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Four Cards Are Sufficient for a Card-Based Three-Input Voting Protocol Utilizing Private Permutations

  • Takeshi Nakai
  • Satoshi Shirouchi
  • Mitsugu IwamotoEmail author
  • Kazuo Ohta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10681)

Abstract

The card-based cryptographic protocol is a variant of multi-party computation that enables us to compute a certain function securely by using playing cards. In existing card-based cryptographic protocols, a special operation of cards called a shuffle is used to achieve the information-theoretic security. Recently, card-based cryptographic protocols have been reconsidered from the viewpoint of multi-party computations. In this direction, a new model of card-based cryptographic protocol including a new assumption called Private Permutations (PP, for short) is introduced and succeeds in constructing efficient protocols for the millionaires’ protocol. In this paper, we construct efficient card-based cryptographic OR and XOR protocols based on the existing AND protocol. Furthermore, by unifying AND and OR protocols, it is shown that a majority voting protocol with three inputs is efficiently obtained. Our construction requires only four cards thanks to PPs, whereas the previous work requires eight cards.

Keywords

Card-based cryptographic protocols Multi-party computation Logic gates Majority voting Private permutation 

Notes

Acknowledgement

The authors are grateful to the anonymous reviewers for their helpful comments. They also would like to thank Prof. Takaaki Mizuki for drawing the authors’ attention to [2]. This work was partially supported by JSPS KAKENHI Grant Numbers JP15H02710 and JP17H01752.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Takeshi Nakai
    • 1
  • Satoshi Shirouchi
    • 1
  • Mitsugu Iwamoto
    • 1
    Email author
  • Kazuo Ohta
    • 1
  1. 1.Department of InformaticsThe University of Electro-CommunicationsChofuJapan

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