Provability of Security and E ciency of Quantum Key Distribution (QKD) Algorithms

Abstract

With recent developments in quantum communications, much of the focus has been put on development of di erent Quantum Key Distribution(QKD) protocols that can successfully generate a symmetric key over insecure quan- tum channel. In this thesis, I have discussed in-depth security proof of a well known secure protocol named as BB84 protocol. This simple version of proof was rst pro- posed by Shor and Preskill[1], in year 2000. It involves two step derivation of BB84 protocol from a 'Lo-Chau' protocol, which has already been proven secure. I shall provide proof of exponentially lower bounds on mutual infor- mation shared between sender/receiver and an adversary, therfore proving its security. Along with it, I have also introduced another varient of Lo-Chau protocol which is more e cient in terms of shared resources, i.e. it uses almost 50% lesser quantum states exchanged over channel. I shall also prove it to be secure using the same technique used for BB84. iii