A fundamental result in classical cryptography is that pseudorandom generators are equivalent to one-way functions and in fact implied by nearly every classical cryptographic primitive requiring computational assumptions. In this work, we consider a variant of pseudorandom generators called quantum pseudorandom generators (QPRGs), which are quantum algorithms that (pseudo)deterministically map short random seeds to long pseudorandom strings. We provide evidence that QPRGs can be as useful as PRGs by providing cryptographic applications of QPRGs such as commitments and encryption schemes. Our main result is showing that QPRGs can be constructed assuming the existence of logarithmic-length quantum pseudorandom states. This raises the possibility of basing QPRGs on assumptions weaker than one-way functions. We also consider quantum pseudorandom functions (QPRFs) and show that QPRFs can be based on the existence of logarithmic-length pseudorandom function-like states. Our primary technical contribution is a method for pseudodeterministically extracting uniformly random strings from Haar-random states.

翻译：经典密码学的一个基本结论是，伪随机生成器等价于单向函数，实际上几乎所有需要计算假设的经典密码学原语都隐含这一结论。本文研究了一种名为量子伪随机生成器（QPRGs）的伪随机生成器变体，这是一种（伪）确定性量子算法，可将短随机种子映射到长伪随机字符串。我们通过展示QPRGs在承诺方案和加密方案等密码学应用中的价值，提供了QPRGs可与PRGs同样有用的证据。我们的主要结果表明，假设存在对数长度的量子伪随机态，即可构造QPRGs。这引发了基于比单向函数更弱的假设来构建QPRGs的可能性。我们还考虑了量子伪随机函数（QPRFs），并证明QPRFs可基于存在对数长度的伪随机函数态来构造。本文的核心技术贡献在于提出了一种从Haar随机态中伪确定性提取均匀随机字符串的方法。