Four Cards Are Sufficient for a Card-Based Three-Input Voting Protocol Utilizing Private Permutations
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.
KeywordsCard-based cryptographic protocols Multi-party computation Logic gates Majority voting Private permutation
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 . This work was partially supported by JSPS KAKENHI Grant Numbers JP15H02710 and JP17H01752.
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