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
