Semantically-Secure Coding Scheme Achieving the Capacity of a Gaussian Wiretap Channel

We extend a recently proposed wiretap coding scheme to the Gaussian wiretap channel and show that it is semantically-secure. Denoting by SNR the signal-to-noise ratio of the eavesdropper’s channel, the proposed scheme converts a transmission code of rate R for the channel of the legitimate receiver into a code of rate R− 0.5 log(1 + SNR) for the Gaussian wiretap channel. The conversion has a polynomial complexity in the codeword length and the proposed scheme achieves semantic security. In particular, when the underlying transmission code is capacity achieving, this scheme achieves the secrecy capacity of the Gaussian wiretap channel. Our security analysis relies on a single-shot bound on the mutual information between the message and the eavesdropper’s observation for the proposed scheme, which may be of independent interest.