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Card-based cryptographic protocols provide secure multi-party computations using a deck of physical cards. The most important primitive of those protocols is the shuffling operation, and most of the existing protocols rely on uniform cyclic shuffles (such as the random cut and random bisection cut) in which each possible outcome is equally likely and all possible outcomes constitute a cyclic subgroup. However, a couple of protocols with non-uniform and/or non-cyclic shuffles were proposed by Koch, Walzer, and Härtel at Asiacrypt 2015. Compared to the previous protocols, their protocols require fewer cards to securely produce a hidden AND value, although to implement of such unconventional shuffles appearing in their protocols remains an open problem. This paper introduces “pile-shifting scramble,” which can be a secure implementation of those shuffles. To implement such unconventional shuffles, we utilize physical cases that can store piles of cards, such as boxes and envelopes. Therefore, humans are able to perform the shuffles using these everyday objects. Furthermore, we show that a certain class of non-uniform and/or non-cyclic shuffles having two possible outcomes can be implemented by the pile-shifting scramble. This also implies that we can improve upon the known COPY protocol using three card cases so that the number of cases required can be reduced to two.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E101-A No.9 pp.1494-1502

- Publication Date
- 2018/09/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E101.A.1494

- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

- Category

Akihiro NISHIMURA

Tohoku University

Yu-ichi HAYASHI

Nara Institute of Science and Technology

Takaaki MIZUKI

Tohoku University

Hideaki SONE

Tohoku University

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Akihiro NISHIMURA, Yu-ichi HAYASHI, Takaaki MIZUKI, Hideaki SONE, "Pile-Shifting Scramble for Card-Based Protocols" in IEICE TRANSACTIONS on Fundamentals,
vol. E101-A, no. 9, pp. 1494-1502, September 2018, doi: 10.1587/transfun.E101.A.1494.

Abstract: Card-based cryptographic protocols provide secure multi-party computations using a deck of physical cards. The most important primitive of those protocols is the shuffling operation, and most of the existing protocols rely on uniform cyclic shuffles (such as the random cut and random bisection cut) in which each possible outcome is equally likely and all possible outcomes constitute a cyclic subgroup. However, a couple of protocols with non-uniform and/or non-cyclic shuffles were proposed by Koch, Walzer, and Härtel at Asiacrypt 2015. Compared to the previous protocols, their protocols require fewer cards to securely produce a hidden AND value, although to implement of such unconventional shuffles appearing in their protocols remains an open problem. This paper introduces “pile-shifting scramble,” which can be a secure implementation of those shuffles. To implement such unconventional shuffles, we utilize physical cases that can store piles of cards, such as boxes and envelopes. Therefore, humans are able to perform the shuffles using these everyday objects. Furthermore, we show that a certain class of non-uniform and/or non-cyclic shuffles having two possible outcomes can be implemented by the pile-shifting scramble. This also implies that we can improve upon the known COPY protocol using three card cases so that the number of cases required can be reduced to two.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E101.A.1494/_p

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@ARTICLE{e101-a_9_1494,

author={Akihiro NISHIMURA, Yu-ichi HAYASHI, Takaaki MIZUKI, Hideaki SONE, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Pile-Shifting Scramble for Card-Based Protocols},

year={2018},

volume={E101-A},

number={9},

pages={1494-1502},

abstract={Card-based cryptographic protocols provide secure multi-party computations using a deck of physical cards. The most important primitive of those protocols is the shuffling operation, and most of the existing protocols rely on uniform cyclic shuffles (such as the random cut and random bisection cut) in which each possible outcome is equally likely and all possible outcomes constitute a cyclic subgroup. However, a couple of protocols with non-uniform and/or non-cyclic shuffles were proposed by Koch, Walzer, and Härtel at Asiacrypt 2015. Compared to the previous protocols, their protocols require fewer cards to securely produce a hidden AND value, although to implement of such unconventional shuffles appearing in their protocols remains an open problem. This paper introduces “pile-shifting scramble,” which can be a secure implementation of those shuffles. To implement such unconventional shuffles, we utilize physical cases that can store piles of cards, such as boxes and envelopes. Therefore, humans are able to perform the shuffles using these everyday objects. Furthermore, we show that a certain class of non-uniform and/or non-cyclic shuffles having two possible outcomes can be implemented by the pile-shifting scramble. This also implies that we can improve upon the known COPY protocol using three card cases so that the number of cases required can be reduced to two.},

keywords={},

doi={10.1587/transfun.E101.A.1494},

ISSN={1745-1337},

month={September},}

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TY - JOUR

TI - Pile-Shifting Scramble for Card-Based Protocols

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1494

EP - 1502

AU - Akihiro NISHIMURA

AU - Yu-ichi HAYASHI

AU - Takaaki MIZUKI

AU - Hideaki SONE

PY - 2018

DO - 10.1587/transfun.E101.A.1494

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E101-A

IS - 9

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - September 2018

AB - Card-based cryptographic protocols provide secure multi-party computations using a deck of physical cards. The most important primitive of those protocols is the shuffling operation, and most of the existing protocols rely on uniform cyclic shuffles (such as the random cut and random bisection cut) in which each possible outcome is equally likely and all possible outcomes constitute a cyclic subgroup. However, a couple of protocols with non-uniform and/or non-cyclic shuffles were proposed by Koch, Walzer, and Härtel at Asiacrypt 2015. Compared to the previous protocols, their protocols require fewer cards to securely produce a hidden AND value, although to implement of such unconventional shuffles appearing in their protocols remains an open problem. This paper introduces “pile-shifting scramble,” which can be a secure implementation of those shuffles. To implement such unconventional shuffles, we utilize physical cases that can store piles of cards, such as boxes and envelopes. Therefore, humans are able to perform the shuffles using these everyday objects. Furthermore, we show that a certain class of non-uniform and/or non-cyclic shuffles having two possible outcomes can be implemented by the pile-shifting scramble. This also implies that we can improve upon the known COPY protocol using three card cases so that the number of cases required can be reduced to two.

ER -