Tight exponential analysis of universally composable privacy amplification and its applications

TL;DR

This paper provides a tight exponential analysis of privacy amplification using universal hash functions, offering new bounds on Eve's distinguishability and applications to wire-tap channels and secret key generation.

Contribution

It introduces a novel upper bound based on Renyi entropy for universal composability in privacy amplification, achieving tight exponential decay rates.

Findings

Derived a new upper bound on Eve's distinguishability

Established the tight exponential rate for i.i.d. distributions

Applied results to wire-tap channels and secret key distillation

Abstract

Motivated by the desirability of universal composability, we analyze in terms of L_1 distinguishability the task of secret key generation from a joint random variable. Under this secrecy criterion, using the Renyi entropy of order 1+s for s in [0,1, we derive a new upper bound of Eve's distinguishability under the application of the universal2 hash functions. It is also shown that this bound gives the tight exponential rate of decrease in the case of independent and identical distributions. The result is applied to the wire-tap channel model and to secret key generation (distillation) by public discussion.