Card-based Protocols Using Triangle Cards

Abstract

Suppose that three boys and three girls attend a party. Each boy and girl have a crush on exactly one of the three girls and three boys, respectively. The following dilemma arises: On one hand, each person thinks that if there is a mutual affection between a girl and boy, the couple should go on a date the next day. On the other hand, everyone wants to avoid the possible embarrassing situation in which their heart is broken "publicly." In this paper, we solve the dilemma using novel cards called triangle cards. The number of cards required is only six, which is minimal in the case where each player commits their input at the beginning of the protocol. We also construct multiplication and addition protocols based on triangle cards. Combining these protocols, we can securely compute any function f: {0,1,2}^n --> {0,1,2}