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：近期研究引入了密码学的"量子计算经典通信"(QCCC)范式(Chung等人)。已有证据表明单向谜题(OWPuzz)是该范式中天然的核心密码学原语(Khurana与Tomer)。作为核心原语需具备若干特征：应具备良好性质(本文中体现为可放大性、组合器与通用构造)；应能被多种其他原语推导；且应与某些实用原语类等价。本文为OWPuzz提出了组合器、正确性与安全性放大及通用构造。我们的安全性放大证明采用了从OWPuzz构造EFI的全新简洁版本(相较于Khurana和Tomer的结果)，该构造可推广至弱OWPuzz，是本文技术最复杂的部分。已知OWPuzz可由承诺方案、对称密钥加密、单向态生成器(OWSG)等重要原语推导，因此也可由伪随机态(PRS)推导。然而，我们通过证明通用OWPuzz与受限OWPuzz类(具备高效验证的OWPuzz，称为EV-OWPuzz)间的黑盒分离，排除了OWPuzz与多数这些原语的等价性。继而证明EV-OWPuzz同样可由这些原语推导，从而将其与OWPuzz分离。该分离结果同时将扩展PRS与高压缩PRS相分离，解答了Ananth等人提出的开放性问题。