Card-Based Protocol Counting Connected Components of Graphs

Card-based cryptography is a research area for realizing cryptographic functionality, such as secure multiparty computation and zero-knowledge proofs, by using a deck of physical cards and/or other non-electrical tools. Motivated by zero-knowledge proofs for solutions in pencil puzzles, there is a direction of recent studies on card-based protocols to verify connectivity of a set of cells or edges on lattice-shaped boards. In this paper, we generalize the problem to counting connected components of a subset of the vertex set on any graph, and propose a card-based protocol for the problem.