Secure Message Transmission on Directed Networks

37 Pages Posted: 27 Jun 2012

See all articles by Jerome Renault

Jerome Renault

University of Toulouse 1 - Toulouse School of Economics (TSE)

Ludovic Renou

Queen Mary University of London

Tristan Tomala

Université Paris I Panthéon-Sorbonne

Date Written: April 16, 2012

Abstract

Consider a sender and a receiver as two distant nodes in a network. The sender wishes to transmit a secret to the receiver, but faces an adversary controlling an unknown set of nodes. We characterize the directed networks for which there exist \epilson-secret and \epsilon-strongly secure communication protocols (for all \epsilon > 0): if all nodes are obedient the receiver learns the secret with probability at least 1−\epsilon and no information is leaked (secrecy), and this property is maintained under every strategy of the adversary (security). For secrecy, a necessary and sufficient condition is that there is a directed path from the sender to the receiver, and for each possible adversarial coalition A, there is an undirected path from the sender to the receiver that contains no node in A. For security, a necessary and sufficient condition is that for every possible adversarial coalition A, the graph obtained by removing all nodes in A still has the previous property.

Keywords: secure communication, protocols, communication

JEL Classification: C72, D82

Suggested Citation

Renault, Jerome and Renou, Ludovic and Tomala, Tristan, Secure Message Transmission on Directed Networks (April 16, 2012). Available at SSRN: https://ssrn.com/abstract=2093156 or http://dx.doi.org/10.2139/ssrn.2093156

Jerome Renault

University of Toulouse 1 - Toulouse School of Economics (TSE) ( email )

Place Anatole-France
Toulouse Cedex, F-31042
France

Ludovic Renou (Contact Author)

Queen Mary University of London ( email )

Mile End Road
London, London E1 4NS
United Kingdom

Tristan Tomala

Université Paris I Panthéon-Sorbonne ( email )

12, place du Panthéon
Paris, IL
France

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