Resilient Network Coding in the Presence of Byzantine Adversaries

Abstract

Abstract-Network coding substantially increases network throughput. But since it involves mixing of information inside the network, a single corrupted packet generated by a malicious node can end up contaminating all the information reaching a destination, preventing decoding. This paper introduces distributed polynomial-time rate-optimal network codes that work in the presence of Byzantine nodes. We present algorithms that target adversaries with different attacking capabilities. When the adversary can eavesdrop on all links and jam zO links, our first algorithm achieves a rate of C 02zO, where C is the network capacity. In contrast, when the adversary has limited eavesdropping capabilities, we provide algorithms that achieve the higher rate of C 0 zO.Our algorithms attain the optimal rate given the strength of the adversary. They are information-theoretically secure. They operate in a distributed manner, assume no knowledge of the topology, and can be designed and implemented in polynomial time. Furthermore, only the source and destination need to be modified; nonmalicious nodes inside the network are oblivious to the presence of adversaries and implement a classical distributed network code. Finally, our algorithms work over wired and wireless networks.

Signing a Linear Subspace: Signature Schemes for Network Coding

“…Information-theoretic methods for enabling recovery from malicious faults are possible by introducing redundancy into the original packets transmitted by the sender [16,18,19]. Such techniques have the advantage of not relying on any computational assumptions, but are limited to offering security only against a relatively limited class of adversaries: rather than limit the adversary's computational power, these constructions place limitations on the number of nodes the adversary can corrupt, the number of packets that can be modified, and/or the number of links on which the adversary can eavesdrop.…”

“…In contrast to information-theoretic schemes for achieving resilient network coding [18,19], our schemes are resilient to an arbitrary number of faults (as long as a minimum number of correct packets reach the receiver) and have substantially lower communication overhead. On the other hand, the computational requirements of our schemes are higher, and security is proven only relative to unproven (but standard) cryptographic assumptions.…”

Secure Network Coding over the Integers

“…Early efforts to deal with pollution attacks focused on information-theoretic solutions that use error-correction techniques to ensure that targets can reconstruct the file as long as the ratio of valid to invalid vectors received is sufficiently high [8,11,12]. Unfortunately, these techniques (inherently) impose limitations on the number of nodes the adversary can corrupt, the number of packets that can be modified, and/or the number of links on which the adversary can eavesdrop.…”

Multi-source operator channels: Efficient capacity-achieving codes

“…Further works by [4], [5], [6] provided network error-correcting codes with design and implementation complexity that is low (i.e., polynomial in size of the network parameters).…”

“…Every finite field F p , where p is a prime power, can be algebraically extended 4 [12] to a larger finite field F q , where q = p n for any positive integer n. Since F q includes F p as a subfield thus any matrix A ∈ F p m×ℓ is also a matrix in F q m×ℓ . Hence throughout the paper matrix multiplication over different fields (one over the base field and the other from the extended field) is allowed and computed over the extended field.…”