How to Detect Malicious Behaviors in a Card-Based Majority Voting Protocol with Three Inputs

Card-based protocol is a multi-party computation using cards. The card-based protocol using operations called private operation has an advantage that the number of cards and the number of times of communication are smaller than the card-based protocol using operations called shuffle. However, there is a disadvantage that private operation allows dishonest players to perform malicious behaviors. Although the method to detect malicious behaviors in private operations was proposed, the method was available only in committed-format protocols, where inputs and outputs are represented by a pair of cards called commitment. In this paper, we show how to detect malicious behaviors in non-committed-format protocol with an example of a three-input majority voting protocol using private operations. Our majority voting protocol requires a smaller number of cards than the minimum number of cards required for committed-format protocols.