Card-Based Protocols Using Unequal Division Shuffles

Akihiro Nishimura; Takuya Nishida; Yu-ichi Hayashi; Takaaki Mizuki; Hideaki Sone

Paper 2017/425

Card-Based Protocols Using Unequal Division Shuffles

Akihiro Nishimura, Takuya Nishida, Yu-ichi Hayashi, Takaaki Mizuki, and Hideaki Sone

Abstract

Card-based cryptographic protocols can perform secure computation of Boolean functions. In 2013, Cheung et al. presented a protocol that securely produces a hidden AND value using five cards; however, it fails with a probability of 1/2. The protocol uses an unconventional shuffle operation called an unequal division shuffle; after a sequence of five cards is divided into a two-card portion and a three-card portion, these two portions are randomly switched so that nobody knows which is which. In this paper, we first show that the protocol proposed by Cheung et al. securely produces not only a hidden AND value but also a hidden OR value (with a probability of 1/2). We then modify their protocol such that, even when it fails, we can still evaluate the AND value in the clear. Furthermore, we present two five-card copy protocols (which can duplicate a hidden value) using unequal division shuffle. Because the most efficient copy protocol currently known requires six cards, our new protocols improve upon the existing results. We also design a general copy protocol that produces multiple copies using an unequal division shuffle. Furthermore, we show feasible implementations of unequal division shuffles by the use of card cases.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Soft Computing
DOI: 10.1007/s00500-017-2858-2
Keywords: Card-based protocols
Contact author(s): tm-paper+card5cop @ g-mail tohoku-university jp
History: 2017-09-26: last of 2 revisions; 2017-05-22: received; See all versions
Short URL: https://ia.cr/2017/425
License: CC BY

BibTeX

@misc{cryptoeprint:2017/425,
      author = {Akihiro Nishimura and Takuya Nishida and Yu-ichi Hayashi and Takaaki Mizuki and Hideaki Sone},
      title = {Card-Based Protocols Using Unequal Division Shuffles},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/425},
      year = {2017},
      doi = {10.1007/s00500-017-2858-2},
      url = {https://eprint.iacr.org/2017/425}
}