构建量子密码学中对相干访问的需求
Need for Coherent Access in Constructing Quantum Cryptography
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- KAIST（韩国科学技术院）
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中文总结 AI 辅助
本研究构造量子预言机，证明经典可访问预言机下量子安全单向函数存在但超对数长度伪随机态不存在，揭示构建伪随机态需相干访问，并给出对数与超对数长度伪随机态间的预言机分离。
中文摘要 AI 辅助
我们构造了量子预言机，相对于这些预言机，量子安全单向函数（OWFs）存在，但输出长度超对数的伪随机态（PRSs）不存在。乍一看，这似乎与已知的基于量子安全OWFs的PRS生成器的黑盒构造相矛盾。区别在于对预言机的访问模型；我们的预言机分离使用了经典可访问的随机预言机，即使量子算法也只能经典地访问这些预言机。事实上，我们的PRS不可能性适用于替代随机预言机的任何经典可访问的经典预言机，同时保持其他预言机组件不变，这表明在构建PRS时需要相干访问。我们进一步表明，相对于我们的预言机，存在对数输出长度的伪随机函数态（PRFSs），从而在经典可访问的对数长度PRFSs和超对数长度PRSs之间给出了预言机分离。这表明，从对数到超对数输出长度的完全黑盒PRS长度扩展必须对底层短PRS使用相干访问。
英文摘要
We construct quantum oracles relative to which quantum-secure one-way functions (OWFs) exist but pseudorandom states (PRSs) with superlogarithmic output length do not. At first glance, this appears to contradict the known black-box constructions of PRS generators from quantum-secure OWFs. The distinction lies in the access model to the oracles; our oracle separation uses \emph{classical-accessible} random oracles that can be accessed only classically even by quantum algorithms. In fact, our impossibility of PRSs applies to \emph{any} classically accessible classical oracle in place of the random oracle, while keeping the other oracle component unchanged, showing the need for coherent access in constructing PRSs. We further show that logarithmic output length pseudorandom function-like states (PRFSs) exist relative to our oracles, giving an oracle separation between classically accessible logarithmic length PRFSs and superlogarithmic length PRSs. This shows that fully black-box PRS length extension from logarithmic to superlogarithmic output length must use coherent access to the underlying short PRS.
