We show new constructions for pseudorandom quantum states (PRS) and pseudorandom function-like quantum state (PRFS) generators satisfying scalability, which means the security parameter can be much larger than the number of qubits, quantum accessibility, which means the adversary can provide quantum input, and adaptivity, which means the adversary can query it adaptively. We present an isometric procedure to prepare quantum states that can be arbitrarily random (i.e., the trace distance from the Haar-random state can be arbitrarily small for the true random case, or the distinguishing advantage can be arbitrarily small for the pseudorandom case). This naturally gives the first construction for scalable, quantum-accessible, and adaptive PRFS assuming quantum-secure one-way functions. Compared to prior PRFS works, we use a stronger definition of quantum accessibility in which the adversary can be ancilla-assisted, i.e., the input state may not be pure and could be entangled with other quantum registers. Thus, our result also gives the first (fully) quantum-accessible PRFS. Our PRFS construction implies various primitives, including long-input PRFS, short-input PRFS, short-output PRFS, non-adaptive PRFS, and classically-accessible adaptive PRFS. This new construction may be helpful in simplifying the microcrypt zoo.

翻译：我们提出了满足可扩展性（即安全参数可远大于量子比特数）、量子可访问性（即敌手可提供量子输入）和自适应性（即敌手可进行自适应查询）的伪随机量子态及类伪随机函数量子态生成器的新构造。我们提出了一种等距过程来制备可任意随机的量子态（对于真随机情形，其与哈尔随机态的迹距离可任意小；对于伪随机情形，其区分优势可任意小）。这自然给出了首个基于量子安全单向函数的可扩展、量子可访问且自适应的类伪随机函数构造。与先前类伪随机函数研究相比，我们采用了更强的量子可访问性定义，允许敌手进行辅助辅助操作，即输入态不必是纯态且可能与其他量子寄存器纠缠。因此，我们的结果也给出了首个（完全）量子可访问的类伪随机函数。我们的类伪随机函数构造可推导出多种原语，包括长输入类伪随机函数、短输入类伪随机函数、短输出类伪随机函数、非自适应类伪随机函数以及经典可访问的自适应类伪随机函数。这一新构造可能有助于简化微观密码学体系。