It is known that, using just a deck of cards, an arbitrary number of parties with private inputs can securely compute the output of any function of their inputs. In 2009, Mizuki and Sone constructed a six-card COPY protocol, a four-card XOR protocol, and a six-card AND protocol, based on a commonly used encoding scheme in which each input bit is encoded using two cards. However, up until now, it has remained an open problem to construct a set of COPY, XOR, and AND protocols based on a two-cards-per-bit encoding scheme, which all can be implemented using only four cards. In this paper, we show that it is possible to construct four-card COPY, XOR, and AND protocols using polarizing plates as cards and a corresponding two-cards-per-bit encoding scheme. Our protocols are optimal in the setting of two-cardsper- bit encoding schemes since four cards are always required to encode the inputs. As applications of our protocols, we show constructions of optimal input-preserving XOR and AND protocols, which we combine to obtain optimal half-adder, full-adder, voting protocols, and more.
CITATION STYLE
Shinagawa, K., Mizuki, T., Schuldt, J., Nuida, K., Kanayama, N., Nishide, T., … Okamoto, E. (2015). Secure multi-party computation using polarizing cards. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9241, pp. 281–297). Springer Verlag. https://doi.org/10.1007/978-3-319-22425-1_17
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