Card-Based Cryptographic Protocols with the Minimum Number of Rounds Using Private Operations

Ono, Hibiki; Manabe, Yoshitsugu

doi:10.1007/978-3-030-31500-9_10

Cited by 11 publications

(3 citation statements)

References 34 publications

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“…All the protocols mentioned thus far in this paper can be executed publicly: every operation by players is supposed to be conducted with all eyes fixed on how the cards are manipulated. In contrast, there is another model wherein players are allowed to use "private" operations: it is known that such a somewhat strong assumption results in protocols with fewer cards, e.g., [11,12,14,15,20].…”

Section: Resultsmentioning

confidence: 99%

Five-Card AND Computations in Committed Format Using Only Uniform Cyclic Shuffles

et al. 2021

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In card-based cryptography, designing AND protocols in committed format is a major research topic. The state-of-the-art AND protocol proposed by Koch, Walzer, and Härtel in ASIACRYPT 2015 uses only four cards, which is the minimum permissible number. The minimality of their protocol relies on somewhat complicated shuffles having non-uniform probabilities of possible outcomes. Restricting the allowed shuffles to uniform closed ones entails that, to the best of our knowledge, six cards are sufficient: the six-card AND protocol proposed by Mizuki and Sone in 2009 utilizes the random bisection cut, which is a uniform and cyclic (and hence, closed) shuffle. Thus, a question has arisen: “Can we improve upon this six-card protocol using only uniform closed shuffles?” In other words, the existence or otherwise of a five-card AND protocol in committed format using only uniform closed shuffles has been one of the most important open questions in this field. In this paper, we answer the question affirmatively by designing five-card committed-format AND protocols using only uniform cyclic shuffles. The shuffles that our protocols use are the random cut and random bisection cut, both of which are uniform cyclic shuffles and can be easily implemented by humans.

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Section: Resultsmentioning

confidence: 99%

Five-Card AND Computations in Committed Format Using Only Uniform Cyclic Shuffles

et al. 2021

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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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“…The number of rounds was considered as the time complexity of the protocol with private operations. The definition of rounds is as follows [39]. The first round is (possibly parallel) local executions by each player using the cards initially given to each player.…”

Section: Primitive 3 (Private Reveal) a Player Privately Opens A Given Committed Bit The Player Does Not Disclose The Value To The Other mentioning

confidence: 99%

Card-Based Cryptographic Logical Computations Using Private Operations

Ono

Manabe

2020

New Gener. Comput.

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This paper proposes new card-based cryptographic protocols to calculate logic functions with the minimum number of cards using private operations under the semi-honest model. Though various card-based cryptographic protocols were shown, the minimum number of cards used in the protocol has not been achieved yet for many problems. Operations executed by a player where the other players cannot see are called private operations. Private operations have been introduced in some protocols to solve a particular problem or to input private values. However, the effectiveness of introducing private operations to the calculation of general logic functions has not been considered. This paper introduces three new private operations: private random bisection cuts, private reverse cuts, and private reveals. With these three new operations, we show that all of AND, XOR, and copy protocols are achieved with the minimum number of cards by simple three-round protocols. This paper then shows a protocol to calculate any logical functions using these private operations. Next, we consider protocols with malicious players.

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Card-Based Cryptographic Protocols with the Minimum Number of Rounds Using Private Operations

Cited by 11 publications

References 34 publications

Five-Card AND Computations in Committed Format Using Only Uniform Cyclic Shuffles

Five-Card AND Computations in Committed Format Using Only Uniform Cyclic Shuffles

Evaluating card-based protocols in terms of execution time

Card-Based Cryptographic Logical Computations Using Private Operations

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