Information leakage due to operative errors in card-based protocols

Card-based protocols provide secure multi-party computation using a deck of physical cards via a series of operations, such as shuffling and turning over cards, that are executed by humans. Although almost all existing protocols have been designed to be perfectly secure, operative errors by humans can lead to information leakage. In this paper, we propose a technique for analyzing information leakage due to operative errors in card-based protocols. In particular, we introduce a concept, which we call a “probability trace,” and by enhancing the KWH diagram proposed by Koch, Walzer, and Härtel, we propose a diagrammatic representation for displaying the amount of information leaked. By applying our diagram to a card-based protocol with an operative error, we can precisely reveal the leakage of players' inputs from the protocol output. In addition, we discuss how to detect human errors when people execute the existing six-card AND protocol.