Efficient Card-Based Protocols with a Standard Deck of Playing Cards Using Partial Opening

Card-based protocols are cryptographic protocols that use a deck of physical cards. In this paper, we deal with card-based protocols using a standard deck of playing cards, which are commonly and commercially available. For finite-runtime committed-format protocols, Mizuki (CANS 2016) proposed an eight-card AND protocol with four random bisection cuts and a six-card COPY protocol with one random bisection cut. In this paper, we propose a partial-open action, which reveals any position of the face of cards, by generalizing the half-open action introduced by Miyahara and Mizuki (IJTCS-FAW 2022). Using the partial-open action, we propose four-card AND protocols with three random cuts, a four-card COPY protocol with three random cuts, and a four-card base conversion protocol with a random cut. We note that, without partial-open actions, these AND and COPY protocols with random cuts only are known to be impossible to construct using four cards. Therefore, the partial-open actions are inherently necessary to obtain our results.