On the secrecy exponent of the wire-tap channel

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 [12] which is, to the best of our knowledge, the best exponent that exists in the literature. Our proof (like those of [17], [18]) is exclusively based on an i.i.d. random coding construction while that of [12], in addition, requires the use of random universal hash functions.