Balance-Based ZKP Protocols for Pencil-and-Paper Puzzles
Résumé
In this paper, we propose zero-knowledge proof (ZKP) protocols using physical objects for four pencil-and-paper puzzles: the wellknown
Sudoku as well as Makaro, Futoshiki, and Kakuro. That is, our protocols allow a prover to convince a verifier that the prover knows a solution to a puzzle without relying on the use of computers. While previous physical ZKP protocols for puzzles have mainly relied on decks of cards, our research introduces a novel approach utilizing a balance scale and coins to design balance-based ZKP protocols; moreover we show its flexibility by adapting it to the four different puzzles. We compare the number of coins and operations in our protocols with the existing cardbased protocols and show that, for certain puzzles, our balance-based protocol outperforms the card-based method. Finally, we prove that our protocols achieve perfect completeness, perfect soundness and are perfectly zero-knowledge.
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