发表机构
UCSB; UIUC; NTT Research（加州大学圣塔芭芭拉分校; 伊利诺伊大学厄巴纳-香槟分校; NTT研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明伪随机酉算子可在无量子可计算单向函数时存在，通过经典随机预言机构造安全PRU，并加强现有黑盒分离结果。
AI 中文摘要
我们首次提供了相对于经典预言机的证据，表明伪随机酉算子（PRU）可以在没有量子可计算单向函数的情况下存在。为获得此结果，我们首先证明五个独立的随机对角相位层与Hadamard变换交错排列 \[ U=F_5HF_4HF_3HF_2HF_1 \] 构成强PRU，其在自适应、受控访问酉算子及其逆、转置和复共轭下具有安全性。我们的主要结果是，当相位层使用经典随机预言机O实现时，该构造对具有对经典输入$QMA^{PH}^{O}}$决策问题的合适布尔完备化的相干访问的均匀BQP敌手仍然安全。这样的敌手可以求逆（甚至量子可计算的）单向函数，并解决相对于O定义的可高效验证的单向谜题。因此，我们的结果提供了经典预言机证据，表明PRU不蕴含量子可计算单向函数，以黑盒分离的形式呈现。我们大幅加强了Kretschmer、Qian和Tal（STOC 2025）的经典预言机结果，获得了对这些QMA辅助敌手安全的PRU。我们的构造还包含一个简单、高效的电路，该电路查询随机函数，提示了通过随机预言机启发式进行具体实现的途径。
英文摘要
We provide the first evidence relative to a classical oracle that pseudorandom unitaries (PRUs) can exist without quantum-computable one-way functions. To obtain this result, we first prove that five independent random diagonal phase layers interleaved with Hadamard transforms \[ U=F_5HF_4HF_3HF_2HF_1 \] form a strong PRU with security under adaptive, controlled access to the unitary, its inverse, transpose, and complex conjugate. Our main result is that, when the phase layers are implemented using a classical random oracle O, the construction remains secure against uniform BQP adversaries with coherent access to suitable Boolean completions of classical-input $QMA^{PH}^{O}}$ decision problems. Such an adversary can invert (even quantum-computable) one-way functions and solve efficiently verifiable one-way puzzles defined relative to O. Our result therefore provides classical-oracle evidence that PRUs do not imply quantum-computable one-way functions, in the form of a black-box separation. We substantially strengthen the classical-oracle result of Kretschmer, Qian, and Tal (STOC 2025) by obtaining PRUs secure against these QMA-aided adversaries. Our construction also consists of a simple, efficient circuit that queries a random function, suggesting a route to concrete implementation via the random-oracle heuristic.
