On the Equivalency of Reliability and Security Metrics for Wireline Networks

TL;DR

This paper demonstrates the equivalency of various security and reliability metrics in wireline networks, showing that under certain conditions, different secrecy and error constraints are effectively interchangeable.

Contribution

It establishes the equivalency between weak and strong secrecy conditions, and between perfect secrecy with zero-error and weak secrecy with small error, for linear network coding.

Findings

Weak and strong secrecy are equivalent in broad network coding scenarios.

Perfect secrecy with zero-error is equivalent to weak secrecy with small error in linear codes.

The results unify different security and reliability metrics in wireline networks.

Abstract

In this paper, we show the equivalency of weak and strong secrecy conditions for a large class of secure network coding problems. When we restrict to linear operations, we show the equivalency of "perfect secrecy and zero-error constraints" with "weak secrecy and $\epsilon$-error constraints".