Quantum Physical Unclonable Functions: Possibilities and Impossibilities

Myrto Arapinis1, Mahshid Delavar1, Mina Doosti1, and Elham Kashefi1,2

1School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh EH8 9AB, UK
2Departement Informatique et Reseaux, CNRS, Sorbonne Université, 4 Place Jussieu 75252 Paris CEDEX 05, France

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Abstract

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.

Physical Unclonable Functions (PUFs) are physical devices with unique behaviour, due to the imperfections and natural randomness during their manufacturing procedure, which makes them hard to clone. A large variety of PUF schemes have been mass-produced for a large domain of applications from anti-counterfeiting, identification, authentication and key generation to advanced protocols such as oblivious transfer, key exchange, key renovation and virtual proof of reality. Considering the importance of PUFs as a hardware security primitive in these real-world applications, it is crucial to investigate their security in the quantum regime as well. Recently, the inherent unclonability of quantum states has been exploited for defining quantum analogue to classical PUFs. We provide the first comprehensive study of the Quantum Physical Unclonable Functions (QPUFs) and develop a formal quantum security framework for our analysis. In doing so we define a new class of quantum attacks, called General Quantum Emulation Attack (QEA) that similar to the classical setting, where machine learning techniques have been developed to demonstrate the vulnerability of PUF, our QEA also exploits previously captured valid challenge-response pairs to emulate the action of an unknown quantum transformation on new input. We devise a concrete attack based on an existing quantum emulation algorithm and use it to show that a family of QPUFs do not provide previously claimed strong security. Our investigation, however, put forward the most general definitions of QPUFs that remains secure against the strongest possible quantum adversary, compatible with a practical setting where most of QPUF will be utilised.

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[1] Mina Doosti, Niraj Kumar, Mahshid Delavar, and Elham Kashefi, "Client-server Identification Protocols with Quantum PUF", ACM Transactions on Quantum Computing 2 3, 1 (2021).

[2] Giulio Gianfelici, Hermann Kampermann, and Dagmar Bruß, "Theoretical framework for physical unclonable functions, including quantum readout", Physical Review A 101 4, 042337 (2020).

[3] Koustubh Phalak, Abdullah Ash- Saki, Mahabubul Alam, Rasit Onur Topaloglu, and Swaroop Ghosh, "Quantum PUF for Security and Trust in Quantum Computing", IEEE Journal on Emerging and Selected Topics in Circuits and Systems 11 2, 333 (2021).

[4] Niraj Kumar, Rawad Mezher, and Elham Kashefi, "Efficient Construction of Quantum Physical Unclonable Functions with Unitary t-designs", arXiv:2101.05692.

[5] Mina Doosti, Mahshid Delavar, Elham Kashefi, and Myrto Arapinis, "A Unified Framework For Quantum Unforgeability", arXiv:2103.13994.

[6] Sreeja Chowdhury, Ana Covic, Rabin Yu Acharya, Spencer Dupee, Fatemeh Ganji, and Domenic Forte, "Physical Security in the Post-quantum Era: A Survey on Side-channel Analysis, Random Number Generators, and Physically Unclonable Functions", arXiv:2005.04344.

[7] Juan Carlos Garcia-Escartin, "Physical Unclonable Functions with Boson Sampling", arXiv:1911.08417.

[8] Georgios M. Nikolopoulos, "Remote quantum-safe authentication of entities with physical unclonable functions", arXiv:2108.00468.

[9] Pidong Wang, Feiliang Chen, Dong Li, Song Sun, Feng Huang, Taiping Zhang, Qian Li, Kun Chen, Yongbiao Wan, Xiao Leng, and Yao Yao, "Authentication of Optical Physical Unclonable Functions Based on Single-Pixel Detection", Physical Review Applied 16 5, 054025 (2021).

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