Physical Zero-Knowledge Proof for Ball Sort Puzzle

TL;DR

This paper introduces a physical zero-knowledge proof protocol using playing cards that allows a prover to demonstrate knowledge of a solution to the ball sort puzzle without revealing it, marking the first such protocol for an interactive moving-object puzzle.

Contribution

It presents the first physical zero-knowledge proof protocol for an interactive puzzle involving moving objects, specifically the ball sort puzzle, using a deck of playing cards.

Findings

First zero-knowledge proof protocol for a moving-object puzzle.

Enables physical demonstration of knowledge without revealing the solution.

Applicable to interactive puzzles with moving components.

Abstract

Ball sort puzzle is a popular logic puzzle consisting of several bins containing balls of multiple colors. Each bin works like a stack; a ball has to follow the last-in first-out order. The player has to sort the balls by color such that each bin contains only balls of a single color. In this paper, we propose a physical zero-knowledge proof protocol for the ball sort puzzle using a deck of playing cards, which enables a prover to physically show that he/she knows a solution with $t$ moves of the ball sort puzzle without revealing it. Our protocol is the first zero-knowledge proof protocol for an interactive puzzle involving moving objects.