Formalization of the Secrecy Capacity in Non-degraded Wiretap Channel

Unlike the traditional key-exchange based cryptography, physical layer security is built on information theory and aims to achieve unconditional security by exploiting the physical characteristics of wireless channels. With the growth of the number of wireless devices, physical layer security has been gradually emphasized by researchers. Various physical layer security protocols have been proposed for different communication scenarios. Since these protocols are based on information-theoretic security and the formalization work for information theory were not complete when these protocols were proposed, the security of these protocols lacked formal proofs. In this paper, we propose a formal definition for the secrecy capacity in non-degraded wiretap channel model and a formal proof for the secrecy capacity in binary symmetric channel with the help of SSReflect/Coq theorem prover.