A Polynomial Time Procedure Converting Error Correcting Codes to Semantically Secure Wiretap Codes

Abstract

We furnish a procedure based on universal hash families that can convert an error correcting code of rate R to a semantically secure wiretap code of rate R−ξ where ξ is some parameter derived from the eavesdropper’s channel. This conversion is shown to be polynomial time efficient with block length and is applicable to any discrete time channel. To prove the induced wiretap code is semantically secure, we have upgraded recent leakage bounds by maximizing over all message distributions. The semantic leakage is shown to be exponentially decreasing with block length. As an explicit application, we construct a concrete, polynomial time efficient, semantically secure wiretap code that can achieve the secrecy capacity of the AWGN wiretap channel. Moreover, this wiretap coding scheme has both probability of error and semantic leakage exponentially diminishing with block length.