Differential privacy is a widely used notion of security that enables the processing of sensitive information. In short, differentially private algorithms map "neighbouring" inputs to close output distributions. Prior work proposed several quantum extensions of differential privacy, each of them built on substantially different notions of neighbouring quantum states. In this paper, we propose a novel and general definition of neighbouring quantum states. We demonstrate that this definition captures the underlying structure of quantum encodings and can be used to provide exponentially tighter privacy guarantees for quantum measurements. Our approach combines the addition of classical and quantum noise and is motivated by the noisy nature of near-term quantum devices. Moreover, we also investigate an alternative setting where we are provided with multiple copies of the input state. In this case, differential privacy can be ensured with little loss in accuracy combining concentration of measure and noise-adding mechanisms. En route, we prove the advanced joint convexity of the quantum hockey-stick divergence and we demonstrate how this result can be applied to quantum differential privacy. Finally, we complement our theoretical findings with an empirical estimation of the certified adversarial robustness ensured by differentially private measurements.
Differential privacy provides a theoretical framework for processing a dataset about $n$ users, in a way that the output reveals a minimal information about any single user. Such notion of privacy is usually ensured by noise-adding mechanisms and amplified by several processes, including subsampling, shuffling, iteration, mixing and diffusion. In this work, we provide privacy amplification bounds for quantum and quantum-inspired algorithms. In particular, we show for the first time, that algorithms running on quantum encoding of a classical dataset or the outcomes of quantum-inspired classical sampling, amplify differential privacy. Moreover, we prove that a quantum version of differential privacy is amplified by the composition of quantum channels, provided that they satisfy some mixing conditions.
In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with respect to diamond distance. For the former, we present an efficient average-case algorithm along with a nearly matching lower bound with respect to the number of observables to be predicted. For the latter, we present average-case query complexity lower bounds for learning classes of unitaries. We obtain an exponential lower bound for learning unitary 2-designs and a doubly exponential lower bound for Haar-random unitaries. Finally, we demonstrate the practical relevance of our access model by applying our learning algorithm to attack an authentication protocol using Classical-Readout Quantum Physically Unclonable Functions, partially addressing an important open question in quantum hardware security.
The impossibility of creating perfect identical copies of unknown quantum systems is a fundamental concept in quantum theory and one of the main non-classical properties of quantum information. This limitation imposed by quantum mechanics, famously known as the no-cloning theorem, has played a central role in quantum cryptography as a key component in the security of quantum protocols. In this thesis, we look at Unclonability in a broader context in physics and computer science and more specifically through the lens of cryptography, learnability and hardware assumptions. We introduce new notions of unclonability in the quantum world, namely quantum physical unclonability, and study the relationship with cryptographic properties and assumptions such as unforgeability, and quantum pseudorandomness. The purpose of this study is to bring new insights into the field of quantum cryptanalysis and into the notion of unclonability itself. We also discuss several applications of this new type of unclonability as a cryptographic resource for designing provably secure quantum protocols. Furthermore, we present a new practical cryptanalysis technique concerning the problem of approximate cloning of quantum states. We design a quantum machine learning-based cryptanalysis algorithm to demonstrate the power of quantum learning tools as both attack strategies and powerful tools for the practical study of quantum unclonability.
Present-day quantum computing is cloud-based, where a user submits a circuit to a service provider's proprietary backend hardware. While providers may wish to hide implementation details, scheduling choices, or even which physical device was used, noisy finite-shot outputs can carry backend-specific fingerprints: information imprinted in the classical output distribution that can reveal the backend identity. So far, such fingerprints have mostly been studied from a benchmarking perspective, with limited attention to privacy considerations for users and providers. This work develops the first formal framework for backend identifiability and its privacy implications. We introduce a backend-identifiability game and use it to formalise routing anonymity as a security notion for quantum cloud services. We show that backend identifiability is a hypothesis-testing problem and prove that, under passive i.i.d. access to a single backend, routing anonymity decays exponentially at the Chernoff rate. We also establish a utility-anonymity trade-off, imposing fundamental limits on how much backend-specific information can be removed from classical outputs without degrading their usefulness. In addition, we observe that, for noisy quantum hardware, identifying fingerprints are inherently an intermediate-depth phenomenon, and establish a depth principle using Pauli-transfer-matrix tools. We complement the theory with experiments on Amazon Braket on AWS, using ion-trap and superconducting quantum processors. We observe 87-90% classification between superconducting backends and 96-100% classification across physical platforms, and find that identifiability can survive natural forms of post-processing. Overall, these results establish routing anonymity as a distinct security requirement for quantum cloud computing, and provide a framework for quantifying and controlling the utility-anonymity trade-off.
Christopher Battarbee, Suchetana Goswami, Elham Kashefi et al.
In this review, we survey the cryptographic task of authentication from the perspective of quantum communication. We review three main flavours of authentication that are often conflated in the literature: authentication of classical messages, authentication of quantum messages, and entity authentication, also covering recent hardware-assisted approaches. We compare representative protocols for each functionality in terms of their security assumptions, set-up requirements, composability, and scalability in large or dynamic networks, and use these criteria to identify and recommend suitable candidates. Finally, applications are surveyed: we provide a detailed case study of authentication and quantum key distribution (QKD), then extend the discussion to protocols beyond QKD, where the role of authentication is more complex. Our take-home message is that an authentication requirement is not an intrinsic limitation of quantum networks: as with all secure communication, each protocol relies on a particular authentication resource, and the security claim of that protocol is meaningful only once the authentication resource and its deployment assumptions are made explicit. At the same time, the existing classical and quantum literature already offers a range of quantum-secure authentication schemes, which can support different applications when carefully matched to the required functionality, assumptions, and security guarantees.
Characterizing a quantum system by learning its state or evolution is a fundamental problem in quantum physics and learning theory with a myriad of applications. Recently, as a new approach to this problem, the task of agnostic state tomography was defined, in which one aims to approximate an arbitrary quantum state by a simpler one in a given class. Generalizing this notion to quantum processes, we initiate the study of agnostic process tomography: given query access to an unknown quantum channel $Φ$ and a known concept class $\mathcal{C}$ of channels, output a quantum channel that approximates $Φ$ as well as any channel in the concept class $\mathcal{C}$, up to some error. In this work, we propose several natural applications for this new task in quantum machine learning, quantum metrology, classical simulation, and error mitigation. In addition, we give efficient agnostic process tomography algorithms for a wide variety of concept classes, including Pauli strings, Pauli channels, quantum junta channels, low-degree channels, and a class of channels produced by $\mathsf{QAC}^0$ circuits. The main technical tool we use is Pauli spectrum analysis of operators and superoperators. We also prove that, using ancilla qubits, any agnostic state tomography algorithm can be extended to one solving agnostic process tomography for a compatible concept class of unitaries, immediately giving us efficient agnostic learning algorithms for Clifford circuits, Clifford circuits with few T gates, and circuits consisting of a tensor product of single-qubit gates. Together, our results provide insight into the conditions and new algorithms necessary to extend the learnability of a concept class from the standard tomographic setting to the agnostic one.
In this work, we study the learnability of quantum circuits in the near term. We demonstrate the natural robustness of quantum statistical queries for learning quantum processes, motivating their use as a theoretical tool for near-term learning problems. We adapt a learning algorithm for constant-depth quantum circuits to the quantum statistical query setting, and show that such circuits can be learned in our setting with only a linear overhead in the query complexity. We prove average-case quantum statistical query lower bounds for learning, within diamond distance, random quantum circuits with depth at least logarithmic and at most linear in the system size. Finally, we prove that pseudorandom unitaries (PRUs) cannot be constructed using circuits of constant depth by constructing an efficient distinguisher using existing learning algorithms. To show the correctness of our distinguisher, we prove a new variation of the quantum no free lunch theorem.
This paper, for the first time, addresses the questions related to the connections between the quantum pseudorandomness and quantum hardware assumptions, specifically quantum physical unclonable functions (qPUFs). Our results show that the efficient pseudorandom quantum states (PRS) are sufficient to construct the challenge set for the universally unforgeable qPUF, improving the previous existing constructions that are 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) 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.
Mina Doosti, Mahshid Delavar, Elham Kashefi et al.
In this paper, we continue the line of work initiated by Boneh and Zhandry at CRYPTO 2013 and EUROCRYPT 2013 in which they formally define the notion of unforgeability against quantum adversaries specifically, for classical message authentication codes and classical digital signatures schemes. We develop a general and parameterised quantum game-based security model unifying unforgeability for both classical and quantum constructions allowing us for the first time to present a complete quantum cryptanalysis framework for unforgeability. In particular, we prove how our definitions subsume previous ones while considering more fine-grained adversarial models, capturing the full spectrum of superposition attacks. The subtlety here resides in the characterisation of a forgery. We show that the strongest level of unforgeability, namely existential unforgeability, can only be achieved if only orthogonal to previously queried messages are considered to be forgeries. In particular, we present a non-trivial attack if any overlap between the forged message and previously queried ones is allowed. We further show that deterministic constructions can only achieve the weaker notion of unforgeability, that is selective unforgeability, against such restricted adversaries, but that selective unforgeability breaks if general quantum adversaries (capable of general superposition attacks) are considered. On the other hand, we show that PRF is sufficient for constructing a selective unforgeable classical primitive against full quantum adversaries. Moreover, we show similar positive results relying on Pseudorandom Unitaries (PRU) for quantum primitives. These results demonstrate the generality of our framework that could be applicable to other primitives beyond the cases analysed in this paper.
Cryptanalysis on standard quantum cryptographic systems generally involves finding optimal adversarial attack strategies on the underlying protocols. The core principle of modelling quantum attacks in many cases reduces to the adversary's ability to clone unknown quantum states which facilitates the extraction of some meaningful secret information. Explicit optimal attack strategies typically require high computational resources due to large circuit depths or, in many cases, are unknown. In this work, we propose variational quantum cloning (VQC), a quantum machine learning based cryptanalysis algorithm which allows an adversary to obtain optimal (approximate) cloning strategies with short depth quantum circuits, trained using hybrid classical-quantum techniques. The algorithm contains operationally meaningful cost functions with theoretical guarantees, quantum circuit structure learning and gradient descent based optimisation. Our approach enables the end-to-end discovery of hardware efficient quantum circuits to clone specific families of quantum states, which in turn leads to an improvement in cloning fidelites when implemented on quantum hardware: the Rigetti Aspen chip. Finally, we connect these results to quantum cryptographic primitives, in particular quantum coin flipping. We derive attacks on two protocols as examples, based on quantum cloning and facilitated by VQC. As a result, our algorithm can improve near term attacks on these protocols, using approximate quantum cloning as a resource.
Myrto Arapinis, Mahshid Delavar, Mina Doosti et al.
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.