Construction of Codes for the Wiretap Channel and the Secret Key Agreement From Correlated Source Outputs Based on the Hash Property

The aim of this paper is to prove coding theorems for the wiretap channel and the secret key agreement based on the the notion of a hash property for an ensemble of functions. These theorems imply that codes using sparse matrices can achieve the optimal rate. Furthermore, fixed-rate universal coding theorems for a wiretap channel and a secret key agreement are also proved.