Quantum commitments from structured one-way quantum state generators, and more

Abstract One-way quantum state generators (), which serve as the quantum analog of one-way functions (), have attracted significant interest due to their potential applications and the reduced assumption requirements compared to . 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.