An Improved Physical ZKP for Nonogram and Nonogram Color

TL;DR

This paper presents a practical, card-based zero-knowledge proof protocol for Nonogram and its color variant, eliminating the need for special tools and achieving perfect soundness.

Contribution

It introduces a new, practical protocol using regular paper cards for Nonogram and extends it to support Nonogram Color, improving upon prior methods.

Findings

Protocol uses only regular paper cards

Achieves perfect soundness

Supports Nonogram Color

Abstract

Nonogram is a pencil puzzle consisting of a rectangular white grid where the player has to paint some cells black according to given constraints. In 2010, Chien and Hon constructed a physical card-based zero-knowledge proof protocol for Nonogram, which enables a prover to physically show that he/she knows a solution of the puzzle without revealing it. However, their protocol requires special tools such as scratch-off cards and a sealing machine, making it impractical to implement in real world. The protocol also has a nonzero soundness error. In this paper, we develop a more practical card-based protocol for Nonogram with perfect soundness that uses only regular paper cards. We also show how to modify our protocol to make it support Nonogram Color, a generalization of Nonogram where the player has to paint the cells with multiple colors.