Card-based protocols for securely computing the conjunction of multiple variables

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.