Network Information Theoretic Security

TL;DR

This paper extends Shannon's perfect secrecy concept from point-to-point to complex networks, establishing fundamental limits and proposing practical schemes for secure communication with shared secret bits.

Contribution

It introduces a theoretical framework for network information-theoretic security, deriving conditions for perfect secrecy and proposing efficient secure communication schemes.

Findings

Perfect secrecy is achievable if the sum rate of unhacked channels does not exceed shared secret bits.

A tradeoff exists between individual channel rates and overall network security.

Two practical schemes are proposed that balance network and channel rates with perfect secrecy.

Abstract

Shannon showed that to achieve perfect secrecy in point-to-point communication, the message rate cannot exceed the shared secret key rate giving rise to the simple one-time pad encryption scheme. In this paper, we extend this work from point-to-point to networks. We consider a connected network with pairwise communication between the nodes. We assume that each node is provided with a certain amount of secret bits before communication commences. An eavesdropper with unlimited computing power has access to all communication and can hack a subset of the nodes not known to the rest of the nodes. We investigate the limits on information-theoretic secure communication for this network. We establish a tradeoff between the secure channel rate (for a node pair) and the secure network rate (sum over all node pair rates) and show that perfect secrecy can be achieved if and only if the sum rate of any subset of unhacked channels does not exceed the shared unhacked-secret-bit rate of these channels. We also propose two practical and efficient schemes that achieve a good balance of network and channel rates with perfect secrecy guarantee. This work has a wide range of potential applications for which perfect secrecy is desired, such as cyber-physical systems, distributed-control systems, and ad-hoc networks.