Abstract
It is established that secure computation can be achieved by using a deck of physical cards. Almost all existing card-based protocols are based on a specific deck of cards. In this study, we design card-based protocols that are executable using any deck of cards (e.g., playing cards, UNO, and trading cards). Specifically, we construct a card-based protocol for any Boolean function based on any deck of cards. As corollaries of our result, a standard deck of playing cards (having 52 cards) enables secure computation of any 22-variable Boolean function, and UNO (having 112 cards) enables secure computation of any 53-variable Boolean function.
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- 1.
This type of protocols is called non-committed format. Meanwhile, the other type of protocols, where the output is not revealed, is called committed format. We focus on committed format protocols throughout this paper.
- 2.
Prior to executing the AND–XOR protocol, for each complementary literal \(\bar{x}_j\) in \(T_i\), we negate the corresponding commitment by swapping the two cards.
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Acknowledgments
This work was supported in part by JSPS KAKENHI Grant Numbers 17J01169 and 17K00001.
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Shinagawa, K., Mizuki, T. (2019). Secure Computation of Any Boolean Function Based on Any Deck of Cards. In: Chen, Y., Deng, X., Lu, M. (eds) Frontiers in Algorithmics. FAW 2019. Lecture Notes in Computer Science(), vol 11458. Springer, Cham. https://doi.org/10.1007/978-3-030-18126-0_6
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