IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Cryptography and Information Security
A Computationally Efficient Card-Based Majority Voting Protocol with Fewer Cards in the Private Model
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2023 Volume E106.A Issue 3 Pages 315-324


Card-based cryptography realizes secure multiparty computation using physical cards. In 2018, Watanabe et al. proposed a card-based three-input majority voting protocol using three cards. In a card-based cryptographic protocol with n-bit inputs, it is known that a protocol using shuffles requires at least 2n cards. In contrast, as Watanabe et al.'s protocol, a protocol using private permutations can be constructed with fewer cards than the lower bounds above. Moreover, an n-input protocol using private permutations would not even require n cards in principle since a private permutation depending on an input can represent the input without using additional cards. However, there are only a few protocols with fewer than n cards. Recently, Abe et al. extended Watanabe et al.'s protocol and proposed an n-input majority voting protocol with n cards and n + ⌊n/2⌋ + 1 private permutations. This paper proposes an n-input majority voting protocol with ⌈n/2⌉ + 1 cards and 2n-1 private permutations, which is also obtained by extending Watanabe et al.'s protocol. Compared with Abe et al.'s protocol, although the number of private permutations increases by about n/2, the number of cards is reduced by about n/2. In addition, unlike Abe et al.'s protocol, our protocol includes Watanabe et al.'s protocol as a special case where n=3.

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