TY - JOUR
T1 - Card-based protocols for securely computing the conjunction of multiple variables
AU - Mizuki, Takaaki
N1 - Funding Information:
We thank the anonymous referees whose comments helped us to improve the presentation of the paper. This work was supported by JSPS KAKENHI Grant Number 26330001 .
Publisher Copyright:
© 2016 Elsevier B.V.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/4/4
Y1 - 2016/4/4
N2 - Consider a deck of real cards with faces that are either black or red and backs that are all identical. Then, using two cards of different colors, we can commit a secret bit to a pair of face-down cards so that its order (i.e., black to red, or red to black) represents the value of the bit. Given such two commitments (consisting of four face-down cards in total) together with one additional black card, the "five-card trick" invented in 1989 by den Boer securely computes the conjunction of the two secret bits. In 2012, it was shown that such a two-variable secure AND computation can be done with no additional card. In this paper, we generalize this result to an arbitrary number of variables: we show that, given any number of commitments, their conjunction can be securely computed with no additional card.
AB - Consider a deck of real cards with faces that are either black or red and backs that are all identical. Then, using two cards of different colors, we can commit a secret bit to a pair of face-down cards so that its order (i.e., black to red, or red to black) represents the value of the bit. Given such two commitments (consisting of four face-down cards in total) together with one additional black card, the "five-card trick" invented in 1989 by den Boer securely computes the conjunction of the two secret bits. In 2012, it was shown that such a two-variable secure AND computation can be done with no additional card. In this paper, we generalize this result to an arbitrary number of variables: we show that, given any number of commitments, their conjunction can be securely computed with no additional card.
KW - Card games
KW - Card-based protocols
KW - Cryptography without computers
KW - Real-life hands-on cryptography
KW - Secure multiparty computations
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U2 - 10.1016/j.tcs.2016.01.039
DO - 10.1016/j.tcs.2016.01.039
M3 - Article
AN - SCOPUS:84958177123
VL - 622
SP - 34
EP - 44
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
ER -