Network Coding Multicast Key-Capacity

TL;DR

This paper explores the capacity limits of secure key dissemination in noiseless network coding, highlighting differences from traditional multicast and proposing new insights into achievable key rates.

Contribution

It introduces the study of key-dissemination in noiseless networks, analyzing its potential to surpass traditional multicast in key-rate capacity and security considerations.

Findings

Key-dissemination allows more flexible shared keys than traditional multicast.

The study characterizes the supremum of achievable key-rates under security constraints.

Differences between secure multicast and key-dissemination are analyzed in noiseless network contexts.

Abstract

For a multi-source multi-terminal noiseless network, the key-dissemination problem involves the task of multicasting a secret key K from the network sources to its terminals. As in secure multicast network-coding, in the key-dissemination problem the source nodes have access to independent randomness and, as the network is noiseless, the resulting key K is a function of the sources' information. However, different from traditional forms of multicast, in key-dissemination the key K need not consist of source messages, but rather may be any function of the information generated at the sources, as long as it is shared by all terminals. Allowing the shared key K to be a mixture of source information grants a flexibility to the communication process which gives rise to the potential of increased key-rates when compared to traditional secure multicast. The multicast key-capacity is the supremum of achievable key-rates, subject to the security requirement that the shared key is not revealed to an eavesdropper with predefined eavesdropping capabilities. The key-dissemination problem (termed also, secret key-agreement) has seen significant studies over the past decades in memoryless network structures. In this work, we initiate the study of key-dissemination in the context of noiseless networks, i.e., network coding. In this context, we study similarities and differences between traditional secure-multicast and the more lenient task of key-dissemination.