Universal Secure Error-Correcting Schemes for Network Coding

TL;DR

This paper introduces a universal, secure, and error-correcting network coding scheme that guarantees zero-error, information-theoretic security against eavesdroppers and jammers, achieving optimal rate with low complexity.

Contribution

It presents a universal scheme based on rank-metric codes that attains the maximum secure rate for any network topology and field size, with minimal packet length.

Findings

Achieves the maximum rate of n - μ - 2t packets per transmission.

Provides a universal scheme applicable to any network topology.

Proves the scheme's optimality in minimal packet length.

Abstract

This paper considers the problem of securing a linear network coding system against an adversary that is both an eavesdropper and a jammer. The network is assumed to transport n packets from source to each receiver, and the adversary is allowed to eavesdrop on \mu arbitrarily chosen links and also to inject up to t erroneous packets into the network. The goal of the system is to achieve zero-error communication that is information-theoretically secure from the adversary. Moreover, this goal must be attained in a universal fashion, i.e., regardless of the network topology or the underlying network code. An upper bound on the achievable rate under these requirements is shown to be n-\mu-2t packets per transmission. A scheme is proposed that can achieve this maximum rate, for any n and any field size q, provided the packet length m is at least n symbols. The scheme is based on rank-metric codes and admits low-complexity encoding and decoding. In addition, the scheme is shown to be optimal in the sense that the required packet length is the smallest possible among all universal schemes that achieve the maximum rate.