Classical Knowledge for Quantum Cryptographic Reasoning

We prove that quantum key distribution is secure against several types of attacks within the framework of classical knowledge knowledge for quantum systems, a formal model which was developed in [D'Hondt, E. and P. Panangaden, Reasoning about quantum knowledge, in: Proceedings of the 25th Conference on Foundations of Software Technology and Theoretical Computer Science, LNCS 3821, 2005, p. 0544c (to appear), quant-ph/0507176]. In particular we rephrase security as a logical property and use meta-logic reasoning on the finite state machine corresponding to the quantum key distribution protocol. While these security issues have been studied before, it is the logical-based approach that is original here.