Quantum-Key Distribution (QKD) Fundamentals

Abstract

This chapter is devoted to QKD fundamentals. The chapter starts with description of key differences between conventional cryptography, classical physical-layer security (PLS), and QKD. In section on QKD basics, after historical overview, we review different QKD types and describe briefly common postprocessing steps, namely, information reconciliation and privacy amplification steps. In the same section, we provide two fundamental theorems on which QKD relies on, no-cloning theorem and the theorem of inability to unambiguously distinguish non-orthogonal quantum states. In section on discrete variable (DV)-QKD systems, we describe in detail BB84 and B92 protocols as well as Ekert (E91) and EPR protocols. In the same section, the time-phase encoding protocol is also described. Regarding the BB84 protocols, different versions, suitable for different technologies, are described. In section on QKD security, the secret-key rate (SKR) is represented as the product of raw key rate and fractional rate, followed by the description of different limitations to the raw key rate. After that, the generic expression for the fractional rate is provided, followed by description of different eavesdropping strategies including individual (independent or incoherent) attacks, collective attacks, coherent attacks, and the quantum hacking/side-channel attacks. For individual and coherent attacks, the corresponding secrete fraction expressions are described. The next section is devoted to various definitions of security, including the concept of e-security. After that, the generic expressions for 2-D DV-QKD schemes are derived for both prepare-and-measure and decoy-state-based protocols. To facilitate the description of continuous variable (CV)-QKD protocols, the fundamentals of quantum optics are introduced first. In section on CV-QKD protocols, both squeezed state-based and coherent state-based protocols are described. Given that the coherent states are much easier to generate and manipulate, the coherent state-based protocols with both homodyne and heterodyne detections are described in detail. The secret fraction is derived for both direct- and reverse-reconciliation-based CV-QKD protocols. Furthermore, the details on practical aspects of GG02 protocol are provided. In the same section, the secret fraction calculation for collective attacks is discussed. After that, the basic concepts for measurement-device-independent (MDI)-QKD protocols are introduced. Then final section in the chapter provides some relevant concluding remarks.