Abstract
We propose a new technique to construct physical Zero-Knowledge Proof (ZKP) protocols for games that require a single loop draw feature. This feature appears in Slitherlink, a puzzle by Nikoli. Our approach is based on the observation that a loop has only one hole and this property remains stable by some simple transformations. Using this trick, we can transform a simple big loop, visible to anyone, into the solution loop by using transformations that do not disclose any information about the solution. As a proof of concept, we apply this technique to construct the first physical ZKP protocol for Slitherlink.
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Notes
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In the above example, the bottom edge corresponds to the pile which is 4 piles away from the chosen pile. Note that the distance between any two piles never changes because only Pile-Shifting Shuffle is applied.
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Acknowledgement
We thank the anonymous referees, whose comments have helped us to improve the presentation of the paper. This work was supported by JSPS KAKENHI Grant Number JP17K00001 and JP19J21153.
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Lafourcade, P., Miyahara, D., Mizuki, T., Sasaki, T., Sone, H. (2019). A Physical ZKP for Slitherlink: How to Perform Physical Topology-Preserving Computation. In: Heng, SH., Lopez, J. (eds) Information Security Practice and Experience. ISPEC 2019. Lecture Notes in Computer Science(), vol 11879. Springer, Cham. https://doi.org/10.1007/978-3-030-34339-2_8
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