Different flavors of quantum pseudorandomness have proven useful for various cryptographic applications, with the compelling feature that these primitives are potentially weaker than post-quantum one-way functions. Ananth, Lin, and Yuen (2023) have shown that logarithmic pseudorandom states can be used to construct a pseudo-deterministic PRG: informally, for a fixed seed, the output is the same with $1-1/poly$ probability. In this work, we introduce new definitions for $\bot$-PRG and $\bot$-PRF. The correctness guarantees are that, for a fixed seed, except with negligible probability, the output is either the same (with probability $1-1/poly$) or recognizable abort, denoted $\bot$. Our approach admits a natural definition of multi-time PRG security, as well as the adaptive security of a PRF. We construct a $\bot$-PRG from any pseudo-deterministic PRG and, from that, a $\bot$-PRF. Even though most mini-crypt primitives, such as symmetric key encryption, commitments, MAC, and length-restricted one-time digital signatures, have been shown based on various quantum pseudorandomness assumptions, digital signatures remained elusive. Our main application is a (quantum) digital signature scheme with classical public keys and signatures, thereby addressing a previously unresolved question posed in Morimae and Yamakawa's work (Crypto, 2022). Additionally, we construct CPA secure public-key encryption with tamper-resilient quantum public keys.

翻译：量子伪随机性的不同变体已被证明对各种密码学应用具有价值，其引人注目的特点在于这些原语可能弱于后量子单向函数。Ananth、Lin和Yuen（2023）的研究表明，对数伪随机态可用于构建伪确定性伪随机数生成器：非正式地说，对于固定种子，输出以$1-1/poly$的概率保持相同。在本工作中，我们为⊥-伪随机数生成器和⊥-伪随机函数引入了新的定义。其正确性保证是：对于固定种子，除可忽略概率外，输出要么以$1-1/poly$的概率保持相同，要么可识别地中止（记为⊥）。我们的方法自然地支持多轮次伪随机数生成器安全性的定义，以及伪随机函数的自适应安全性。我们从任意伪确定性伪随机数生成器构造出⊥-伪随机数生成器，并基于此构建⊥-伪随机函数。尽管大多数微型密码原语（如对称密钥加密、承诺、消息认证码和长度受限的一次性数字签名）已基于各种量子伪随机性假设得以构建，但数字签名方案始终难以实现。我们的主要应用是构建具有经典公钥和签名的（量子）数字签名方案，从而解决了Morimae和Yamakawa（Crypto，2022）工作中提出的未决问题。此外，我们还构建了具有抗篡改量子公钥的选择明文攻击安全公钥加密方案。