Quantum Cryptography and Hardness of Non-Collapsing Measurements

2025-10-05

AI Summary

How can one construct one-way puzzles (OWPuzzs) based solely on the computational hardness of non-collapsing measurements, without relying on classical one-way function (OWF) assumptions? Method: We introduce the complexity class SampPDQP to characterize average-case hardness of quantum sampling, define distributed collision-resistant puzzles (dCRPuzzs), and design classical-quantum hybrid protocols within a non-collapsing measurement oracle model. Contribution: We provide the first proof that average-case hardness of SampPDQP implies the existence of OWPuzzs. Furthermore, we establish bidirectional reductions between dCRPuzzs and several existing quantum cryptographic primitives—including quantum signatures and quantum zero-knowledge proofs—thereby laying a new theoretical foundation and offering practical construction pathways for OWF-free quantum cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

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.

Problem

• Establishing quantum one-way puzzles based on non-collapsing measurement hardness
• Introducing SampPDQP complexity class for sampling with non-collapsing oracles
• Linking distributional collision-resistant puzzles to average-case SampPDQP hardness

Innovation

• Bases OWPuzzs on hardness of non-collapsing measurements
• Introduces SampPDQP class for sampling with non-collapsing oracle
• Shows dCRPuzzs imply average-case hardness of SampPDQP