Physical Zero-Knowledge Proof for Ripple Effect

Abstract

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.

arXiv commentA preliminary version of this paper has appeared at WALCOM 2021

References in corpus (4)

• Physical Zero-Knowledge Proof for Numberlink Puzzle and $k$ Vertex-Disjoint Paths Problem
• Two Standard Decks of Playing Cards are Sufficient for a ZKP for Sudoku
• Physical ZKP for Connected Spanning Subgraph: Applications to Bridges Puzzle and Other Problems
• Secure Grouping Protocol Using a Deck of Cards

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