Recent work has introduced the "Quantum-Computation Classical-Communication" (QCCC) (Chung et. al.) setting for cryptography. There has been some evidence that One Way Puzzles (OWPuzz) are the natural central cryptographic primitive for this setting (Khurana and Tomer). For a primitive to be considered central it should have several characteristics. It should be well behaved (which for this paper we will think of as having amplification, combiners, and universal constructions); it should be implied by a wide variety of other primitives; and it should be equivalent to some class of useful primitives. We present combiners, correctness and security amplification, and a universal construction for OWPuzz. Our proof of security amplification uses a new and cleaner version construction of EFI from OWPuzz (in comparison to the result of Khurana and Tomer) that generalizes to weak OWPuzz and is the most technically involved section of the paper. It was previously known that OWPuzz are implied by other primitives of interest including commitments, symmetric key encryption, one way state generators (OWSG), and therefore pseudorandom states (PRS). However we are able to rule out OWPuzz's equivalence to many of these primitives by showing a black box separation between general OWPuzz and a restricted class of OWPuzz (those with efficient verification, which we call EV-OWPuzz). We then show that EV-OWPuzz are also implied by most of these primitives, which separates them from OWPuzz as well. This separation also separates extending PRS from highly compressing PRS answering an open question of Ananth et. al.

翻译：近期研究在密码学中引入了"量子计算-经典通信"（Quantum-Computation Classical-Communication，QCCC）框架（Chung 等人）。已有证据表明，单程谜题（One Way Puzzles，OWPuzz）是该框架下的自然核心密码原语（Khurana 和 Tomer）。一个原语若要被视为核心，应具备若干特征：行为良好（本文中具体表现为具有放大性、组合器和通用构造）；能被多种其他原语蕴含；应与某类实用原语等价。我们为 OWPuzz 提出了组合器、正确性与安全性放大方案及通用构造。其中安全性放大的证明采用了基于 OWPuzz 构建 EFI 的全新简化版本（相较于 Khurana 和 Tomer 的结果），该方案可推广至弱 OWPuzz，是本文技术性最强的部分。此前已知 OWPuzz 可被承诺方案、对称密钥加密、单程态生成器（One Way State Generator，OWSG）及由此衍生的伪随机态（Pseudorandom States，PRS）等原语所蕴含。但通过证明通用 OWPuzz 与受限类 OWPuzz（具有高效验证性的 EV-OWPuzz）之间存在黑盒分离，我们排除了 OWPuzz 与上述多种原语的等价性。进一步研究表明，EV-OWPuzz 同样能被这些原语蕴含，从而实现了 OWPuzz 与 EV-OWPuzz 的分离。该分离同时将扩展型 PRS 与高压缩型 PRS 区分开，回应了 Ananth 等人提出的开放问题。