Quantum Physical Unclonable Function based on Chaotic Hamiltonians

TL;DR

This work addresses secure hardware-based cryptographic primitives by replacing impractical Haar-random unitaries with chaotic Hamiltonian dynamics to realize Quantum Physical Unclonable Functions (QPUFs). It proves that a chaotic QPUF via U(t)=exp(-iHt) achieves comparable security to Haar-based QPUFs, with the required evolution time scaling linearly with the number of qudits and remaining publicly verifiable. The authors establish selective unforgeability for chaotic QPUFs and MB-QPUFs, and propose two practical implementations: a physical SYK-based design and a pseudo-chaotic variant for scenarios with limited adversarial access. They also outline a Kagome-lattice architecture for SYK-inspired devices and discuss resource estimates, experimental feasibility, and future directions, bridging theoretical security with practical realization.

Abstract

Quantum Physical Unclonable Functions (QPUFs) are hardware-based cryptographic primitives with strong theoretical security. This security stems from their modeling as Haar-random unitaries. However, implementing such unitaries on Intermediate-Scale Quantum devices is challenging due to exponential simulation complexity. Previous work tackled this using pseudo-random unitary designs but only under limited adversarial models with only black-box query access. In this paper, we propose a new QPUF construction based on chaotic quantum dynamics. We modeled the QPUF as a unitary time evolution under a chaotic Hamiltonian and proved that this approach offers security comparable to Haar-random unitaries. Intuitively, we show that while chaotic dynamics generate less randomness than ideal Haar unitaries, the randomness is still sufficient to make the QPUF unclonable in polynomial time. Moreover, we show that the evolution time required to achieve security scales linearly with number of qudits used in the scheme and can be kept public. We identified the Sachdev-Ye-Kitaev (SYK) model as a candidate for the QPUF Hamiltonian. Recent experiments using nuclear spins and cold atoms have shown progress toward achieving this goal. Inspired by recent experimental advances, we present a schematic architecture for realizing our proposed QPUF device based on optical Kagome Lattice with disorder. For adversaries with only query access, we also introduce an efficiently simulable pseudo-chaotic QPUF. Our results lay the preliminary groundwork for bridging the gap between theoretical security and the practical implementation of QPUFs for the first time.

Figures (5)

• Figure 1: Selective Unforgeability. In the enrollment phase, the verifier and the adversary collect and store information from the QPUF device by querying it. Then, the QPUF device is handed over to the honest prover. In the verification phase, the verifier sends a challenge state and the adversary attempts to send back the correct response. The validity of the response is measured by a SWAP TestSWAP_Mina.
• Figure 2: Single Round verification with $M$ trials. The query phases describes how the verifier stores $M$ Choi states of the QPUF $U$ and transfers the device to the prover. The verification phase describes, the challenge generation via measurements and subsequent verification with SWAP test. This figure is taken from Ghosh2024.
• Figure 3: Level spacing statistics. The spacing between the $p^{\text{th}}$ and $(p+1)^{\text{th}}$ energy levels is denoted by $S_p$.
• Figure 4: QPUF device architecture. The left panel displays the external view, highlighting user controls and interface elements, while the right panel shows the internal view, detailing the underlying operational components.
• Figure 5: Qubit case: Number of qubits of the QPUF system ($\lambda$) as a function of the adversary’s success probability $p$ in forging the QPUF, where $\lambda = -\log_2(p)$.

Theorems & Definitions (9)

• Definition 1: Selective Unforgeability
• Definition 2: Measurement Selective Unforgeability
• Theorem 1: Measurement Selective Unforgeability Ghosh2024
• Remark 2
• Theorem 3: Measurement Selective Unforgeability
• proof
• Theorem 4
• proof
• Definition 3: Pseudo-Chaotic Hamiltonian Ensemble