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

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.