Universal Secure Multiplex Network Coding with Dependent and Non-Uniform Messages

TL;DR

This paper demonstrates that a random linear precoder in secure network coding can achieve strong and universal security even with dependent and non-uniform messages, broadening practical applicability.

Contribution

It proves strong and universal security for network coding with dependent and non-uniform messages, relaxing previous independence and uniformity assumptions.

Findings

Achieves strong security in network coding with dependent messages

Ensures universal security with arbitrary small mutual information

Extends security proofs to more practical message distributions

Abstract

We consider the random linear precoder at the source node as a secure network coding. We prove that it is strongly secure in the sense of Harada and Yamamoto and universal secure in the sense of Silva and Kschischang, while allowing arbitrary small but nonzero mutual information to the eavesdropper. Our security proof allows statistically dependent and non-uniform multiple secret messages, while all previous constructions of weakly or strongly secure network coding assumed independent and uniform messages, which are difficult to be ensured in practice.