The Minimum Number of Cards in Practical Card-Based Protocols

Kästner, Julia; Koch, Alexander; Walzer, Stefan; Miyahara, Daiki; Hayashi, Yu Ichi; Mizuki, Takaaki; Sone, Hideaki

doi:10.1007/978-3-319-70700-6_5

Cited by 41 publications

(20 citation statements)

References 13 publications

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“…Thus, the KWH-tree in Figure 1 guarantees that our proposed protocol is correct and secure. (As stated in Proposition 1 of [4], the KWH-tree is a witness for the correctness and security. )…”

Section: Correctness and Securitymentioning

confidence: 97%

“…To confirm that our protocol is correct and secure, we make use of the KWH-tree, which is a beautiful tool developed by Koch, Walzer, and Härtel [6]. That is, if one is able to write a KWH-tree satisfying some properties for a protocol, then it automatically implies that the protocol is correct and secure; see [4,6,8] for the details.…”

Section: Correctness and Securitymentioning

confidence: 99%

See 1 more Smart Citation

Six-Card Finite-Runtime XOR Protocol with Only Random Cut

Toyoda

Miyahara

Mizuki

et al. 2020

Proceedings of the 7th ACM Workshop on ASIA Public-Key Cryptography

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Executing a card-based cryptographic protocol is an attractive way to perform secure multiparty computation (MPC) with a deck of physical cards. Crèpeau and Kilian at CRYPTO 1993 proposed cardbased AND and XOR protocols that can deal with a logical conjunction and exclusive-or of variables. Their protocols use a familiar shuffling action called a random cut that can be easily implemented by humans, while the numbers of required cards and shuffles are not small enough to be efficient and the protocols are Las Vegas algorithms, i.e., they are not finite-runtime. Several researchers have improved upon the protocols for a quarter of a century. Eventually, there are many AND protocols in the literature, some of which are quite efficient and practical to execute. By contrast, there are only three XOR protocols including the Crèpeau-Kilian protocol mentioned above. In this paper, we design an efficient XOR protocol using only random cuts; the numbers of required cards and shuffles are six and two (which is fixed), respectively. Our proposed XOR protocol is the first construction of a finite-runtime XOR protocol if we restrict ourselves to use only random cuts. CCS CONCEPTS • Security and privacy → Cryptography.

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Section: Correctness and Securitymentioning

confidence: 97%

Section: Correctness and Securitymentioning

confidence: 99%

Six-Card Finite-Runtime XOR Protocol with Only Random Cut

Toyoda

Miyahara

Mizuki

et al. 2020

Proceedings of the 7th ACM Workshop on ASIA Public-Key Cryptography

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“…A random cut, meaning a cyclic shuffling operation, uniformly randomly shifts the positions of the sequence without changing the order 1 . Mathematically, one permutation is uniformly randomly selected from {id, (1 2 3 4 5), (1 2 3 4 5) 2 , (1 2 3 4 5) 3 , (1 2 3 4 5) 4 }, and the selected permutation is applied to the sequence of the five cards, where id is the identity permutation and (i 1 i 2 . .…”

Section: The Five-card Trickmentioning

confidence: 99%

“…Theorem 3 [4] There is no four-card expected-finite-runtime AND protocol in committed format with only uniform closed shuffles.…”

Section: Optimality Of Our Protocolmentioning

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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“…Koch et al [5, §6] showed that there is no four-card AND protocol with finite runtime. Kastner et al [4] later proved that there is no finite five-card AND protocol using only closed shuffles, and no restart-free Las Vegas four-card AND protocol using only uniform closed shuffles.…”

Section: Lower Boundmentioning

confidence: 99%

AND Protocols Using only Uniform Shuffles

Ruangwises

Itoh

2019

Lecture Notes in Computer Science

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Secure multi-party computation using a deck of playing cards has been a subject of research since the "five-card trick" introduced by den Boer in 1989. One of the main problems in card-based cryptography is to design committed-format protocols to compute a Boolean AND operation subject to different runtime and shuffle restrictions by using as few cards as possible. In this paper, we introduce two AND protocols that use only uniform shuffles. The first one requires four cards and is a restart-free Las Vegas protocol with finite expected runtime. The second one requires five cards and always terminates in finite time.

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The Minimum Number of Cards in Practical Card-Based Protocols

Cited by 41 publications

References 13 publications

Six-Card Finite-Runtime XOR Protocol with Only Random Cut

Six-Card Finite-Runtime XOR Protocol with Only Random Cut

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

AND Protocols Using only Uniform Shuffles

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