Physical Zero-Knowledge Proof for Connected Spanning Subgraph Problem and Bridges Puzzle
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An undirected graph G is known to both the prover P and the verifier V, but only P knows a subgraph H of G. P wants to convince V that H is a connected spanning subgraph of G, i.e. H is connected and contains all vertices of G, without revealing any information about H to V. In this paper, we propose a physical protocol of zero-knowledge proof for this problem using a deck of cards, which enables P to physically show that H satisfies the condition without revealing it. We also show one possible application of this protocol to verify a solution of a famous logic puzzle called Bridges.
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