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.
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Notes
- 1.
Slightly modified for later discussion, but essentially the same as the protocol in [2].
- 2.
Hereafter, we remove the frame of cards for simplicity.
References
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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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Nakai, T., Shirouchi, S., Iwamoto, M., Ohta, K. (2017). Four Cards Are Sufficient for a Card-Based Three-Input Voting Protocol Utilizing Private Permutations. In: Shikata, J. (eds) Information Theoretic Security. ICITS 2017. Lecture Notes in Computer Science(), vol 10681. Springer, Cham. https://doi.org/10.1007/978-3-319-72089-0_9
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