Securely computing XOR with 10 cards

There exist several protocols by which Alice and Bob can securely compute some function using a deck of cards. The most efficient protocol currently known is given by Stiglic: his elaborate but simple protocol can allow Alice and Bob to securely compute the AND function using only 8 cards. The existence of the AND protocol implies that one can design a protocol which securely computes any Boolean function: for example, the XOR function can be securely computed using 12 cards, although the computation requires a relatively large task such as copying the input and repeating the AND protocol. This paper addresses efficient secure computation of XOR, and gives a simple protocol which securely computes the XOR function using only 10 cards.