The goal of this work is to provide a largely self-contained, rigorous proof of the security of quantum key distribution in the finite key regime. For our analysis we consider an entanglement-based protocol based on BBM92 as well as a prepare-and-measure protocol based on BB84. Our presentation differs from previous work in that we are careful to model all the randomness that is used throughout the protocol and take care of all the transcripts of the communication over the public channel. We hope that this work will be a good starting point for readers interested in finite key analysis of protocols in quantum cryptography.
The goal of this work is to provide a largely self-contained, rigorous proof of the security of quantum key distribution in the finite key regime. For our analysis we consider an entanglement-based protocol based on BBM92 as well as a prepare-and-measure protocol based on BB84. Our presentation differs from previous work in that we are careful to model all the randomness that is used throughout the protocol and take care of all the transcripts of the communication over the public channel. We hope that this work will be a good starting point for readers interested in finite key analysis of protocols in quantum cryptography.
In this work we present a security analysis for quantum key distribution, establishing a rigorous tradeoff between various protocol and security parameters for a class of entanglement-based and prepare-and-measure protocols. The goal of this paper is twofold: 1) to review and clarify the stateof-the-art security analysis based on entropic uncertainty relations, and 2) to provide an accessible resource for researchers interested in a security analysis of quantum cryptographic protocols that takes into account finite resource effects. For this purpose we collect and clarify several arguments spread in the literature on the subject with the goal of making this treatment largely self-contained. More precisely, we focus on a class of prepare-and-measure protocols based on the Bennett-Brassard (BB84) protocol as well as a class of entanglement-based protocols similar to the Bennett-Brassard-Mermin (BBM92) protocol. We carefully formalize the different steps in these protocols, including randomization, measurement, parameter estimation, error correction and privacy amplification, allowing us to be mathematically precise throughout the security analysis. We start from an operational definition of what it means for a quantum key distribution protocol to be secure and derive simple conditions that serve as sufficient condition for secrecy and correctness. We then derive and eventually discuss tradeoff relations between the block length of the classical computation, the noise tolerance, the secret key length and the security parameters for our protocols. Our results significantly improve upon previously reported tradeoffs.
We present a rigorous and complete security proof of the decoy-state BB84 quantum key distribution (QKD) protocol. Our analysis aims to achieve a high standard of mathematical rigour and completeness, thereby providing the necessary foundation for certification and standardization efforts. Beyond establishing the security of a specific protocol, this work develops a general and modular framework that can be readily adapted to a broad class of QKD protocols, including both prepare-and-measure and entanglement-based variants. Our framework unifies all major ingredients required for the analysis of realistic QKD protocols, including the analysis of classical authentication and classical processing, source-replacement schemes, finite-size analysis, source maps, squashing maps, and decoy-state techniques. In doing so, this work consolidates a diverse range of techniques scattered across the QKD literature into a unified formalism, representing a general and rigorous treatment of QKD security. Finally, it outlines a clear path towards incorporating practical imperfections within the same framework, thereby laying the groundwork for addressing implementation security in future analysis.
In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a full understanding of a security proof is scattered across numerous publications, it has proven difficult to gain a comprehensive understanding of all steps involved in the process and their limitations without considerable effort and attention to detail. Our paper aims to address this issue by providing a rigorous and comprehensive security proof for the finite-size 1-decoy and 2-decoy BB84 protocols against coherent attacks within Renner's entropic uncertainty relation framework. We resolve important technical flaws found in previous works regarding the fixed-length treatment of protocols and the careful handling of acceptance testing. To this end, we provide various technical arguments, including an analysis accounting for the important distinction of the 1-decoy protocol where statistics are computed after error correction, along with a slight improvement of the secure-key length. We also explicitly clarify the aspect of conditioning on events, addressing a technical detail often overlooked and essential for rigorous proofs. We extensively consolidate and unify concepts from many works, thoroughly discussing the underlying assumptions and resolving technical inconsistencies. Therefore, our contribution represents a significant advancement towards a broader and deeper understanding of QKD security proofs.
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies. Although they offer significant promise, practical implementations of quantum key distribution are often not as rigorous as theory predicts. This study demonstrates how two instances of such discrepancies can be resolved by taking advantage of an enotropic formulation of the uncertainty principle.
The thesis starts with a high-level introduction into cryptography and quantum mechanics. Chapter 2 gives a theoretical foundation by introducing probability theory, information theory, functional analysis, quantum mechanics and quantum information theory. Chapter 3, 4 and 5 are editions of work published earlier.\n\nIn Chapter 3, we present a quantum-information-theoretic tool to analyze random sampling in a quantum setting. In particular, we present two new rigorous security proofs that make use of our new sampling tool: one for BB84 quantum key distribution, and one for a quantum reduction from oblivious transfer (OT) to bit commitment.\n\nChapter 4 studies the problem of message authentication from a weak key (which is a key that is not uniformly random, e.g., a password) in a new scenario. In this scenario, the weak key is a one-time session key that is derived from a public source of randomness with the help of a long-term key (e.g., a password). We propose a new four-round protocol for message authentication from a weak (session) key. \n\nIn Chapter 5 we present a new entropic uncertainty relation and furthermore we consider the task of password-based identification. We devise a new quantum identification protocol that is secure in two security models simultaneously.