Network coding achieves optimal throughput in multicast networks. However, throughput optimality relies on the network nodes or routers to code correctly. A Byzantine node may introduce junk packets in the network (thus polluting downstream packets and causing the sinks to receive the wrong data) or may choose coding coecients
We consider the problem of achieving capacity through network coding when some of the nodes act covertly as Byzantine adversaries. For several case-study networks, we investigate rates of reliable communication through network coding and upper bounds on capacity. We show that linear codes are inadequate in general, and a slight augmentation of the class of linear codes can increase throughput. Furthermore, we show that even this nonlinear augmentation may not be enough to achieve capacity. We introduce a new class of codes known as bounded-linear that make use of distributions defined over bounded sets of integers subject to linear constraints using real arithmetic. 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 links, our first algorithm achieves a rate of , where is the network capacity. In contrast, when the adversary has limited eavesdropping capabilities, we provide algorithms that achieve the higher rate of . 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.