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 available commercially. 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 a four-card AND protocol with three random cuts and a four-card COPY protocol with three random cuts. We note that, without partial-open actions, these protocols are known to be impossible to construct. Therefore, the partial-open actions are inherently necessary to obtain our results.