Quantum cryptography has shed light on the potential redundancy of one-way functions (OWFs) in certain applications, where it would otherwise be required classically. It has been revealed that many such cryptographic primitives can be constructed using the concept of pseudorandom quantum states (PRSs), which represent a potentially weaker foundational assumption. In this work, we aim to investigate and provide a more comprehensive understanding of the relationship between PRSs and OWFs. To begin, we introduce the novel notion of pseudo-deterministic one-way functions (QPD-OWFs). These are similar to conventional OWFs with the exception that the output is deterministic only with high probability. Our study demonstrates that QPD-OWFs can indeed be derived from PRSs, utilizing recent developments in the construction of pseudo-deterministic pseudorandom functions from PRSs. As a direct outcome of this revelation, we present a (many-time) digital signature scheme for classical messages with classical signatures, thereby addressing a previously unresolved question posed in Morimae and Yamakawa's work (Crypto, 2022). Furthermore, we devise a quantum public-key encryption scheme featuring reusable public-keys, constructed from pseudorandom function-like states. This contribution supersedes previous constructions, which relied on stronger assumptions or failed to ensure reusability.

翻译：量子密码学已揭示单向函数（OWF）在某些应用中可能具有冗余性，而在经典场景中这些应用本应依赖OWF。研究表明，许多此类密码学原语可通过伪随机量子态（PRS）这一潜在更弱的基础假设来构造。本文旨在更全面地探究PRS与OWF之间的关系。首先，我们引入伪确定性单向函数（QPD-OWF）的新概念——其与传统OWF相似，但输出仅以高概率保持确定性。基于PRS构造伪确定性伪随机函数的最新进展，我们证明QPD-OWF确实可以从PRS中导出。该发现直接贡献于：我们提出面向经典消息的（多次）数字签名方案（使用经典签名），从而解决了Morimae与Yamakawa（Crypto 2022）工作中遗留的未决问题。此外，我们利用类伪随机函数态构造了具备可重用公钥的量子公钥加密方案，该成果优于此前依赖于更强假设或无法保证可重用性的方案。