Universal Secure Network Coding via Rank-Metric Codes

Abstract

Abstract-The problem of securing a network coding communication system against an eavesdropper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop on µ arbitrarily chosen links. The objective is to provide reliable communication to all receivers, while guaranteeing that the source information remains information-theoretically secure from the adversary. A coding scheme is proposed that can achieve the maximum possible rate of n − µ packets. The scheme, which is based on rank-metric codes, has the distinctive property of being universal: it can be applied on top of any communication network without requiring knowledge of or any modifications on the underlying network code. The only requirement of the scheme is that the packet length be at least n, which is shown to be strictly necessary for universal communication at the maximum rate. A further scenario is considered where the adversary is allowed not only to eavesdrop but also to inject up to t erroneous packets into the network, and the network may suffer from a rank deficiency of at most ρ. In this case, the proposed scheme can be extended to achieve the rate of n−ρ−2t−µ packets. This rate is shown to be optimal under the assumption of zero-error communication.

Universal secure rank-metric coding schemes with optimal communication overheads

“…We will consider the secret message S to be a uniform random variable in S = F αm×ℓ q , and we will consider noisy wire-tap channels (which can also be thought of as distributed storage systems) as given in [22]: Definition 1 (Coherent linearized channel [22]). We define a coherent linearized noisy wire-tap channel with t errors, ρ erasures with erasure matrix A ∈ F N ×n q of rank at least n−ρ, and µ observations as a channel with input a variable X ∈ X = F αm×n q , output to the receiver Y ∈ Y = F αm×N q , and output to the eavesdropper W ∈ W = F αm×µ q , together with a conditional probability distribution P (Y, W |X) such that…”

“…We now give the details of Example 1 and Example 2, which share the same construction: With the given parameters, the construction in [22,Th. 11] gives ℓ = 16 by choosing k 1 = 24 and k 2 = 8.…”

“…Universal secure linear network coding with errors and erasures was first studied in [22], where rank-metric coding schemes were proposed to protect messages sent over a linearly coded network from link errors, erasures and information leakage to a wiretapper. Similarly, rank-metric codes have been applied to storage systems where data is stored as a matrix and where errors and erasures affect several rows and/or columns, also called crisscross errors and erasures [21].…”

Adaptive Network Coding Scheme for TCP over Wireless Sensor Networks

“…In recent years, it has received much attention and has been generated huge research in communication networks [2]. TCP/NC [3] is the first one that incorporates network coding into TCP with minor changes to the protocol stack.…”

Untrusting network coding

“…One approach to dealing with untrusted networks is to impose strict security requirements, namely, to require that the network nodes learn nothing about the source messages. We can indeed use secure network coding designs [1], [2], [3], [4], [5], [6] to protect from a passive eavesdropper, Eve, who has access to at most k edges of the network; in our setting, where Eve has access to a network node, k would be the number of incoming edges in Eve's node. The security comes at the cost of throughput; namely, applying the techniques of [1]- [6], we cannot hope to achieve an information rate higher than h − k. Thus, if Eve's node has the same min-cut as a receiver, our throughput becomes zero.…”