Card-Based Covert Lottery

Before starting to play a two-player board game such as Chess and Shogi (namely, Japanese chess), we have to determine who makes the first move. Players’ strategies of Chess and Shogi often rely on whether they will move first or not, and most players have their own preferences. Therefore, it would be nice if we can take their individual requests into account when determining who goes first. To this end, if the two players simply tell their preferable moves to each other, they will notice the other’s strategy. Thus, we want the players to determine the first move according to their requests while hiding any information about them. Note that this problem cannot be solved by a typical way done in Chess, namely, a coin-flipping. In this paper, we formalize this problem in a cryptographic perspective and propose a secure protocol that solves this problem using a deck of physical cards. Moreover, we extend this problem to the multi-player setting: Assume that there is a single prize in a lottery drawing among more than two players, each of who has an individual secret feeling ‘Yes’ or ‘No’ that indicates whether he/she really wants to get the prize or not. If one or more players have ‘Yes,’ we want to randomly and covertly choose a winner among those having ‘Yes.’ If all of them have ‘No,’ we want to randomly pick a winner among all the players. We solve this extended problem, which we call the “covert lottery” problem, by proposing a simple card-based protocol.