Coping with Physical Attacks on Random Network Structures

Coping with Physical Attacks on Random Network StructuresOmer Gold omergolden@gmail.comJoint work with Reuven Cohen (BIU)

To appear in the Proceedings of IEEE International Conference on Communications (ICC), June, 2014.

ContentProblem and motivationPrevious work OverviewRandom Network modelAlgorithms and Analyses Summary

Problems and motivationCommunication networks are vulnerable to natural disasters, such as earthquakes or oods, as well as to physical attacks, such as an Electromagnetic Pulse (EMP) attack.

Such real-world events happen in specic geographical locations and disrupt specic parts of the network.

Therefore, the geographical layout of the network determines the impact of such events on the networks connectivity.4Large Scale Physical Attacks/DisastersEMP (Electromagnetic Pulse) attack, Solar Flares, and other Natural Disasterswill destroy backbone nodes and links

Physical attacks or disasters affect a specific geographical areaFibers, routers, generators, and power lines have a physical location

Source: Report of the Commission to Assess the threat to the United States from Electromagnetic Pulse (EMP) Attack, 2008 4Problems and motivationAn interesting question is to identify the most vulnerable parts of the network.

That is, the locations of disasters that would have the maximum disruptive effect on the network in terms of capacity and connectivity.

We consider graph models in which nodes and links are geographically located on a plane, and model the disaster event as a line segment or a circular cut.Problems and motivationDenition 1 (Performance Measures):The performance measures of a cut are (the last 3 are dened as the values after the removal of the intersected links): TEC - The total expected capacity of the intersected links. ATTR - The average two terminal reliability of the network. (Connectivity measure) MFST - The maximum ow between a given pair of nodes s and t. AMF - The average value of maximum ow between all pairs of nodes.

Example Circular cut73297Q. What is the TEC measure for this cut?A. 2+3+7+9+7 = 28*The black links are not affecetd by the cut.Problems and motivationDenition 2 (Worst-Case Cut):

Under a specic performance measure, a worst-case cut is a cut which maximizes/minimizes the value of the performance measure.Problems and motivationGeographical Network Inhibition by Circles (GNIC) Problem (2009): Given a graph, cut radius, link probabilities, and capacities, nd a worst-case circular cut under performance measure TEC.After solving TEC measure problem in polynomial time, it can be shown that the other performance measures(ATTR, MFST, AMF) are also polynomial. (Zussman, Neumayer, Cohen, Modiano. 2009).We will focus from now on the TEC measure.

The ber backbone operated by a major U.S. network provider Example Real NetworkWe want to find a cut that maximizes TEC,denote as worst-cut.

Previous Work OverviewPrevious Work OverviewNetwork Reliability Under Random Line-Segment Cut:Calculate some network performance metrics to such a disaster in polynomial time.S. Neumayer, E. Modiano (IEEE Infocom 2010)Network Reliability Under Random Circular-Cutdisasters that take the form of a `randomly' located disk in a plane. Approximate some network performance metrics in case of such a disaster in polynomial time.S. Neumayer, E. Modiano (IEEE Globecom 2011)Previous Work: Probabilistic FailuresMajor work has been made recently about generalizing previous failure model to probabilistic failure model and simultaneous attack failures. Work by:Pankaj K. Agarwal, Alon Efrat, Shashidhara K. Ganjugunte, David Hay, Swaminathan Sankararaman, Gil Zussman: The resilience of WDM networks to probabilistic geographical failures. INFOCOM 2011: 1521-1529

Later improved version in: IEEE/ACM Trans. Netw. 21(5): 1525-1538 (2013)

Another improvement and variation has been recently made by:Pankaj K. Agarwal, Sariel Har-Peled, Haim Kaplan, Micha Sharir: Union of Random Minkowski Sums and Network Vulnerability Analysis.

Previous Work OverviewFailure ModelsDeterministic: Fails definitely if within range Probabilistic: Simple: fails with a probability q if within rangeSpatial Probability FunctionsLinear, Gaussian, Arbitrary*

P. Agrawal, A. Efrat, S. Ganjugunte, D. Hay, S. Sankararaman, G. Zussman IEEE Infocom 2011Random NetworkAs we saw, models with deterministic, random and probabilistic failures have been recently studied extensively .

What about Random Networks? This is what we are going to talk about here.Our work is about developing algorithms for finding worst-cuts in Random Networks, as well as developing methods to model a random network from a given data, such as: demographic map, terrain conditions, economic considerations, etc.Random Network- MotivationThe attacker (adversary) has partial or no knowledge about the network topology.

Adversary has a noisy network topology map.

Assessing the reliability of hidden networks.

Real-life networks topology sometimes presents similar characteristics to a random network topology.Random Network- Our Model

Random Network- Our ModelRandom Network- Our ModelRandom Network- ModelRandom Network- ModelAlgorithm Evaluate DamageWe present Polynomial Time Approximation Algorithms for finding the Expected Worst Case cuts location and damage in the Random Network model, i.e. cut that maximizes the total expected capacity of the intersected links (TEC).

For this goal we first develop an algorithm to evaluate the TEC (Damage) for a given cut.

Evaluate Damage of a Circular Attack (i.e. cut)Example:

Example Circular cut73297Evaluate Damage of Circular Attack

Evaluate Damage of Circular Attack

Evaluate Damage of Circular Attack

Evaluate Damage of Circular AttackAlgorithm to Evaluate the Expected Damage for a given Cut.Algorithm to Evaluate the Expected Damage for a given Cut.Algorithm to Evaluate the Expected Damage for a given Cut.

Example:

Evaluate the Expected Damage for a given Cut.Algorithm to Evaluate the Expected Damage for a given Cut.Algorithm to Evaluate the Expected Damage for a given Cut.We run over the squares center-point.Size of the Grid (squares) is determined by the requested accuracy parameters.How? Algorithm to Evaluate the Expected Damage for a given Cut.

Numerical AccuracyNumerical AccuracyNumerical Accuracy

Numerical Accuracy

For simplicity, lets look at thisNumerical Accuracy

Numerical AccuracyFirst, lets look at the extreme case:

Numerical AccuracyFirst, lets look at the extreme case:

Numerical AccuracyNow, back to the general case:

47Additive ApproximationAdditive ApproximationAdditive ApproximationAdditive Approximation Additive Approximation Running Time Additive Approximation Running TimeAdditive ApproximationMultiplicative ApproximationReceives also the multiplicative accuracy parameterMultiplicative ApproximationProbably no time for technical details for this analysis.

Lets jump a few slides straight to the running time.

Now we work to represent it as a multiplicative of

Note also that

Note also that

Note also that

We have

We have

Multiplicative factorAdditive termMultiplicative Approximation Running TimeFind Sensitive Locations SchemeFind Sensitive Locations SchemeFind Sensitive Locations SchemeFind Sensitive Locations SchemeFind Sensitive Locations SchemeSimulations, Numerical Results.Simulations, Numerical Results.

Color map of the the USA population density in logarithmic scale. The The values determines the intensity function used as the input for the simulationSimulations, Numerical Results.Simulations, Numerical Results.

Color map of the centers of circular cuts with radius r = 5 (approximately 130km). Red is most harmful.Simulations, Numerical Results.Color map of the centers of circular cuts with radius r = 5 (approximately 208km). Red is most harmful.

Simulations, Numerical Results.Color map of the centers of circular cuts with radius r = 5 (approximately 130km). Red is most harmful.

Simulations, Numerical Results.Color map of the centers of circular cuts with radius r = 10 (approximately 260km). Red is most harmful.

Simulations, Numerical Results.Comparing the results to the results obtained in previous work for a deterministic ber backbone in the USA it can be seen that some similarities and some dissimilarities exist.

Simulations, Numerical Results.Previous work on deterministic network line cuts simulations.

Line segments cuts of length approximately 120 miles optimizing TEC the red cuts maximize TEC and the black lines are nearly worst-case cuts.Simulations, Numerical Results.Previous work on deterministic network MFST measure: The maximum flow between a given pair of nodes s and t.

The impact of circular cuts of radius approximately 120 miles on the MFST between Los Angeles and NYC. Red circles represent cuts that result in MFST = 0 and black circles result in MFST = 1. **Cuts which intersect the nodes representing Los Angeles or NYC are not shown.

Simulations, Numerical Results.Our results imply that some information on the network sensitivity and vulnerabilities can be deduced from the population alone, with no information on any physical links and nodes.

However, our algorithm can be used in conjunction with more complicated modeling assumptions, including topographic features and economic considerations to give more accurate results.Conclusions, SummaryOur schemes allows to examine how valuable is public information (such as demography, topography and economic considerations) to an attackers destruction assessment capabilities, and examine the affect of hiding the actual physical location of the fibers on the attack strategy.

Thereby, the schemes can be used as a tool for policy makers and engineers to design more robust networks by placing links along paths that avoid areas of high damage cuts, or identifying locations which require additional protection efforts (e.g., equipment shielding).Conclusions, SummaryRecent contributions to this emerging field of geographical failures focused on deterministic networks, studied various failure models.

We described polynomial time approximation algorithms for nding the damage caused by cuts at different points in our spatial random network model and to approximate the location and damage of the worst case cuts.

To the best of our knowledge this work is the first to study such geographical failures in the context of spatial random networks.

Future work The discussion about finding vulnerable geographic locations to physical attacks naturally leads to the question of robust network design in the face of geographical failures. Several questions are proposed:Designing the networks physical topology under some demand constraints (e.g., nodes that should be located within a specific region, capacity and flow demands) such that the damage by a large-scale physical attack is minimized.Study the effect of adding minimal infrastructure (e.g., lighting-up dark fibers) on network resilience, and determine how to use low-cost shielding for existing components to mitigate large-scale physical attacks.

Future work Another related research direction is to develop a framework for attack and defense strategies for opponents having no knowledge of each others strategy.

Using a game-theoretic approach, study a two player zero sum game where one player (the defender) attempts to design a network as resilient to physical attacks as possible under some demand constraints, while the other player (the attacker) picks a location for the cut, without having complete knowledge about the actual networks physical structure.

Improving Running Time (Idea):