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The aim of this paper is to prove coding theorems for the wiretap channelcoding problem and secret key agreement problem based on the the notion of ahash property for an ensemble of functions. These theorems imply that codesusing sparse matrices can achieve the optimal rate. Furthermore, fixed-rateuniversal coding theorems for a wiretap channel and a secret key agreement arealso proved.

Construction of Codes for Wiretap Channel and Secret Key Agreement from Correlated Source Outputs by Using Sparse Matrices