Exponential decreasing rate of leaked information in universal random privacy amplification

TL;DR

This paper introduces a new upper bound on Eve's information in secret key generation, improving previous bounds by utilizing a different R\'enyi entropy and applying it to wire-tap channels and secret key agreement.

Contribution

It presents a novel upper bound on leaked information using R\'enyi entropy of order 1+s, enhancing the analysis of secret key security.

Findings

New exponential upper bound for Eve's information.

Improved bound compared to previous work in additive cases.

Application to secret key agreement protocols.

Abstract

We derive a new upper bound for Eve's information in secret key generation from a common random number without communication. This bound improves on Bennett et al(1995)'s bound based on the R\'enyi entropy of order 2 because the bound obtained here uses the R\'enyi entropy of order $1+s$ for $s \in [0,1]$. This bound is applied to a wire-tap channel. Then, we derive an exponential upper bound for Eve's information. Our exponent is compared with Hayashi(2006)'s exponent. For the additive case, the bound obtained here is better. The result is applied to secret key agreement by public discussion.