Intentional Attacks on Complex Network

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Intentional Attacks on Complex Network

Speaker: Shin-Ming ChengAdvisor: Kwang-Cheng Chen

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Outline

Introduction Intentional attack

- Cascade-based attack- Analytical model- Numerical result

Attack with global information Attack with local information Conclusion Reference

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Introduction

Intentional attack- Is an attack that aim at bringing down network nodes in decreasing order of nodal

degrees Whether the fragility indeed exists in Internet?

- Doyle and his colleagues [1] argued that, as a result of careful design for maximizing network throughput, the hub nodes at the router level are typically the edge nodes with a large number of low-capacity connections.

- The removal of these hub nodes, though disastrous to the large number of low-capacity users connected to them, will not bring down the Internet

Is the retrieval of global information in Internet possible?- Internet is too large for anyone to obtain their global topology information, which

means an accurate, intentional attack is hardly feasible.- Distributed attack by using local information

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Traditional Intentional attack

Cascading Failures on Power Transmission Grid Systems- Each node deals with a load of power- Removal of nodes can cause redistribution of loads over all network- A cascade of overloading failure is triggered.

- On August 10, 1996, a 1300-mw electrical line in southern Oregon sagged in the summer heat resulting in break-up into four islands, with loss of 30,390 MW of load affecting 7.49 million customers in western North America [2]

- On August 14, 2003, an initial disturbance in Ohio triggered the largest blackout in the U.S.’s history in which millions of people remained without electricity for as long as 15 hours

Cascading Failures on Internet- Traffic is rerouted to bypass malfunctioning routers- Eventually leading to an avalanche of overloads on other routers that are not

equipped to handle extra traffic.

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Input Parameters and Output Measure

The load at node i is defined as the total number of shortest paths passing through this node.

The capacity of a node is the maximum load that the node can handle. The capacity Ci of node i is proportional to its initial load Li

- - where the constant is the tolerance parameter.

The removal of nodes in general changes the distribution of shortest paths.

Cascading failures can be conveniently quantified by the relative size of the largest connected component- - where N and N’ are the numbers of nodes in the largest component before and after

the cascade, respectively.

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ii LC )1( 0

NNG /'

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Before the attack

Degree distribution: Load distribution:

- where k is the degree variable, and a and b are positive constants. Thus, we have

- where kmax is the largest degree in the network and S is the total load of the network.

Then we have , and , where

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akkP )(bkkL )(

max

1)(

kNdkkP max

1)()(

kSdkkLkP

)1()1(

1max

k

Na

)1( maxka

Sb 1

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After the attack

Degree distribution: Load distribution: Since only a small fraction of nodes are removed from the network, we

assume that and

Then , and

For the node with k links, the difference in load before and after the attack can be written as

The maximum load increase that the nodes can handle is Thus, the nodes still function if

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'')(' kakP'')(' kbkL

kakP ')(' kbkL ')('

)1()1(' 1

max'

k

Na

)1('

''max'ka

Sb

)(]1)/'[()'()( kLbbkbbkL

)()()( kLkLkC ]1)/'[( bb

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The critical value of the tolerance parameter

When (i.e., infinite scale-free network),- , which indicates that the network cannot be brought down by a single attack

if For a finite size network

- , thus , suggesting that breakdown can occur for

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1'11

1')(11'11

1'11

111'

max'

maxmax'

max'maxmax

max'

max

max'1max

1max'

SS

kkk

SSkk

SS

kk

SS

kk

kk

bbac

N0c

0

0max' k 0c c

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Numerical ResultsCascading failure in scale-free networks

In the case of the removal of the node with the highest degree, This phase transition phenomenon seems to be robust for different

sizes of network

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1.0c

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Numerical ResultsCascading failure in scale-free networks

Removal of a single node chosen - at random (squares), or among those with largest degrees (asterisks), or highest loads

(circles)

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Numerical ResultsCascading failure in homogeneous networks

All nodes are set to have the same degree k=3 and N=5000 In the inset, k≥2, γ=3, and N=5000. The resulting average degree [k] ≈3.1

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Numerical ResultsRobustness of the scale-free network

Internet hubs are of very high degrees.- The nodal degree of the biggest hub is 1458, whereas in the BA model, it is only 386.

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(a) Barabási-Albert (BA) model (b) real-world Internet model by the NLANR Project

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Numerical ResultsRobustness of the scale-free network

Greedy sequential attack:- chooses the largest-degree, live node adjacent to the node crashed in the last step as its

next-step target. Coordinated attack:

- Searches through all the live nodes adjacent to any crashed node and selects among them the largest-degree node as its next-step target.

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Conclusion

The scale-free network has “robust yet fragile” property, whereas the random graph is robust to both random and intentional attacks.- Internet is vulnerable to intentional attack. - However, a random attack does not significantly affect the network performance.

Performance of attacks based on incomplete/inaccurate network-topology information and local information- Incomplete information can degrade the efficiency of an intentional attack

significantly, especially if a big hub is missed.- Distributed attacks can be highly effective, sometimes almost as efficient as an

accurate global information-based attack.

Connection with current works?

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Reference

1. J. C. Doyle et al., “The ‘Robust Yet Fragile’ Nature of the Internet,” Proc. Nat’l. Acad. Sci., vol. 102, no. 41, Oct. 2005, pp. 1497-1502.

2. D. N. Kosterev, C. W. Taylor, and W. A. Mittelstadt, “Model validation for the August 10, 1996 WSCC system outage,” IEEE Transactions on Power Systems, vol. 14, no. 3, Aug 1999, pp. 967-979

3. A. E. Motter and Y.-C. Lai, “Cascade-based attacks on complex networks,” Phys. Rev. E, vol. 66, p. 065102(R), 2002.

4. L. Zhao, K. Park, and Y.-C. Lai, “Attack vulnerability of scale-free networks due to cascading breakdown,” Phys. Rev. E, vol. 70, p.035101(R), 2004.

5. P. Crucitti, V. Latora, and M. Marchiori, “Model for cascading failures in complex networks,” Phys. Rev. E, vol. 69, p. 045104(R), 2004.

6. Y. Xia and D. J. Hill, “Attack Vulnerability of Complex Communication Networks,” IEEE Transactions on Circuits and Systems, vol. 55, no. 1, Jan. 2008, pp. 65-69

7. S. Xiao, G. Xiao, and T. H. Cheng, “Tolerance of intentional attacks in complex communication networks,” IEEE Communication Magazine, vol. 46, no. 1, Jan 2008, pp. 146-152

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