Network coding for information security

Network coding has generated much interest in information and coding theory, networking, wireless communications, cryptography, and computer science in the past few years. Consider a point-to-point communication network on which a number of information sources are mulitcast to certain sets of destination nodes. The problem is to characterize the maximum possible thruputs. Contrary to one\´s intuition, network coding theory reveals that it is in general not optimal to regard the information to be multicast as a "fluid" which can simply be routed or replicated. Rather, by employing coding at the nodes, bandwidth can in general be saved. Cai and Yeung introduced the model of secure network coding which subsumes both secret sharing and the wiretapped channel II. In this model, an information source is multicast from a source node to a set of destination nodes. A collection of subsets of the channels in the network is given, and a wiretapper is allowed to access any one (but not more than one) of these subsets without being able to obtain any information about the information source. This talk is based on the paper as well as the subsequent papers. In particular, we will discuss a construction of secure network codes which is optimal for the special case that the wiretapper may choose to access any subset of channels of a fixed size.