Hide a Liar: Card-Based ZKP Protocol for Usowan

Abstract

A Zero-Knowledge Proof (ZKP) protocol allows a participant to prove the knowledge of some secret without revealing any information about it. While such protocols are typically executed by computers, there exists a line of research proposing physical instances of ZKP protocols. Up to now, many card-based ZKP protocols for pen-and-pencil puzzles, like Sudoku, have been designed. Those games, mostly edited by Nikoli, have simple rules, yet designing them in card-based ZKP protocols is non-trivial. This is partly due to the fact that the solution should not be leaked during the protocol. In this work, we propose a card-based protocol for Usowan, a Nikoli game. In Usowan, for each room of a puzzle instance, there is exactly one piece of false information. The goal of the game is to detect this wrong data amongst the correct data and also to satisfy the other rules. Designing a card-based ZKP protocol to deal with the property of detecting a liar has never been done. In some sense, we propose a physical ZKP for hiding of a liar.

ZKP Protocols for Usowan, Herugolf, and Five Cells

“…In some sense, we propose a physical ZKP for hiding of a liar. This work extends a previous paper appearing in [33].…”

“…Designing a card-based ZKP protocol to deal with the property of detecting a liar has never been done.In some sense, we propose a physical ZKP for hiding of a liar. This work extends a previous paper appearing in [33].In this extension, we propose two other protocols, for Herugolf and Five Cells. The puzzles are specifically chosen because each of those three puzzles shares a common constraint, connectivity.…”

“…In [33], we presented a physical ZKP protocol for Usowan [1] which is a pencil puzzle played with a rectangular grid composed of numbered cells and white cells delimited by regions (thick edges).…”

Physical Zero-Knowledge Proof for Ball Sort Puzzle

“…Recently, card-based ZKP protocols for several types of logic puzzles have been developed: Akari [1], Bridges [24], Heyawake [16], Hitori [16], Juosan [13], Kakuro [1,14], KenKen [1], Makaro [2,25], Masyu [12], Nonogram [3,19], Norinori [4], Numberlink [22], Nurikabe [16], Nurimisaki [17], Ripple Effect [23], Shikaku [21], Slitherlink [12], Sudoku [8,20,26], Suguru [15], Takuzu [1,13], and Usowan [18]. All of them are pencil puzzles where a solution is a written answer.…”

Physical zero-knowledge proof for Ripple Effect

“…In recent years, physical card-based ZKP protocols for many pencil puzzles have been developed, including Sudoku [8,20,26], Nonogram [4,19], Akari [1], Takuzu [1,12], Kakuro [1,13], KenKen [1], Makaro [2,25], Norinori [5], Slitherlink [11], Juosan [12], Numberlink [22], Suguru [15], Ripple Effect [23], Nurikabe [16], Hitori [16], Bridges [24], Masyu [11], Heyawake [16], Shikaku [21], Usowan [18], and Nurimisaki [17].…”