Finite-Length Analysis of Wiretap Codes using Universal Hash Functions

TL;DR

This paper analyzes the finite-length performance of wiretap codes constructed with universal hash functions, linking second-order coding rates to leaked information and providing new bounds and achievability results.

Contribution

It generalizes bounds on smooth max information and applies universal hashing techniques to wiretap channels, offering new insights into finite-length security analysis.

Findings

Second-order coding rate exceeds rac12; (n) for some functions f(n).

Derived new upper bounds on rac12; (n) for wiretap codes.

Established achievability results assuming a conjecture holds.

Abstract

This paper investigates the relation between the second-order coding rate, where the second-order turns out to be strictly larger than $\sqrt{n}$, and the mutual information as the leaked information for a fixed error probability by using wiretap codes constructed by universal$_2$ hash functions. We first generalize the upper bound on $\epsilon$-smooth max information in \cite{tyagi} and use it in our analysis where we adopt the method in \cite{hayashi-tan}, which uses universal hashing for compressing a source and making it secure from another correlated source, and apply it to the wiretap channel. We prove first- and second-order achievability results by assuming that the conjecture we state holds true.