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Finite-Length Analysis of Wiretap Codes using Universal Hash Functions

Kagan Akcay

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 $ε$-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.

Finite-Length Analysis of Wiretap Codes using Universal Hash Functions

Abstract

This paper investigates the relation between the second-order coding rate, where the second-order turns out to be strictly larger than , and the mutual information as the leaked information for a fixed error probability by using wiretap codes constructed by universal hash functions. We first generalize the upper bound on -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.
Paper Structure (9 sections, 10 theorems, 41 equations)

This paper contains 9 sections, 10 theorems, 41 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Channel Model
  4. Types and Typicality
  5. Max-Information
  6. Divergence Bounds
  7. Universal Hashing
  8. Achievability Bounds on the Wiretap Channel
  9. Conclusion

Key Result

Lemma 1

info The number of different types of sequences in $\textbf{X}^n$ is less than $(n+1)^{\vert{}\textbf{X}\vert{}}$.

Theorems & Definitions (30)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • ...and 20 more