Intentional Attacks on Complex Network

1. Intentional Attacks on Complex Network Speaker: Shin-Ming Cheng Advisor: Kwang-Cheng Chen

2. Outline • Introduction • Intentional attack • Cascade-based attack • Analytical model • Numerical result • Attack with global information • Attack with local information • Conclusion • Reference 2

3. 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 3

4. 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. 4

5. Input Parameters and Output Measure • The load at nodeiis 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. 5

6. Before the attack • Degree distribution: • Load distribution: • where k is the degree variable, and a and b are positive constants. • Thus, we have • wherekmaxis the largest degree in the network and Sis the total load of the network. • Then we have , and , where 6

7. 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 7

8. 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 8

9. 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 9

10. 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) 10

11. Numerical ResultsCascading failure in homogeneous networks • All nodes are set to have the same degree k=3and N=5000 • In the inset, k≥2, γ=3, andN=5000. The resulting average degree [k]≈3.1 11

12. 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. (b) real-world Internet model by the NLANR Project (a) Barabási-Albert (BA) model 12

13. 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. 13

14. 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? 14

15. Reference • 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. • 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 • A. E. Motter and Y.-C. Lai, “Cascade-based attacks on complex networks,” Phys. Rev. E, vol. 66, p. 065102(R), 2002. • 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. • P. Crucitti, V. Latora, and M. Marchiori, “Model for cascading failures in complex networks,” Phys. Rev. E, vol. 69, p. 045104(R), 2004. • 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 • 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 15