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This paper explores the applications of structured  and presents several results: We construct efficiently samplable, statistically far but computationally indistinguishable pairs of distributions ( pairs) from secretly-verifiable  with somewhat injectivity, which has implications for quantum commitment schemes; We demonstrate that somewhat injective  can be derived from almost regular ; We also focus on a specific type of , termed , and prove that the existence of a single-copy-secure hard-core predicate for these  is both necessary and sufficient for constructing  pairs; Moreover, we propose a simple quantum commitment scheme based on the decisional  assumption, offering improved parameter choices and flexibility over classical schemes. These findings contribute to the understanding and potential applications of  in quantum cryptography.<\/jats:p>","DOI":"10.1186\/s42400-024-00316-7","type":"journal-article","created":{"date-parts":[[2025,5,5]],"date-time":"2025-05-05T01:02:54Z","timestamp":1746406974000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantum commitments from structured one-way quantum state generators, and more"],"prefix":"10.1186","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0278-0923","authenticated-orcid":false,"given":"Shujiao","family":"Cao","sequence":"first","affiliation":[]},{"given":"Rui","family":"Xue","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,5]]},"reference":[{"key":"316_CR1","doi-asserted-by":"publisher","unstructured":"Adcock M, Cleve R (2002) A quantum goldreich-levin theorem with cryptographic applications. 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