One-way puzzles (OWPuzzs) introduced by Khurana and Tomer [STOC 2024] are a natural quantum analogue of one-way functions (OWFs), and one of the most fundamental primitives in ''Microcrypt'' where OWFs do not exist but quantum cryptography is possible. OWPuzzs are implied by almost all quantum cryptographic primitives, and imply several important applications such as non-interactive commitments and multi-party computations. A significant goal in the field of quantum cryptography is to base OWPuzzs on plausible assumptions that will not imply OWFs. In this paper, we base OWPuzzs on hardness of non-collapsing measurements. To that end, we introduce a new complexity class, $\mathbf{SampPDQP}$, which is a sampling version of the decision class $\mathbf{PDQP}$ introduced in [Aaronson, Bouland, Fitzsimons, and Lee, ITCS 2016]. We show that if $\mathbf{SampPDQP}$ is hard on average for quantum polynomial time, then OWPuzzs exist. $\mathbf{SampPDQP}$ is the class of sampling problems that can be solved by a classical polynomial-time algorithm that can make a single query to a non-collapsing measurement oracle, which is a ''magical'' oracle that can sample measurement results on quantum states without collapsing the states. Such non-collapsing measurements are highly unphysical operations that should be hard to realize in quantum polynomial-time. We also study upperbounds of the hardness of $\mathbf{SampPDQP}$. We introduce a new primitive, distributional collision-resistant puzzles (dCRPuzzs), which are a natural quantum analogue of distributional collision-resistant hashing [Dubrov and Ishai, STOC 2006]. We show that dCRPuzzs imply average-case hardness of $\mathbf{SampPDQP}$ (and therefore OWPuzzs as well). We also show that two-message honest-statistically-hiding commitments with classical communication and one-shot signatures [Amos, Georgiou, Kiayias, Zhandry, STOC 2020] imply dCRPuzzs.
From Worst-Case Hardness of $\mathsf{NP}$ to Quantum Cryptography via Quantum Indistinguishability Obfuscation
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；NTT Social Informatics Laboratories（NTT社会信息学实验室）；NTT Research Center for Theoretical Quantum Information（NTT理论量子信息中心）
Post-Quantum Cryptography from Quantum Stabilizer Decoding
Massachusetts Institute of Technology（麻省理工学院）；Boston University（波士顿大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；California Institute of Technology（加州理工学院）
QUBO Modeling of Module Learning With Errors: Stability and Scaling in Post-Quantum Cryptography
D Y Patil International University（D Y Patil 国际大学）；Birla Institute of Technology and Science Pilani, Dubai（比拉理工学院皮拉尼分校，迪拜）；QbitForce Quantum Pvt. Ltd.（QbitForce 量子私人有限公司）；SRM University-AP（SRM 大学安得拉邦校区）；University of Stuttgart（斯图加特大学）
A Practically Scalable Approach to the Closest Vector Problem for Sieving via QAOA with Fixed Angles
Department of Computer Science, University of Oxford（牛津大学计算机科学系）；Quantum Software Lab, School of Informatics, University of Edinburgh（爱丁堡大学信息学院量子软件实验室）
On the practicality of quantum sieving algorithms for the shortest vector problem
HUN-REN Alfréd Rényi Institute of Mathematics（匈牙利科学院阿尔弗雷德·雷尼数学研究所）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；David R. Cheriton School of Computer Science, University of Waterloo（滑铁卢大学大卫R.切里顿计算机科学学院）
