发表机构
Freie Universität Berlin; Helmholtz-Zentrum Berlin für Materialien und Energie; Fraunhofer Heinrich Hertz Institute; Massachusetts Institute of Technology; Simons Institute for the Theory of Computing, University of California at Berkeley; ETH Zürich; Technische Universität Wien; Vienna Center for Quantum Science and Technology, TU Wien; Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences; African Institute for Mathematical Sciences (AIMS); Stellenbosch University; National Institute for Theoretical and Computational Sciences (NITheCS)（柏林自由大学; 柏林亥姆霍兹材料能源中心; 弗劳恩霍夫海因里希赫兹研究所; 麻省理工学院; 加州大学伯克利分校西蒙斯计算理论研究所; 苏黎世联邦理工学院; 维也纳工业大学; 维也纳量子科学与技术中心，维也纳工业大学; 奥地利科学院量子光学与量子信息研究所; 非洲数学科学研究所; 斯坦伦布什大学; 国家理论与计算科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究否证了HPS假设可在无单向函数下成立，证明其蕴含单向函数，并通过定制态认证协议为构建单向谜题提供新方法。
AI 中文摘要
近期工作引入了哈密顿相位态（HPS）假设，该假设认为哈密顿相位态可用于实例化伪随机态生成器和单向态生成器。此外，有人推测即使单向函数不存在，这些假设也可能成立。这令人兴奋，因为如果成立，HPS假设将为Microcrypt的实例化提供一条路径。在本工作中，我们通过证明若HPS假设成立则单向函数存在，从而否证了这一推测。虽然这排除了使用哈密顿相位态实例化真正Microcrypt密码学的可能性，但它表明HPS假设为经典密码学的构建提供了新颖的固有量子假设。在技术上，我们通过一种从单向态生成器和定制的“先测量后询问”态认证协议构建单向谜题的方法实现了这一点。这推广了先前通过经典阴影从单向态生成器构建单向谜题的方法，并使我们能够将单向谜题的性质与构建中使用的态认证协议的性质联系起来。具体而言，若态认证协议允许高效的经典后处理，则获得可高效验证的单向谜题；若态认证协议在某种意义下可被高效经典模拟，则获得经典单向谜题，这蕴含单向函数。后一观察使我们能够利用相位态的态认证协议的性质来证明HPS假设蕴含单向函数。前一观察为通过利用针对伪随机和单向态生成器的定制态认证协议构建可高效验证的单向谜题提供了新工具包。
英文摘要
Recent work has introduced the Hamiltonian phase state (HPS) assumptions, which postulate that Hamiltonian phase states can be used to instantiate pseudorandom and one-way state generators. Additionally, it has been conjectured that these assumptions can be true, even if one-way functions do not exist. This is exciting, because if true, then the HPS assumptions provide a route to the instantiation of Microcrypt. In this work we falsify this conjecture, by proving that if the HPS assumptions are true, then one-way functions exist. While this removes the possibility of instantiating genuine Microcrypt cryptography with Hamiltonian phase states, it shows that the HPS assumptions provide novel inherently quantum assumptions for the construction of classical cryptography. Technically we achieve this via a method for the construction of one-way puzzles from one-way state generators and tailored "measure first, ask later" state certification protocols. This generalizes prior constructions of one-way puzzles from one-way state generators via classical shadows and allows us to relate properties of the one-way puzzle to properties of the state certification protocol used in the construction. Specifically, if the state certification protocol admits efficient classical post-processing then one obtains an efficiently verifiable one-way puzzle, and if the state certification protocol can be efficiently classically simulated in a certain sense, then one obtains a classical one-way puzzle, which implies one-way functions. The latter observation allows us to prove that the HPS assumptions imply one-way functions, by exploiting properties of state certification protocols for phase states. The former observation provides a new toolbox for the construction of efficiently verifiable one-way puzzles by exploiting tailored state certification protocols for pseudorandom and one-way state generators.
Comments52 pages, 2 figures
