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A drawback of their protocol is that it requires additional verifications to guarantee a single loop. In this study, we propose a more efficient ZKP protocol for such a puzzle with fewer additional verifications. For this, we employ the previous work of Robert et al., which addressed the connectivity property in a puzzle. That is, we verify that a solution is connected but not split, to be a single loop. Applying our proposal, we construct a card-based ZKP protocol for Moon-or-Sun, which has its specific rule of alternating pattern in addition to the single-loop condition.<\/jats:p>","DOI":"10.1007\/s00354-024-00274-1","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T15:02:39Z","timestamp":1724079759000},"page":"449-477","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Efficient Card-Based ZKP for Single Loop Condition and Its Application to Moon-or-Sun"],"prefix":"10.1007","volume":"42","author":[{"given":"Samuel","family":"Hand","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Koch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascal","family":"Lafourcade","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5818-8937","authenticated-orcid":false,"given":"Daiki","family":"Miyahara","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L\u00e9o","family":"Robert","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,19]]},"reference":[{"key":"274_CR1","unstructured":"Bultel, X., Dreier, J., Dumas, J., et\u00a0al.: Physical zero-knowledge proofs for Akari, Takuzu, Kakuro and KenKen. 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