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Physical Review Research

Existential unforgeability in quantum authentication from quantum physical unclonable functions based on random von Neumann measurement

Soham S. Ghosh, Vladlen Galetsky, Pol Juliá Farré, Christian Deppe, Roberto Ferrara, Holger Boche

Published Dec 23, 2024• 6 citations
Publisher

Abstract

Physical unclonable functions (PUFs) leverage inherent, nonclonable physical randomness to generate unique input-output pairs, serving as secure fingerprints for cryptographic protocols like authentication. Quantum PUFs (QPUFs) extend this concept by using quantum states as input-output pairs, offering advantages over classical PUFs, such as challenge reusability via public channels and eliminating the need for trusted parties due to the no-cloning theorem. Recent work introduced a generalized mathematical framework for QPUFs. It was shown that random unitary QPUFs cannot achieve existential unforgeability against quantum polynomial time (QPT) adversaries. Security was possible only with additional uniform randomness. To avoid the cost of external randomness, we propose a novel measurement-based scheme. Here, the randomness naturally arises from quantum measurements. Additionally, we introduce a second model where the QPUF functions as a nonunitary quantum channel, which guarantees existential unforgeability. These are the first models in the literature to demonstrate a high level of provable security. Finally, we show that the quantum phase estimation (QPE) protocol, applied to a Haar random unitary, serves as an approximate implementation of the second type of QPUF by approximating a von Neumann measurement on the unitary's eigenbasis. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.043306

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Physical unclonable functions (PUFs) leverage inherent, nonclonable physical randomness to generate unique input-output pairs, serving as secure fingerprints for cryptographic protocols like authentication. Quantum PUFs (QPUFs) extend this concept by using quantum states as input-output pairs, offering advantages over classical PUFs, such as challenge reusability via public channels and eliminating the need for trusted parties due to the no-cloning theorem. Recent work introduced a generalized mathematical framework for QPUFs. It was shown that random unitary QPUFs cannot achieve existential unforgeability against quantum polynomial time (QPT) adversaries. Security was possible only with additional uniform randomness. To avoid the cost of external randomness, we propose a novel measurement-based scheme. Here, the randomness naturally arises from quantum measurements. Additionally, we introduce a second model where the QPUF functions as a nonunitary quantum channel, which guarantees existential unforgeability. These are the first models in the literature to demonstrate a high level of provable security. Finally, we show that the quantum phase estimation (QPE) protocol, applied to a Haar random unitary, serves as an approximate implementation of the second type of QPUF by approximating a von Neumann measurement on the unitary's eigenbasis. Published by the American Physical Society 2024
Physical Unclonable Functions (PUFs) are hardware devices with the assumption of possessing inherent, non-clonable physical randomness which leads to unique pairs of inputs and outputs that provide a secure fingerprint for cryptographic protocols like Authentication. In the case of quantum PUFs (QPUFs), the input-output pairs consists of quantum states instead of classical bitstrings, offering advantages over classical PUFs (CPUFs) such as challenge reusability via public channels and non-reliance over any trusted party due to the no-cloning theorem. In recent literature, a generalized mathematical frame-work for studying QPUFs was developed, which paved the way for having QPUF models with provable security. It was proved that existential unforgeability against Quantum Polynomial Time (QPT) adversaries cannot be achieved by any random unitary QPUF. Since measurements are non-unitary quantum processes, we define a QPUF based on random von Neumann measurements. We prove that such a QPUF is existentially unforgeable. Thus, we introduce the first model in existing literature that depicts such a high level of provable security. We also prove that the Quantum Phase Estimation (QPE) protocol applied on a Haar random unitary serves as an approximate implementation for this kind of QPUF as it approximates a von Neumann measurement on the eigenbasis of the unitary.
Physical Unclonable Functions (PUFs) provide hardware-level security by exploiting intrinsic randomness to produce device-unique responses. However, machine learning and side-channel attacks increasingly undermine their classical assumptions, calling for new approaches to ensure unforgeability. Quantum mechanics naturally supports this goal through intrinsic randomness and the no-cloning theorem, motivating the study of Quantum Physical Unclonable Functions (QPUFs). Yet, existing QPUF models often assume ideal unitary dynamics, neglecting non-unitary effects such as decoherence and dissipation that arise in real quantum devices. This work introduces a new class of non-unitary QPUFs that leverage open quantum system dynamics as a foundation for security. Three architectures are proposed: the Dissipative QPUF (D-QPUF), which uses amplitude damping as an entropy source; the Measurement-Feedback QPUF (MF-QPUF), which employs mid-circuit measurements and conditional unitaries; and the Lindbladian QPUF (L-QPUF), which models Markovian noise via the Lindblad master equation and Trotter-Suzuki decomposition. Simulation results show that these non-unitary designs achieve strong uniqueness, uniformity, and unforgeability, with controllable reliability trade-offs from stochastic noise. The L-QPUF, in particular, exhibits exponential modeling resistance under limited challenge-response access. By reframing environmental noise as a constructive resource, this work establishes a framework for noise-aware quantum hardware authentication and highlights non-unitary evolution as a viable foundation for post-quantum security.
A Physical Unclonable Function (PUF) is a device with unique behaviour that is hard to clone hence providing a secure fingerprint. A variety of PUF structures and PUF-based applications have been explored theoretically as well as being implemented in practical settings. Recently, the inherent unclonability of quantum states has been exploited to derive the quantum analogue of PUF as well as new proposals for the implementation of PUF. We present the first comprehensive study of quantum Physical Unclonable Functions (qPUFs) with quantum cryptographic tools. We formally define qPUFs, encapsulating all requirements of classical PUFs as well as introducing a new testability feature inherent to the quantum setting only. We use a quantum game-based framework to define different levels of security for qPUFs: quantum exponential unforgeability, quantum existential unforgeability and quantum selective unforgeability. We introduce a new quantum attack technique based on the universal quantum emulator algorithm of Marvin and Lloyd to prove no qPUF can provide quantum existential unforgeability. On the other hand, we prove that a large family of qPUFs (called unitary PUFs) can provide quantum selective unforgeability which is the desired level of security for most PUF-based applications.
Quantum Physical Unclonable Functions (QPUFs) offer a physically grounded approach to secure authentication, extending the capabilities of classical PUFs. This review covers their theoretical foundations and key implementation challenges—such as quantum memories and Haar‐randomness—, and distinguishes QPUFs from Quantum Readout PUFs (QR‐PUFs), more experimentally accessible yet less robust against quantum‐capable adversaries. A co‐citation‐based selection method is employed to trace the evolution of QPUF architectures, from early QR‐PUFs to more recent Hybrid PUFs (HPUFs). This method further supports a discussion on the role of information‐theoretic analysis in mitigating inconsistencies in QPUF responses, underscoring the deep connection between secret‐key generation and authentication. Despite notable advances, achieving practical and robust QPUF‐based authentication remains an open challenge.
With the increase of digital devices, the need for robust authentication mechanisms has become crucial. Traditional methods relying on cryptographic key management are susceptible to various risks, particularly the exposure of keys to interception or theft. As cyber threats evolve, the short-comings of these methods are accentuated, necessitating more secure solutions. Physically Unclonable Functions (PUFs) have emerged as a potential alternative, utilizing inherent hardware variations for device authentication without stored secrets. However, recent studies reveal vulnerabilities in conventional PUF implementations. Simultaneously, there's a growing recognition for authentication mechanisms tailored for quantum devices. This recognition has prompted the exploration of Quantum PUFs (QPUFs), which represent a promising solution to enhance security and reliability, leveraging the unique properties of quantum mechanics. In this paper, we propose a novel approach using QPUFs for device authentication that does not require any quantum communication channel or even quantum memory. We design a quantum circuit to serve as a QPUF, evaluating metrics such as instability, randomness, and uniqueness. Additionally, we devise an authentication scheme that exploits the challenge-response paradigm, taking advantage of the distinctive properties of quantum PUFs. Furthermore, we delineate a threat model to identify and mitigate potential risks associated with the authentication process. By assessing the proposed QPUFs efficacy on real real quantum hardware provided by IBM, this research contributes to the advancement of secure authentication protocols in quantum era.
ABSTRACT Quantum Physical Unclonable Functions (QPUFs) offer a physically grounded approach to secure authentication, extending the capabilities of classical PUFs. This review covers their theoretical foundations and key implementation challenges—such as quantum memories and Haar‐randomness—, and distinguishes QPUFs from Quantum Readout PUFs (QR‐PUFs), more experimentally accessible yet less robust against quantum‐capable adversaries. A co‐citation‐based selection method is employed to trace the evolution of QPUF architectures, from early QR‐PUFs to more recent Hybrid PUFs (HPUFs). This method further supports a discussion on the role of information‐theoretic analysis in mitigating inconsistencies in QPUF responses, underscoring the deep connection between secret‐key generation and authentication. Despite notable advances, achieving practical and robust QPUF‐based authentication remains an open challenge.