Abstract This paper, for the first time, addresses the questions related to the connections between quantum pseudorandomness and quantum hardware assumptions, specifically quantum physical unclonable functions (qPUFs). Our results show that efficient pseudorandom quantum states (PRS) are sufficient to construct the challenge set for universally unforgeable qPUFs, improving the previous existing constructions based on the Haar-random states. We also show that both the qPUFs and the quantum pseudorandom unitaries (PRUs) can be constructed from each other, providing new ways to obtain PRS from the hardware assumptions. Moreover, we provide a sufficient condition (in terms of the diamond norm) that a set of unitaries should have to be a PRU in order to construct a universally unforgeable qPUF, giving yet another novel insight into the properties of the PRUs. Later, as an application of our results, we show that the efficiency of an existing qPUF-based client–server identification protocol can be improved without losing the security requirements of the protocol.
Abstract This paper, for the first time, addresses the questions related to the connections between quantum pseudorandomness and quantum hardware assumptions, specifically quantum physical unclonable functions (qPUFs). Our results show that efficient pseudorandom quantum states (PRS) are sufficient to construct the challenge set for universally unforgeable qPUFs, improving the previous existing constructions based on the Haar-random states. We also show that both the qPUFs and the quantum pseudorandom unitaries (PRUs) can be constructed from each other, providing new ways to obtain PRS from the hardware assumptions. Moreover, we provide a sufficient condition (in terms of the diamond norm) that a set of unitaries should have to be a PRU in order to construct a universally unforgeable qPUF, giving yet another novel insight into the properties of the PRUs. Later, as an application of our results, we show that the efficiency of an existing qPUF-based client–server identification protocol can be improved without losing the security requirements of the protocol.
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.
Quantum physical unclonable functions, or QPUFs, are rapidly emerging as theoretical hardware solutions to provide secure cryptographic functionalities such as key-exchange, message authentication, entity identification among others. Recent works have shown that in order to provide provable security of these solutions against any quantum polynomial time adversary, QPUFs are required to be a unitary sampled uniformly randomly from the Haar measure. This however is known to require an exponential amount of resources. In this work, we propose an efficient construction of these devices using unitary t-designs, called QPUF_t. Along the way, we modify the existing security definitions of QPUFs to include efficient constructions and showcase that QPUF_t still retains the provable security guarantees against a bounded quantum polynomial adversary with t-query access to the device. This also provides the first use case of unitary t-design construction for arbitrary t, as opposed to previous applications of t-designs where usually a few (relatively low) values of t are known to be useful for performing some task. We study the noise-resilience of QPUF_t against specific types of noise, unitary noise, and show that some resilience can be achieved particularly when the error rates affecting individual qubits become smaller as the system size increases. To make the noise-resilience more realistic and meaningful, we conclude that some notion of error mitigation or correction should be introduced.
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
Quantum pseudorandomness is an emerging research area. Ji, Liu, and Song defined pseudorandom states (PRSs) and pseudorandom unitaries (PRUs) as quantum analogs of pseudorandom generators and pseudorandom functions. A unitary oracle separation result between one-way functions and PRSs/PRUs, established by Kretschmer, suggests that certain quantum primitives may remain secure even if classical cryptography is compromised. This insight has spurred extensive work on quantum pseudorandomness and its applications in quantum cryptography. Many constructions of PRSs have been established under standard assumptions, yet building a secure PRU was a long-standing open problem. This dissertation aims to narrow the gap between PRSs and PRUs and presents results that go beyond PRSs. We introduce Pseudorandom State Scramblers (PRSSs), a new primitive that lies between PRSs and PRUs. A PRSS maps any pure state to a pseudorandom state, a property shared with PRUs but not with PRSs. We present a construction of PRSSs inspired by the well-known Kac’s walk, and in particular, we develop a parallel variant that significantly accelerates the mixing time, enabling an efficient construction. PRSSs support cryptographic tasks not known to be achievable from PRSs alone, including a quantum encryption scheme and a succinct quantum state commitment. Additionally, when suitable classical randomness is provided, our construction exhibits a special dispersing property not known to be satisfied by any existing construction of quantum pseudorandom primitives. Our subsequent work shows that, without asymptotically increasing the number of steps, our construction based on the parallel Kac’s walk yields PRUs with standard or even strong security. The proof builds on a recently developed technique for establishing adaptive security, known as the path-recording method. This result provides an alternative construction of PRUs and further showcases the power of this proof technique. In addition, this dissertation includes two side projects. The first revisits the Hidden Subgroup Problem over ℤn, providing a simplified analysis of a known quantum algorithm using elementary lattice tools. The second establishes a quantum analogue of a classical impossibility result for statistical non-interactive zero-knowledge arguments, showing limitations of black-box reductions under classical-query quantum adversaries.
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.