Trade-offs between Rate and Security in Linear Multicast Network Coding

We obtain a relationship between the rate and security for secure multi-cast linear network codes in the presence of a 'wire-tap' adversary who can eavesdrop on a bounded number of network edges. Specifically, we show that a network code that can communicate information at rate R and is secure against an adversary eavesdropping on z network edges can be transformed to a code that allows communication at rate R-1 while being secure against a more potent adversary eavesdropping on z+1 network edges. Results of this nature are known under the assumption that only the network source node has the ability to generate random keys used to obfuscate the communicated messages. The novelty of this work lies in studying the setting in which each network node may generate independent random keys.