Securely Computing Three-Input Functions with Eight Cards

Takuya NISHIDA  Yu-ichi HAYASHI  Takaaki MIZUKI  Hideaki SONE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.6   pp.1145-1152
Publication Date: 2015/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.1145
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
card-based protocols,  card games,  cryptography without computers,  secure computations,  

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Assume that Alice, Bob, and Carol, each of whom privately holds a one-bit input, want to learn the output of some Boolean function, say the majority function, of their inputs without revealing more of their own secret inputs than necessary. In this paper, we show that such a secure three-input function evaluation can be performed with a deck of real cards; specifically, the three players can learn only the output of the function using eight physical cards — four black and four red cards — with identical backs.