Secure Computation of Any Boolean Function Based on Any Deck of Cards

Abstract

It is established that secure computation can be achieved by using a deck of physical cards. Almost all existing card-based protocols are based on a specific deck of cards. In this study, we design card-based protocols that are executable using any deck of cards (e.g., playing cards, UNO, and trading cards). Specifically, we construct a card-based protocol for any Boolean function based on any deck of cards. As corollaries of our result, a standard deck of playing cards (having 52 cards) enables secure computation of any 22-variable Boolean function, and UNO (having 112 cards) enables secure computation of any 53-variable Boolean function.