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arXiv:1911.04981 · Physical Review A

Theoretical framework for physical unclonable functions, including quantum readout

Giulio Gianfelici, Hermann Kampermann, Dagmar Bruß

Published Apr 29, 2020• 25 citations
arXivHTMLPDF

Abstract

We propose a theoretical framework to quantitatively describe physical unclonable functions (PUFs), including extensions to quantum protocols, so-called quantum readout PUFs (QR-PUFs). (QR-) PUFs are physical systems with challenge-response behavior intended to be hard to clone or simulate. Their use has been proposed in several cryptographic protocols, with particular emphasis on authentication. Here, we provide theoretical assumptions and definitions behind the intuitive ideas of (QR-) PUFs. This allows us to quantitatively characterize the security of such devices in cryptographic protocols. First, by generalizing previous ideas, we design a general authentication scheme which is applicable to different physical implementations of both classical PUFs and (QR-) PUFs. Then, we define the robustness and the unclonability, which allows us to derive security thresholds for (QR-) PUF authentication and paves the way to develop further new authentication protocols.

DOI
10.1103/physreva.101.042337

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We propose a theoretical framework to quantitatively describe physical unclonable functions (PUFs), including extensions to quantum protocols, so-called quantum readout PUFs (QR-PUFs). (QR-) PUFs are physical systems with challenge-response behavior intended to be hard to clone or simulate. Their use has been proposed in several cryptographic protocols, with particular emphasis on authentication. Here, we provide theoretical assumptions and definitions behind the intuitive ideas of (QR-) PUFs. This allows us to quantitatively characterize the security of such devices in cryptographic protocols. First, by generalizing previous ideas, we design a general authentication scheme which is applicable to different physical implementations of both classical PUFs and (QR-) PUFs. Then, we define the robustness and the unclonability, which allows us to derive security thresholds for (QR-) PUF authentication and paves the way to develop further new authentication protocols.
Physical unclonable functions (PUFs) are physical structures that are hard to clone and have a unique challenge-response behavior. The term PUF was coined by Pappu et al. in 2001. That work triggered a lot of interest, and since then a substantial number of papers has been written about the use of a wide variety of physical structures for different security purposes such as identification, authentication, read-proof key storage, key distribution, tamper evidence, anti-counterfeiting, software-to-hardware binding and trusted computing. In this paper we propose a new security primitive: the quantum-readout PUF (QR-PUF). This is a classical PUF, without internal quantum degrees of freedom, which is challenged using a quantum state, e.g. a single-photon state, and whose response is also a quantum state. By the no-cloning property of unknown quantum states, attackers cannot intercept challenges or responses without noticeably disturbing the readout process. Thus, a verifier who sends quantum states as challenges and receives the correct quantum states back can be certain that he is probing a specific QR-PUF without disturbances, even if the QR-PUF is far away "in the field" and under hostile control. For PUFs whose information content is not exceedingly large, all currently known PUF-based authentication and anti-counterfeiting schemes require trusted readout devices in the field. Our quantum readout scheme has no such requirement. Furthermore, we show how the QR-PUF authentication scheme can be interwoven with quantum key exchange (QKE), leading to an authenticated QKE protocol between two parties. This protocol has the special property that it requires no a priori secret shared by the two parties, and that the quantum channel is the authenticated channel, allowing for an unauthenticated classical channel. We provide security proofs for a limited class of attacks. The proofs depend on the physical unclonability of PUFs and on the practical infeasibility of building a quantum computer.
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.
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.
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 Readout (QR) of Physical Unclonable Functions (PUFs) is a new technique for remotely authenticating objects, which has recently been demonstrated experimentally. The security is based on basic quantum information theoretic principles and holds under the assumption that the adversary cannot clone or physically emulate PUFs. We analyse the security of QR under a class of attacks called ‘digital emulation’, in which the adversary first performs state estimation on the challenge and then bases his response on this estimate. We make use of a result by Bruß and Macchiavello to derive an upper bound on the adversary’s success probability as a function of the Hilbert space dimension K and the photon number n. We prove that QR is unconditionally secure against digital emulation attacks when the challenges are Fock states. For non-Fock-states we provide a security proof under the condition that the attacker’s measurements commute with the particle number operator.