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Quantum Information and Computation

Security analysis of Quantum-Readout PUFs in the case of challenge-estimation attacks

Boris Škorić

Published Jan 1, 2016• 12 citations
Publisher

Abstract

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.

DOI
10.26421/qic16.1-2-4

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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.
Quantum Readout PUFs (QR-PUFs) have been proposed as a technique for remote authentication of ob jects. The security is based on basic quantum information theoretic principles and the assumption that the adversary cannot losslessly implement arbitrary unitary transformations on a K-dimensional state space, with K "large". We consider all possible attacks in which the adversary bases his response on challenge state estimation by measurements. We first analyze the security of QR-PUF schemes in the case where each challenge consists of precisely n identical quanta. We use a result by Bruss and Macchiavello to derive an upper bound on the adversary’s success probability as a function of K and n. Then we generalize to challenges that contain a probabilistic number of quanta, and in particular a Poisson distribution.
The concept of quantum-secure readout of Physical Unclonable Functions (PUFs) has recently been realized experimentally in an optical PUF system. We analyze the security of this system under the strongest type of classical attack: the challenge estimation attack. The adversary performs a measurement on the challenge quantum state in order to learn as much about it as he can. Using this knowledge, he then tries to reconstruct the challenge and to emulate the PUF. We consider quadrature measurements, which are the most informative practical measurements known to us. We prove that even under this attack the expected number of photons detected in the verification mechanism is approximately a factor S + 1 too low; here S is the Quantum Security Parameter, defined as the number of modes in the optical system divided by the number of photons in the challenge. The photon count allows for a reliable distinction between an authentic PUF and a challenge estimation attack.
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.
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.