Physical Zero-knowledge Proofs for Flow Free, Hamiltonian Cycles, and Many-to-many k-disjoint Covering Paths

TL;DR

This paper introduces card-based zero-knowledge proof protocols for Hamiltonian cycles, Flow Free puzzles, and k-disjoint path coverings, enabling privacy-preserving verification of complex combinatorial problems.

Contribution

It presents novel, practical zero-knowledge proof protocols using standard playing cards for these specific combinatorial puzzles.

Findings

Protocols are perfectly sound and zero-knowledge.

Applicable to Hamiltonian cycles and Flow Free puzzles.

Extendable to k-disjoint path covering problems.

Abstract

In this paper we describe protocols which use a standard deck of cards to provide a perfectly sound zero-knowledge proof for Hamiltonian cycles and Flow Free puzzles. The latter can easily be extended to provide a protocol for a zero-knowledge proof of many-to-many k-disjoint path coverings.