Physical Zero-Knowledge Proof for Numberlink Puzzle and k Vertex-Disjoint Paths Problem

• Published in: New generation computing Vol. 39; no. 1; pp. 3 - 17
• Main Authors: Ruangwises, Suthee, Itoh, Toshiya
• Format: Journal Article
• Language: English
• Published: Tokyo Ohmsha 01.04.2021; Springer Nature B.V
• Subjects: Artificial Intelligence; Computer Hardware; Computer Science; Computer Systems Organization and Communication Networks; Software Engineering/Programming and Operating Systems; Card-based cryptography; Zero-knowledge proof; Puzzle; Graph; Numberlink; Vertex-disjoint paths
• ISSN: 0288-3635; 1882-7055
• DOI: 10.1007/s00354-020-00114-y

Numberlink is a logic puzzle with an objective to connect all pairs of cells with the same number by non-crossing paths in a rectangular grid. In this paper, we propose a physical protocol of zero-knowledge proof for Numberlink using a deck of cards, which allows a prover to convince a verifier that he/she knows a solution without revealing it. In particular, the protocol shows how to physically count the number of elements in a list that are equal to a given secret value without revealing that value, the positions of elements in the list that are equal to it, or the value of any other element in the list. Finally, we show that our protocol can be modified to verify a solution of the well-known k vertex-disjoint paths problem, both the undirected and directed settings.