Card-Based Protocols for Any Boolean Function

Card-based protocols that are based on a deck of physical cards achieve secure multi-party computation with information-theoretic secrecy. Using existing AND, XOR, NOT, and copy protocols, one can naively construct a secure computation protocol for any given (multivariable) Boolean function as long as there are plenty of additional cards. However, an explicit sufficient number of cards for computing any function has not been revealed thus far. In this paper, we propose a general approach to constructing an efficient protocol so that six additional cards are sufficient for any function to be securely computed. Further, we prove that two additional cards are sufficient for any symmetric function.