Unclonability and quantum cryptanalysis: from foundations to applications

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 \emph{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 \emph{quantum physical unclonability}, and study the relationship with cryptographic properties and assumptions such as unforgeability, randomness and 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 applications of this new type of unclonability as a cryptographic resource for designing provably secure quantum protocols. First, we study the unclonability of quantum processes and unitaries in relation to their learnability and unpredictability. The instinctive idea of unpredictability from a cryptographic perspective is formally captured by the notion of \emph{unforgeability}. Intuitively, unforgeability means that an adversary should not be able to produce the output of an \emp{unknown} function or process from a limited number of input-output samples of it. Even though this notion is almost easily formalized in classical cryptography, translating it to the quantum world against a quantum adversary has been proven challenging. One of our contributions is to define a new unified framework to analyse the unforgeability property for both classical and quantum schemes in the quantum setting. This new framework is designed in such a way that can be readily related to the novel notions of unclonability that we will define in the following chapters. Another question that we try to address here is "What is the fundamental property that leads to unclonability?" In attempting to answer this question, we dig into the relationship between unforgeability and learnability, which motivates us to repurpose some learning tools as a new cryptanalysis toolkit. We introduce a new class of quantum attacks based on the concept of `emulation' and learning algorithms, breaking new ground for more sophisticated and complicated algorithms for quantum cryptanalysis. Second, we formally represent, for the first time, the notion of physical unclonability in the quantum world by introducing \emph{Quantum Physical Unclonable Functions (qPUF)} as the quantum analogue of Physical Unclonable Functions (PUF). PUF is a hardware assumption introduced previously in the literature of hardware security, as physical devices with unique behaviour, due to manufacturing imperfections and natural uncontrollable disturbances that make them essentially hard to reproduce. We deliver the mathematical model for qPUFs, and we formally study their main desired cryptographic property, namely unforgeability, using our previously defined unforgeability framework. In light of these new techniques, we show several possibility and impossibility results regarding the unforgeability of qPUFs. We will also discuss how the quantum version of physical unclonability relates to randomness and unknownness in the quantum world, exploring further the extended notion of unclonability. Third, we dive deeper into the connection between physical unclonability and related hardware assumptions with quantum pseudorandomness. Like unclonability in quantum information, pseudorandomness is also a fundamental concept in cryptography and complexity. We uncover a deep connection between Pseudorandom Unitaries (PRU) and quantum physical unclonable functions by proving that both qPUFs and the PRU can be constructed from each other. We also provide a novel route towards realising quantum pseudorandomness, distinct from computational assumptions. Next, we propose new applications of unclonability in quantum communication, using the notion of physical unclonability as a new resource to achieve provably secure quantum protocols against quantum adversaries. We propose several protocols for mutual entity identification in a client-server or quantum network setting. Authentication and identification are building-block tasks for quantum networks, and our protocols can provide new resource-efficient applications for quantum communications. The proposed protocols use different quantum and hybrid (quantum-classical) PUF constructions and quantum resources, which we compare and attempt in reducing, as much as possible throughout the various works we present. Specifically, our hybrid construction can provide quantum security using limited quantum communication resources that cause our protocols to be implementable and practical in the near term. Finally, we present a new practical cryptanalysis technique concerning the problem of approximate cloning of quantum states. 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 the hybrid classical-quantum technique. This approach enables the end-to-end discovery of hardware efficient quantum circuits to clone specific families of quantum states, which has applications in the foundations and cryptography. In particular, we use a cloning-based attack on two quantum coin-flipping protocols and show that our algorithm can improve near term attacks on these protocols, using approximate quantum cloning as a resource. Throughout this work, we demonstrate how the power of quantum learning tools as attacks on one hand, and the power of quantum unclonability as a security resource, on the other hand, fight against each other to break and ensure security in the near term quantum era

Quantum Physical Unclonable Functions: Possibilities and Impossibilities

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.Comment: 32 pages including the appendi

Progress toward practical quantum cryptanalysis by variational quantum cloning

Cryptanalysis of quantum cryptographic systems generally involves finding optimal adversarial attack strategies on the underlying protocols. The core principle of modeling quantum attacks often reduces to the ability of the adversary to clone unknown quantum states and to extract thereby meaningful secret information. Explicit optimal attack strategies typically require high computational resources due to large circuit depths or, in many cases, are unknown. Here we introduce variational quantum cloning (VarQlone), a cryptanalysis algorithm based on quantum machine learning, 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 optimization. Our approach enables the end-to-end discovery of hardware-efficient quantum circuits to clone specific families of quantum states, which we demonstrate in an implementation on the Rigetti Aspen quantum hardware. We connect these results to quantum cryptographic primitives and derive explicit attacks facilitated by VarQlone. We expect that quantum machine learning will serve as a resource for improving attacks on current and future quantum cryptographic protocols

Quantum Lock: A Provable Quantum Communication Advantage

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.Comment: Replacement of paper "Hybrid PUF: A Novel Way to Enhance the Security of Classical PUFs" (arXiv:2110.09469

Differential Privacy Amplification in Quantum and Quantum-inspired Algorithms

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.Comment: 16 page

Quantum Physical Unclonable Functions: Possibilities and Impossibilities

47 pages including the appendixPhysical Unclonable Functions (PUFs) are physical devices with unique behavior that are hard to clone. A variety of PUF schemes have been considered in theoretical studies as well as practical implementations of several security primitives such as identification and key generation. Recently, the inherent unclonability of quantum states has been exploited for defining (a partial) quantum analogue to classical PUFs (against limited adversaries). There are also a few proposals for quantum implementations of classical optical PUFs. However, none of these attempts provides a comprehensive study of Quantum Physical Unclonable Functions (QPUFs) with quantum cryptographic tools as we present in this paper. We formally define QPUFs, encapsulating all requirements of classical PUFs as well as introducing new ones inherent to the quantum setting such as testability. We develop a quantum game-based security framework for our analysis and define a new class of quantum attacks, called General Quantum Emulation Attack. This class of attacks 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 quntum emulation algorithm and use it to show that a family of quantum cryptographic primitives that rely on unknown unitary transformations do not provide existential unforgeability while they provide selective unforgeability. Then, we express our results in the case of QPUF as an unknown unitary transformation