Physical zero-knowledge proof for Ripple Effect

• Published in: Theoretical computer science Vol. 895; pp. 115 - 123
• Main Authors: Ruangwises, Suthee, Itoh, Toshiya
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 04.12.2021
• Subjects: Card-based cryptography; Puzzle; Ripple effect; Zero-knowledge proof; Ripple effect; Zero-knowledge proof; Card-based cryptography; Puzzle
• ISSN: 0304-3975; 1879-2294; 1879-2294
• DOI: 10.1016/j.tcs.2021.09.034

Ripple Effect is a logic puzzle where the player has to fill numbers into empty cells in a rectangular grid. The grid is divided into rooms, and each room must contain consecutive integers starting from 1 to its size. Also, if two cells in the same row or column contain the same number x, there must be a space of at least x cells separating the two cells. In this paper, we develop a physical zero-knowledge proof for the Ripple Effect puzzle using a deck of cards, which allows a prover to convince a verifier that he/she knows a solution without revealing it. In particular, given a secret number x and a list of numbers, our protocol can physically verify that x does not appear among the first x numbers in the list without revealing x or any number in the list.