Security Protocols in Relativistic Quantum Cryptography

Abstract

This thesis explores quantum cryptographic protocols designed to provide secure implementation of three key tasks, through mathematical analysis and qualitative discussion. Each chapter focuses on a distinct cryptographic scheme and explores its utility relative to classical and alternative quantum protocols. In Chapter 2, we examine the concept of singlet testing through discussion of two schemes: the Braunstein-Caves and Random Measurement tests. These schemes allow trusted parties to verify the presence of entangled singlet states through the use of simple quantum tools. Through statistical derivation, we demonstrate that the singlet state consistently exhibits the lowest expected value in both tests. We evaluate the performance of both schemes in a range of important scenarios and discuss the consequences of the results. The Random Measurement test emerges as the preferred choice in several natural scenarios, such that it can be considered as an efficient alternative to CHSH-based schemes under certain conditions. Further merits of both schemes are discussed, both in terms of efficiency and practicality. Chapter 3 introduces the concept of quantum tokens and examines a practical S-money scheme for generating unforgeable quantum tokens. This scheme does not require the utilisation of quantum memories or long-distance quantum transmission, rendering it more practical to implement with current technology. We derive a new unforgeability theorem that bounds the probability of a dishonest user successfully presenting the same token at multiple locations. An ongoing experimental implementation of the scheme is discussed, as well as plausible security guarantees which may result from such a setup. In Chapter 4, we discuss quantum position authentication (QPA) schemes with security derived from physical assumptions. The chapter begins by reviewing the impossibility of unconditionally secure QPA schemes and proposes a scheme based on the assumption that a prover and verifier can share a secret timing schedule. We explore the security principles of a timing-based QPA scheme, including the need to protect synchronised clocks against environmental and adversarial disruptions. We also discuss the expected latencies within such a scheme and the resulting operational impact of such deficiencies. This thesis advances our understanding of quantum cryptographic protocols and their practical applications, by offering new insight into singlet verification schemes, secure quantum tokens, and position authentication protocols in quantum communication.