Quantum Lock: A Provable Quantum Communication Advantage

Kaushik Chakraborty1, Mina Doosti1, Yao Ma2, Chirag Wadhwa3, Myrto Arapinis1, and Elham Kashefi1,2

1School of Informatics, University of Edinburgh, Edinburgh, UK
2Laboratoire d’Informatique de Paris 6 (LIP6), Sorbonne Université, Paris, France
3Indian Institute of Technology Roorkee, India

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Abstract

Physical unclonable functions(PUFs) provide a unique fingerprint to a physical entity by exploiting the inherent physical randomness. Gao et al. discussed the vulnerability of most current-day PUFs to sophisticated machine learning-based attacks. We address this problem by integrating classical PUFs and existing quantum communication technology. Specifically, this paper proposes a generic design of provably secure PUFs, called hybrid locked PUFs(HLPUFs), providing a practical solution for securing classical PUFs. An HLPUF uses a classical PUF(CPUF), and encodes the output into non-orthogonal quantum states to hide the outcomes of the underlying CPUF from any adversary. Here we introduce a quantum lock to protect the HLPUFs from any general adversaries. The indistinguishability property of the non-orthogonal quantum states, together with the quantum lockdown technique prevents the adversary from accessing the outcome of the CPUFs. Moreover, we show that by exploiting non-classical properties of quantum states, the HLPUF allows the server to reuse the challenge-response pairs for further client authentication. This result provides an efficient solution for running PUF-based client authentication for an extended period while maintaining a small-sized challenge-response pairs database on the server side. Later, we support our theoretical contributions by instantiating the HLPUFs design using accessible real-world CPUFs. We use the optimal classical machine-learning attacks to forge both the CPUFs and HLPUFs, and we certify the security gap in our numerical simulation for construction which is ready for implementation.

Physical unclonable functions (PUFs) provide a unique fingerprint to a physical entity by exploiting the inherent physical randomness. In the review paper [Nature Electronics, 2020] on PUF technology, Gao et al. discussed the vulnerability of most current-day PUFs to sophisticated machine learning-based attacks, highlighting the design of provably secure PUF as an important open problem. By encoding the outcome of the classical PUFs into qubits, we address this problem. Specifically, this paper proposes a generic design of provably secure PUFs, called hybrid locked PUFs (HLPUFs), providing a practical solution for securing classical PUFs. An HLPUF uses a classical PUF (CPUF) and encodes the output into non-orthogonal quantum states (namely BB84 states, which are widely used for quantum key distribution) to hide the outcomes of the underlying CPUF from any adversary. Similar to the classical lockdown technique [TMSCS, 2016], here we introduce a quantum lock, to protect the HLPUFs from any general adversaries. The indistinguishability property of the non-orthogonal quantum states, together with the quantum lockdown technique, prevent the adversary from accessing the outcome of the CPUFs. We show that, for quantum polynomial-time adversaries, the ratio between the forging probabilities of the HLPUF, and the underlying CPUF is upper bounded by the distinguishing probabilities of those non-orthogonal states that decay exponentially in the number of output bits of the CPUF. Moreover, we show that by exploiting non-classical properties of quantum states, the HLPUF allows the server to reuse the challenge-response pairs for further client authentication. This result provides an efficient solution for running PUF-based client authentication for an extended period while maintaining a small-sized challenge-response pairs database on the server side. Later, we support our theoretical contributions by instantiating the HLPUFs design using accessible real-world CPUFs, called XOR-PUFs. We use the optimal classical machine-learning attacks to forge both the CPUFs and HLPUFs, and we certify the security gap in our numerical simulation for HLPUF construction, which is ready for implementation.

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Cited by

[1] Mina Doosti, "Unclonability and Quantum Cryptanalysis: From Foundations to Applications", arXiv:2210.17545, (2022).

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