The Topology of Covert Conflict

Shishir Nagaraja, Ross Anderson

Cambridge University

Topology and Resilience

• Many real-world networks can be modeled as scale-free – social contacts, disease spread, spread of computer viruses

• Power-law distribution of vertex order, often arising from preferential attachment

• Highly-connected nodes greatly enhance connectivity

• This gives resilience against random failure

Topology and Vulnerability

• Although power-law vertex order distribution gives resilience to random failure, it makes the network vulnerable to targeted attack

• If you attack high-order nodes, the network is rapidly disconnected (Albert, Jeong and Barabási, 2000)

• Example: Sierra Leone HIV/AIDS program treated prostitutes first – only 2% of population infected (vs 40% in Botswana)

Topology and Vulnerability (2)

• Music companies target high-order nodes in peer-to-peer networks (prolific uploaders)

• More traditional example: if you conquer a country, subvert or kill the bourgeoisie first

• What about the dynamic case, e.g. insurgency? Police keep arresting, insurgents keep recruiting

• We set out to study this dynamic case, using evolutionary game theory

Simulation Methodology

• After Axelrod’s work on iterated prisoners’ dilemma

• Scale-free network of 400 nodes• At each round, attacker kills 10 nodes –

their selection is his strategy• Defender recruits 10 more, then

reconfigures network – how he does this is his strategy

• Iterate search for defense, attack strategy

Naïve Defenses Don’t Work!

• Basic vertex-order attack – network dead after 2 rounds

• Random replenishment – 3 rounds

• Scale-free replenishment – 4 rounds

Evolving Defense Strategies

• Black – scalefree replenishment

• Green – replace high-order nodes with rings

• Cyan - replace high-order nodes with cliques

• Cliques work very well against the vertex-order attack

Evolving Attack Strategies• Centrality

attacks are the best counter we found to clique-based defenses

• Rings: G, B cliques: C, M

• Vertex-order attack: B, G, C

• Attack using centrality: R, B, M

Next Evolution …

• Combine two defensive strategies – yellow graph is delegation plus cliques

• Modern terror network?

• 3rd-generation music-sharing network?

What this teaches

• People set out to make peer-to-peer systems robust by arranging the nodes in rings. This didn’t work. Clubs do work

• We have some insight into why insurgents organise themselves in cells

• We can model strategies for wiretapping, surveillance, counterinsurgency …

• What about biology?

Biological Robustness

• Redundancy via homologous genes makes an organism better able to evolve (phenotypic changes less often lethal)

• This evolvability is an important element of robustness (Hiroaki Kitano, Nature, Nov 2004, pp 826–837)

• What we call ‘cells’ biologists think of as conserved clusters, the bows in bow-tie networks, or evolutionary capacitors

• Our work may give an insight into the evolution of hierarchical modularity

Conclusion

• We’ve built a bridge between network analysis and evolutionary game theory

• Using our simulation methodology, we get insights into why revolutionaries use cells, the effects of modern policing, and more

• Simulations let us explore many new attack and defense strategies

• Implications for all sorts of networks – computer, social, political … biological?