Key-Cast Over Networks

For a multi-source multi-terminal noiseless network, the multicast key-dissemination problem, here called the key-cast problem, involves the task of multicasting a (secret) key K from the network sources to its terminals. Unlike traditional communication, where messages must be delivered from source to destination(s) unchanged, key-cast is more flexible since key-cast need not require source reconstruction at destination nodes. Instead, the distributed key can be a mixture of sources from which the sources themselves may be unrecoverable. Key-cast (also known as secret key agreement) in memoryless networks has seen significant studies over the past decades. This work initiates the study of key-cast in noiseless networks, i.e., network coding, and addresses the similarities and differences between traditional forms of communication that require source reconstruction and the less constrained form of communication in the key-cast task. The study varies according to three criteria. The setting can be secure, in which case the shared key is not revealed to an eavesdropper (whose capabilities we constrain), or non-secure, in which case the key need not be hidden. The setting can have one or multiple source nodes capable of generating independent randomness to be used in the key generation process. And the setting can have one or multiple terminal sets, where the latter case is referred to as multiple key-cast. In multiple key-cast, one requires that terminals in each terminal set decode a different shared key. In the given settings, this work derives combinatorial conditions for key-cast and multiple key-cast and designs corresponding communication schemes. In addition, the study compares the key-cast rate with and without the restriction of source reconstruction that is needed in traditional forms of communication. Key-cast achieves a strict advantage in rate when source reconstruction is relaxed.