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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