On the security of the BB84 quantum key distribution protocol

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The BB84 quantum key distribution (QKD) protocol enables two authenticated parties to generate a secret key over an insecure quantum channel. Using a standardized security definition, we prove that BB84 is secure and include explicit bounds on its security. Furthermore, our use of quantum circuit diagrams simplify the Shor-Preskill proof. Namely, we can reduce the Modified Lo-Chau QKD to a practical version of BB84 using the observation from Shor and Preskill that one may ignore a correctable number of phase errors, and the fact that computational basis measurements commute with controls of CNOT operations. The first four chapters provide the required background material on quantum computing, information theory, cryptography, coding theory, and quantum error correcting codes. Chapter 5 presents protocols for entanglement purification. Chapter 6 reduces an entanglement purification protocol to the Modified Lo-Chau QKD, and proves that it is secure. Finally, a reduction from the Modified Lo-Chau QKD to BB84 establishes the security of the latter.
Bibliography: p. 161-166
Cannings, R. (2004). On the security of the BB84 quantum key distribution protocol (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/19009