On the Secrecy Exponent of the Wire-tap Channel

TL;DR

This paper establishes a tight exponential upper bound on information leakage in the wire-tap channel, matching the best known exponent, using an i.i.d. random coding approach.

Contribution

It derives a new exponential bound on the secrecy leakage in wire-tap channels, matching the best known exponent without requiring universal hash functions.

Findings

The derived exponent matches Hayashi's best known result.

The proof uses only i.i.d. random coding, simplifying previous methods.

The bound quantifies how secrecy improves with increased randomness.

Abstract

We derive an exponentially decaying upper-bound on the unnormalized amount of information leaked to the wire-tapper in Wyner's wire-tap channel setting. We characterize the exponent of the bound as a function of the randomness used by the encoder. This exponent matches that of the recent work of Hayashi (2011) which is, to the best of our knowledge, the best exponent that exists in the literature. Our proof---like those of Han et al. (2014) and Hayashi (2015)---is exclusively based on an i.i.d. random coding construction while that of Hayashi (2011), in addition, requires the use of random universal hash functions.