指数量子单向性与EFI对
Exponential Quantum One-Wayness and EFI Pairs
AI总结：
本研究定义了不可高效验证的单向态生成器（IV-OWSGs），证明其与EFI对在指数损失下等价，并建立了混合态下OWSG、IV-OWSG与EFI对之间的蕴含关系，推进了量子密码学基础原语关联的理解。
摘要：
在经典密码学中，单向函数被广泛认为是最小的计算假设。然而，当考虑量子信息时，情况更为微妙。目前有两个主要的最小假设候选：单向函数的搜索量子泛化是单向态生成器（OWSG），而判定性变体是EFI对。量子密码学中一个著名的开放问题是理解这两个原语之间的关系。Khurana和Tomer（STOC'24）最近的一项突破性结果表明，对于纯态的受限情况，OWSG蕴含EFI对。在这项工作中，我们朝着理解一般情况取得了进展。为此，我们定义了不可高效验证的单向态生成器（IV-OWSGs），其中验证算法不需要高效，并证明它们恰好等价于EFI对，但在归约中存在指数损失。重要的是，这种等价性也适用于混合态。因此，我们的工作建立了量子密码学这些基本原语之间的以下关系：（混合）OWSG =>（混合）IV-OWSG ≡_exp EFI对，其中≡_exp表示原语在指数安全性下的等价性。
英文摘要：
In classical cryptography, one-way functions are widely considered to be the minimal computational assumption. However, when taking quantum information into account, the situation is more nuanced. There are currently two major candidates for the minimal assumption: the search quantum generalization of one-way functions are one-way state generators (OWSG), whereas the decisional variant are EFI pairs. A well-known open problem in quantum cryptography is to understand how these two primitives are related. A recent breakthrough result of Khurana and Tomer (STOC'24) shows that OWSGs imply EFI pairs, for the restricted case of pure states. In this work, we make progress towards understanding the general case. To this end, we define the notion of inefficiently-verifiable one-way state generators (IV-OWSGs), where the verification algorithm is not required to be efficient, and show that these are precisely equivalent to EFI pairs, with an exponential loss in the reduction. Significantly, this equivalence holds also for mixed states. Thus our work establishes the following relations among these fundamental primitives of quantum cryptography: (mixed) OWSGs => (mixed) IV-OWSGs $\equiv_{\rm exp}$ EFI pairs, where $\equiv_{\rm exp}$ denotes equivalence up to exponential security of the primitives.
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