While in classical cryptography, one-way functions (OWFs) are widely regarded as the "minimal assumption," the situation in quantum cryptography is less clear. Recent works have put forward two concurrent candidates for the minimal assumption in quantum cryptography: One-way state generators (OWSGs), postulating the existence of a hard search problem with an efficient verification algorithm, and EFI pairs, postulating the existence of a hard distinguishing problem. Two recent papers [Khurana and Tomer STOC'24; Batra and Jain FOCS'24] showed that OWSGs imply EFI pairs, but the reverse direction remained open. In this work, we give strong evidence that the opposite direction does not hold: We show that there is a quantum unitary oracle relative to which EFI pairs exist, but OWSGs do not. In fact, we show a slightly stronger statement that holds also for EFI pairs that output classical bits (QEFID). As a consequence, we separate, via our oracle, QEFID, and one-way puzzles from OWSGs and several other Microcrypt primitives, including efficiently verifiable one-way puzzles and unclonable state generators. In particular, this solves a problem left open in [Chung, Goldin, and Gray Crypto'24]. Using similar techniques, we also establish a fully black-box separation (which is slightly weaker than an oracle separation) between private-key quantum money schemes and QEFID pairs. One conceptual implication of our work is that the existence of an efficient verification algorithm may lead to qualitatively stronger primitives in quantum cryptography.

翻译：在经典密码学中，单向函数（OWFs）被广泛视为“最小假设”，但量子密码学中的情况则不甚明朗。近期研究提出了量子密码学中两个并行的最小假设候选方案：单向态生成器（OWSGs）——假设存在具有高效验证算法的困难搜索问题；以及EFI对——假设存在困难的区分问题。最近的两篇论文[Khurana and Tomer STOC'24; Batra and Jain FOCS'24]表明OWSGs可推导出EFI对，但反向关系仍未解决。本工作给出了反向关系不成立的强有力证据：我们证明存在一个量子酉预言机，使得EFI对存在而OWSGs不存在。实际上，我们证明了一个稍强的结论，该结论对于输出经典比特的EFI对（QEFID）同样成立。由此，我们通过该预言机实现了QEFID与单向谜题从OWSGs及若干其他微密码学原语（包括高效可验证单向谜题与不可克隆态生成器）的分离。这特别解决了[Chung, Goldin, and Gray Crypto'24]中遗留的开放问题。运用类似技术，我们还建立了私钥量子货币方案与QEFID对之间的完全黑盒分离（该结果略弱于预言机分离）。本工作的一个概念性启示是：高效验证算法的存在可能导致量子密码学中产生质变性的更强原语。