Security Proof of BB84 Quantum Key Distribution (QKD) Protocol and Study of Imperfections over the Implementation of the Weak+Vacuum Decoy-state QKD Protocol

Abstract

Quantum cryptographic protocols exploit basic principles of physics in order to conceal the content of the transmitter's message from third parties. This seems to be the end of the interception of communications. However, just like the classical cryptographic protocols, comprehensive studies are needed in order to prove their security from any kind of possible attacks, namely to guarantee their security level information-theoretically.

In the field of Quantum Key Distribution (QKD), where single photons are transferred through fiber networks, the non ideal features of optical components as well other implementation imperfections could cause significant security loopholes. Inspired from this research topic, this diploma thesis contributes to the study of practical real-time implementation of Discrete Variable-QKD (DV-QKD) protocols.

This diploma thesis has three goals. The first goal is the brief study of the proof of security of BB84 QKD protocol using the concept of protocols' equivalence and the CSS codes; at the same time we manage to keep only the main steps of this proof so even readers lacking specialized knowledge will be able to understand it. The second goal of this diploma thesis is the study of the way that we can conduct the mathematical formulas for the efficiency metrics (Secure Key Rate, Quantum Bit Error Rate) of a group of protocols- the decoy-state protocols- in a system that uses a fiber optic for the transmittance. In order to accomplish our third goal we choose, from the aforementioned group of protocols, the weak+vacuum decoy-state QKD protocol. We study the way that the non ideal Variable Optical Attenuator (VOA) affects this protocol's efficiency by generalizing the vacuum decoy state and we conduct new formulas for studying the effect of the afterpulse phenomenon on the efficiency of this protocol. Then, we consider the effect of chromatic dispersion in a setup with two Mach-Zehnder interferometers which are used not only on the aforementioned protocols but on even more protocols, thus the mathematical formulas which we conduct are universal. We find the maximum possible generation rate of the Secure Key Rate that this setup can create as well as the value of each phase shifter of the two interferometers in relation to the communication's length and the error detection due to the interference Visibility that we want to succeed. Finally, we present a graphic representation of the previous imperfection on a Matlab environment.