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PileShifting Scramble for CardBased Protocols
Akihiro NISHIMURA Yuichi HAYASHI Takaaki MIZUKI Hideaki SONE
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E101A
No.9
pp.14941502 Publication Date: 2018/09/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E101.A.1494
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications) Category: Keyword: cardbased protocols, card games, cryptography without computers, reallife handson cryptography, secure multiparty computations,
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Summary:
Cardbased cryptographic protocols provide secure multiparty 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 nonuniform and/or noncyclic 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 “pileshifting 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 nonuniform and/or noncyclic shuffles having two possible outcomes can be implemented by the pileshifting 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.

