Multiple Key-cast over Networks

TL;DR

This paper studies the multiple key-cast problem over networks, proposing combinatorial conditions and schemes for secure and non-secure key dissemination, showing that relaxing source reconstruction improves dissemination rates.

Contribution

It introduces the multiple key-cast problem in network coding, providing new combinatorial conditions, schemes, and rate comparisons for secure and non-secure scenarios.

Findings

Key-cast can outperform traditional communication in rate when source reconstruction is not required.

Combinatorial conditions are established for successful key dissemination.

Multiple key-cast schemes are designed for both secure and non-secure settings.

Abstract

The multicast key-dissemination problem over noiseless networks, introduced by Langberg and Effros [ITW 2022], here called the ``key-cast'' problem, captures the task of disseminating a shared secret random key to a set of terminals over a given network. 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. For example, the distributed keys can be mixtures of sources from which the sources themselves may be unrecoverable. The work at hand considers key dissemination in the single-source, multiple-multicast network coding setting, i.e., the ``multiple key-cast'' problem. Here, distinct keys are to be simultaneously transmitted from a single source node to multiple terminal sets, one shared random key per multicast set. Scenarios include the secure setting, in which only the source and intended destinations gain information about a given key; and the non-secure setting in which the only requirement is that the knowledge of one key does not reveal information about another. In both settings, we present combinatorial conditions for key dissemination and design corresponding multiple key-cast schemes. In addition, we compare the multiple key-cast rate with and without the restriction of source reconstruction, the former corresponding to traditional forms of communication; key-cast achieves a strict advantage in rate when source reconstruction is relaxed.