A Modular Semantically Secure Wiretap Code with Shared Key for Weakly Symmetric Channels

We study the problem of secure communication over a wiretap channel when the sender and the receiver have access to a shared secret key. We propose a modular secure construction of wiretap codes for a shared key setting that achieves secrecy capacity for weakly symmetric wiretap channels, and has computationally efficient encoding and decoding. The construction’s security and reliability guarantees are in terms of semantic security, which is the strongest notion of security for these channels, and worst case error, respectively. We give concrete parameters of the construction for finite length messages to obtain a desired level of security and reliability.