our Contributionmentioning

confidence: 99%

“…For instance, secure computation of the average score, which takes a number of scores and outputs the average of them, is such a canonical example. In order to compute multi-valued functions efficiently, Shinagawa et al [15] proposed a deck of regular polygon cards, whose shape is a regular n-sided polygon for the base number n. They proposed a two-card addition protocol that outputs x + y mod n given two cards having x, y ∈ ℤ∕nℤ.…”

Section: Introductionmentioning

confidence: 99%

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Card-based Cryptography with Dihedral Symmetry

Shinagawa

2021

New Gener. Comput.

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It is known that secure computation can be done by using a deck of physical cards. This area is called card-based cryptography. Shinagawa et al. (in: Provable security—9th international conference, ProvSec 2015, Kanazawa, Japan, 2015) proposed regular n-sided polygon cards that enable to compute functions over $${\mathbb {Z}}/n{\mathbb {Z}}$$ Z / n Z . In particular, they designed efficient protocols for linear functions (e.g. addition and constant multiplication) over $${\mathbb {Z}}/n{\mathbb {Z}}$$ Z / n Z . Here, efficiency is measured by the number of cards used in the protocol. In this paper, we propose a new type of cards, dihedral cards, as a natural generalization of regular polygon cards. Based on them, we construct efficient protocols for various interesting functions such as carry of addition, equality, and greater-than, whose efficient construction has not been known before. Beside this, we introduce a new protocol framework that captures a wide class of card types including binary cards, regular polygon cards, dihedral cards, and so on.

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“…Works on implementing cryptographic protocols using physical objects are numerous, such as in [21]; or in [8] where a physical secure auction protocol was proposed. Other implementations have been studied using cards in [4,15], polarising plates [37], polygon cards [38], a standard deck of playing cards [18], using a PEZ dispenser [2,3], using a dial lock [19], using a 15 puzzle [20], or using a tamper-evident seals [23][24][25]. ZKP's for several other puzzles have been studied such as Sudoku [30,36], Akari [5], Takuzu [5,16], Kakuro [5,17], KenKen [5], Makaro [6,35], Norinori [9], Nonogram [7,29], Slitherlink [15], Suguru [27], Nurikabe [28], Ripple Effect [32], Numberlink [31], Bridges [33], and Cryptarithmetic [12].…”

Section: Introductionmentioning

confidence: 99%

Hide a Liar: Card-Based ZKP Protocol for Usowan

Robert

Miyahara

Lafourcade

et al. 2022

Lecture Notes in Computer Science

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A Zero-Knowledge Proof (ZKP) protocol allows a participant to prove the knowledge of some secret without revealing any information about it. While such protocols are typically executed by computers, there exists a line of research proposing physical instances of ZKP protocols. Up to now, many card-based ZKP protocols for pen-and-pencil puzzles, like Sudoku, have been designed. Those games, mostly edited by Nikoli, have simple rules, yet designing them in card-based ZKP protocols is non-trivial. This is partly due to the fact that the solution should not be leaked during the protocol. In this work, we propose a card-based protocol for Usowan, a Nikoli game. In Usowan, for each room of a puzzle instance, there is exactly one piece of false information. The goal of the game is to detect this wrong data amongst the correct data and also to satisfy the other rules. Designing a card-based ZKP protocol to deal with the property of detecting a liar has never been done. In some sense, we propose a physical ZKP for hiding of a liar.

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Card-Based Protocols Using Regular Polygon Cards

Cited by 41 publications

References 15 publications

Evaluating card-based protocols in terms of execution time

Evaluating card-based protocols in terms of execution time

Card-based Cryptography with Dihedral Symmetry

Hide a Liar: Card-Based ZKP Protocol for Usowan

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