This doctoral thesis explores quantum position verification (QPV)---a cryptographic task where one attempts to confirm someone’s geographical location. The core question that QPV aims to answer is: Are you truly at the location you claim to be? To achieve this, QPV combines two pillars of the fundamental laws of nature: (i) special relativity, which limits the speed at which information can travel to the speed of light in vacuum, and (ii) quantum mechanics, which governs the behavior of quantum particles in ways that defy intuition. QPV protocols rely on (i) timing communication between the entities involved in the protocol, and (ii) transmitting information encoded in quantum particles. However, quantum hackers may attempt to pretend to be at the claimed location while actually being elsewhere. This raises the critical question: Can one be certain that the claimed location is genuine and not forged by hackers? This thesis presents new advances toward a fundamental understanding of QPV, its security against powerful quantum hackers, and the feasibility of secure QPV protocols despite experimental challenges that, if exploited by hackers, can severely compromise their security. Furthermore, related to attacks on QPV protocols, this thesis analyzes quantum correlations that emerge in broader cryptographic primitives.
This doctoral thesis explores quantum position verification (QPV)---a cryptographic task where one attempts to confirm someone’s geographical location. The core question that QPV aims to answer is: Are you truly at the location you claim to be? To achieve this, QPV combines two pillars of the fundamental laws of nature: (i) special relativity, which limits the speed at which information can travel to the speed of light in vacuum, and (ii) quantum mechanics, which governs the behavior of quantum particles in ways that defy intuition. QPV protocols rely on (i) timing communication between the entities involved in the protocol, and (ii) transmitting information encoded in quantum particles. However, quantum hackers may attempt to pretend to be at the claimed location while actually being elsewhere. This raises the critical question: Can one be certain that the claimed location is genuine and not forged by hackers? This thesis presents new advances toward a fundamental understanding of QPV, its security against powerful quantum hackers, and the feasibility of secure QPV protocols despite experimental challenges that, if exploited by hackers, can severely compromise their security. Furthermore, related to attacks on QPV protocols, this thesis analyzes quantum correlations that emerge in broader cryptographic primitives.
In this thesis we explore position-based quantum cryptography zooming in on the task of position verification. In position verification, the idea is to use an individual's geographical location as a cryptographic credential. In practice, such protocols can authenticate that a message originated from a specific location or ensure that messages can only be read at a certain location. In a position-verification protocol, the limitations imposed by the speed of light, as described by special relativity, are used to verify that a party is at their claimed location. It has been shown that any QPV protocol can be broken by attackers that use an amount of entanglement exponential in the input size. However, from a practical point of view, not all is lost. We can still hope for QPV protocols that are secure in practice. This raises the problem of designing protocols that are secure in a practical setting. An important problem that arises is that of signal loss. Signal loss can be detrimental as it allows attackers to only answer on a subset of rounds. We investigate several questions related to the practical implementation of such protocols. We propose a new experimentally feasible protocol, which is fully loss-tolerant against attackers restricted to classical communication. Furthermore, we consider the role of allowing quantum communication with no pre-shared entanglement for attackers and show that this setting is strictly stronger than the classical one, indicating that allowing for quantum communication may break security. Conversely, we then show that any protocol secure against classical communication can be transformed into a protocol secure against quantum communication. Finally, we invert the picture, and consider the task of non-local quantum computation (NLQC), which corresponds to the operations of the attackers in a QPV protocol. We connect NLQC to the wider context of information-theoretic cryptography by relating it to a number of other cryptographic primitives.
This thesis deals with position-based quantum cryptography (PBQC), a type of quantum cryptography. More concretely, we focus on the design and study of quantum position verification (QPV) protocols, which act as a building block for PBQC. We prioritise the development of QPV protocols that are loss-tolerant, error-robust, and feasible with current or near-future technology, concentrating on photon-based protocols and linear-optical equipment. We also theoretically study different attack settings on QPV in the context of state discrimination, dealing with the interplay between non-locality and interaction. We introduce a new QPV protocol based on the SWAP test and Hong-Ou-Mandel interference and study it in detail regarding attacks and practical feasibility. We further provide a solution to a major practical issue of QPV -- signal loss. A minor modification of the standard structure of QPV, namely introducing a small time delay and a commitment to play from the honest prover, allows us to provably make the transmission loss between the verifiers and the honest party irrelevant for security for a class of QPV protocols. Moreover, we generalise and study QPV protocols in the continuous-variable setting. Exploring theoretical aspects of QPV attacks, we focus on the difference between quantum and classical communication. We show new bounds on existing protocols, construct protocols that can be attacked with quantum communication but not locally, show a separation between quantum and classical communication attacks on QPV, and derive a necessary condition on the attack error based on the structure of the QPV input ensemble.
Quantum position verification in one shot: parallel repetition of the f-BB84 and f-routing protocols
Quantum position verification (QPV) aims to verify an untrusted prover's location by timing communication with them. To reduce uncertainty, it is desirable for this verification to occur in a single round. However, previous protocols achieving one-round secure QPV had critical drawbacks: attackers pre-sharing an EPR pair per qubit could perfectly break them, and their security depended on quantum information traveling at the speed of light in vacuum, a major experimental challenge in quantum networks. In this work, we prove that a single round of interaction suffices for secure position verification while overcoming these limitations. We show that security for a one-round protocol can rely only on the size of the classical information rather than quantum resources, making implementation more feasible, even with a qubit error tolerance of up to 3.6%, which is experimentally achievable with current technology -- and showing that the timing constraints have to apply only to classical communication. In short, we establish parallel repetition of the f-BB84 and f-routing QPV protocols. As a consequence of our techniques, we also demonstrate an order-of-magnitude improvement in the error tolerance for the sequential repetition version of these protocols, compared to the previous bounds of Nature Physics 18, 623-626 (2022).
Abstract The geographical position can be a good credential for authentication of a party. This is the basis of position-based cryptography—but classically this cannot be done securely without physical exchange of a private key. Recently it has been shown that by combining quantum mechanics with the speed-of-light limit of special relativity, this might be possible: quantum position verification (QPV). Here we demonstrate experimentally a protocol that uses two-photon Hong–Ou–Mandel interference at a beamsplitter, which, in combination with two additional beam splitters and four detectors is rendering the protocol resilient to loss. With this, we are able to show first results towards an experimental demonstration of QPV.
While quantum position verification aims to certify a prover's location using quantum information, existing security definitions only guarantee that part of the successful adversarial party is in the claimed location. This leaves open the possibility that a distributed team of adversaries can jointly simulate a prover in a way that defeats the intended meaning of `being at a location' in position-based cryptography. We introduce stronger notions of position verification that we call quantum localization, which requires that there is a specified, unclonable state at the verified spacetime point-and that this state can be found nowhere else. We show that quantum localization leads naturally to a meaningful notion of trajectory verification, in which quantum information is verifiably tracked through space and time. We construct quantum localization and trajectory verification protocols using quantum anchor states, which generalize coset states from unclonable cryptography. The security of our schemes is proven in the classical oracle (i.e. ideal obfuscation) model, which can be heuristically instantiated in the plain model using post-quantum indistinguishability obfuscation. We also introduce and instantiate the concept of functionality localization, which guarantees that the adversary has the ability to compute a secret function at the verified spacetime point, and this function cannot be computed anywhere else. This raises the intriguing possibility of localizing computational capabilities in space and time. More broadly, we believe our notions of quantum localization and subsequent feasibility results provide stronger foundations for position-based cryptography. At a conceptual level, our results also explore the tight link between two fundamental notions in physics-location and information-thus serving as a natural foundation for cryptographic capabilities tied to physical spacetime.
Abstract Quantum position verification (QPV) enables multiple verifiers to certify a prover’s location using quantum communication and physical assumptions. With experimental demonstrations of QPV becoming increasingly feasible, enhancing the practicality and security of QPV protocols is more important than ever. In this work, we make three key contributions toward this goal. First, we introduce a robust QPV protocol in which the verifier’s state preparation is independent of channel loss, improving reliability in real-world conditions. Second, we refine existing security analysis techniques to bolster protocol resilience against experimental imperfections. Third, we identify and address some implicit assumptions present in existing security analyses, providing a framework to eliminate such assumptions. Additionally, as an example of QPV application beyond location verification, we illustrate how QPV can be leveraged for authenticating classical communication in quantum key distribution.