Quantum Fourier sampling limits for physical unclonable functions security
Where Quantum Fourier Sampling Stops Short: A Three-Gate Audit Protocol for Delay-PUF Security Models
Cryptography and SecurityMachine Learning
Summary
Physical unclonable functions (PUFs) are devices designed to create unique fingerprints for security. The authors explore whether quantum computing techniques, especially quantum Fourier sampling, can effectively audit or break these fingerprints. They find that certain quantum approaches do not provide a clear advantage over classical methods in realistic settings. The paper introduces a clear protocol to separate theoretical quantum benefits from practical security gains.
What this means in practice
- •For hardware security engineers: Evaluate the practical limits of quantum attacks on delay-based physical unclonable functions using the Three-Gate Quantum Audit Protocol.
- •For quantum algorithm developers: Design and benchmark quantum phase oracles for cryptographic functions while accounting for realistic noise and hardware constraints.
Authors
Owen Friedewald, Ali Shiri Sichani, Chi-Ren Shyu
Abstract
Quantum Fourier sampling may help audit the spectral learnability of delay-based physical unclonable functions (PUFs). We ask whether that promise survives access matching, a strong classical comparator, and oracle synthesis. Three gates structure the evaluation. Structure: low degree is not small support at reachable challenge lengths; for 4-XOR at $n=14$, degree $\le d_f(0.1)$ admits $91\%$ of all $2^n$ characters and the median $90\%$-mass set spans a third of the spectrum. Algorithmics: constructing the phase oracle logically implies classical membership access, making Kushilevitz--Mansour the correct baseline; across 45 tasks it exhausts each finite domain, and no 4-XOR ideal-sampling case reaches $90\%$ mass within $2^n$ calls. A quantum-kernel diagnostic appears more favorable, with geometric difference rising to $2.151$ at $N=512$ challenges, but it correlates $0.991$ with $1/\sqrt{λ_{\min}(K_C)}$ for the classical Gram matrix $K_C$, and the 4-XOR label-complexity ratio does not exceed a balance-preserving permutation null ($p=0.930$). Trace-normalized geometric difference can therefore grow through classical ill-conditioning alone, without task-label alignment. Implementation: a simulator-validated fixed-point phase oracle based on the quantum Fourier transform admits an $18.9\%$ routed-depth reduction, yet the least certified precisions have estimated durations of $1.18$--$1.55\times$ the median dephasing time $T_2$ of the mapped qubits on a static backend snapshot, without hardware execution. We find no end-to-end advantage in the evaluated regime, although ideal sampling does use fewer coherent calls on the thresholded task. The contribution is the Three-Gate Quantum Audit Protocol: a reproducible procedure separating an ideal query advantage from a realizable security benefit. This is not a claim about deployed silicon and not an impossibility result.