A stochastic model of active cyber defense dynamics

Internet Mathematics

Volumn 11, Issue 1, 2015, Pages 23-61

  Xu, Shouhuai ^a   Lu, Wenlian ^b,c   Li, Hualun ^c  

^a University of Texas at San Antonio   (United States)

^b UNIVERSITY OF WARWICK   (United Kingdom)

^c FUDAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84924160239     PISSN: 15427951     EISSN: None     Source Type: Journal    
DOI: 10.1080/15427951.2013.830583     Document Type: Article

References (46)

1. [1] D. Aitel. “Nematodes—Beneficial Worms.” Available online (http://www.immunityinc.com/ downloads/nematodes.pdf), September 2005.
2. [2] R. Albert, H. Jeong, and A. Barabasi. “Error and Attack Tolerance of Complex Networks.” Nature 406 (2000), 378-482
3. [3] F. Ball, D. Sirl, and P. Trapman. “Threshold Behaviour and Final Outcome of an Epidemic on a Random Network with Household Structure.” Adv. in Appl. Probab 41:3 (2009), 765-796.
4. [4] F. Ball, D. Sirl, and P. Trapman. “Analysis of a Stochastic {SIR} Epidemic on a Random Network Incorporating Household Structure.” Mathematical Biosciences 224:2 (2010), 53-73.
5. [5] A. Barabasi and R. Albert. “Emergence of Scaling in Random Networks.” Science 286 (1999), 509-512.
6. [6] N. Berger, C. Borgs, J. Chayes, and A. Saberi. “On the Spread of Viruses on the Internet.” In Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA’05, pp. 301-310, 2005.
7. [7] F. Castaneda, E. Sezer, and J. Xu. “Worm vs. Worm: Preliminary Study of an Active Counterattack Mechanism.” In Proceedings of the 2004 ACM Workshop on Rapid Malcode (WORM’04), pp. 83-93, 2004.
8. [8] D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec, and C. Faloutsos. “Epidemic Thresholds in Real Networks.” ACM Trans. Inf. Syst. Secur. 10:4 (2008), 1-26.
9. [9] S. Chatterjee and R. Durrett. “Contact Processes on Random Graphs with Power Law Degree Distributions Have Critical Value 0.” Ann. Probab. 37:6 (2009), 2332-2356.
10. [10] K. Chung. A Course in Probability Theory, 2nd edition. Academic Press, 2000.
11. [11] F. Chung and L. Lu. Complex Graphs and Networks, CBMS Regional Conference Series in Mathematics. American Mathematical Society, 2006.
12. [12] R. Durrett. Random Graph Dynamics. Cambridge University Press, 2007.
13. [13] A. Ganesh, L. Massoulie, and D. Towsley. “The Effect of Network Topology on the Spread of Epidemics.” In Proceedings of IEEE Infocom 2005, 2005.
14. [14] H. Hethcote. “The Mathematics of Infectious Diseases.” SIAM Rev. 42:4 (2000), 599-653.
15. [15] P. Hill. Rates of Convergence in the Central Limit Theorem. Pitman Advanced Publisher, 1982.
16. [16] J. Kephart and S. White. “Directed-Graph Epidemiological Models of Computer Viruses.” In IEEE Symposium on Security and Privacy, pp. 343-361, 1991.
17. [17] J. Kephart and S. White. “Measuring and Modeling Computer Virus Prevalence.” In IEEE Symposium on Security and Privacy, pp. 2-15, 1993.
18. [18] W. Kermack and A. McKendrick. “A Contribution to the Mathematical Theory of Epidemics.” Proc. of Roy. Soc. Lond. A 115 (1927), 700-721.
19. [19] J. Kesan and C. Hayes. “Mitigative Counterstriking: Self-Defense and Deterrence in Cyberspace.” Harv. J. L. & Tech. 25:2 (2012), 417-527.
20. [20] T. Liggett. Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer-Verlag, 1999.
21. [21] H. Lin. “Lifting the Veil on Cyber Offense.” IEEE Security & Privacy 7:4 (2009), 15-21.
22. [22] L. Lovasz. “Eigenvalues of Graphs.” Available online (http://www.cs.elte.hu/∼lovasz/ eigenvals-x.pdf), 2007.
23. [23] N. Masuda, N. Gibert, and S. Redner. “Heterogeneous Voter Models.” Phys. Rev. E 82 (2010), 010103.
24. [24] W. Matthews. “U.S. Said to Need Stronger, Active Cyber Defenses.” Available online (http:// www.defensenews.com/story.php?i=4824730), October 2010.
25. [25] A. McKendrick. “Applications of Mathematics to Medical Problems.” Proc. of Edin. Math. Society 14 (1926), 98-130.
26. [26] D. Moore, C. Shannon, G. Voelker, and S. Savage. “Internet Quarantine: Requirements for Containing Self-Propagating Code.” In INFOCOM’03, 2003.
27. [27] P. A. P. Moran. The Statistical Processes of Evolutionary Theory. Clarendon Press, 1962.
28. [28] T. Mountford, J.-C. Mourrat, D. Valesin, and Q. Yao. “Exponential Extinction Time of the Contact Process on Finite Graphs”. arXiv:1203.2972, 2012.
29. [29] T. Mountford, D. Valesin, and Q. Yao. “Metastable Densities for Contact Processes on Power Law Random Graphs.” arXiv:1106.4336, 2012.
30. [30] R. Naraine. “’Friendly’ Welchia Worm Wreaking Havoc.” Available online (http://www.internetnews.com/ent-news/article.php/3065761/Friendly-Welchia-Worm-Wreaking-Havoc. htm), August 19, 2003.
31. [31] M. A. Nowak, Evolutionary Dynamics: Exploring the Equations of Life. Harvard University Press, 2006.
32. [32] R. Pastor-Satorras and A. Vespignani. “Epidemic Spreading in Scale-Free Networks.” Phys. Rev. Lett. 86:14 (2001), 3200-3203.
33. [33] E. Pugliese and C. Castellano. “Heterogeneous Pair Approximation for Voter Models on Networks.” Europhysics Letters 88:5 (2009), 58004.
34. [34] B. Schneier. “Benevolent worms.” Available online (http://www.schneier.com/blog/archives/ 2008/02/benevolent worm 1.html), February 19, 2008.
35. [35] F. Schweitzer and L. Behera. “Nonlinear Voter Models: The Transition from Invasion to Coexistence.” European Physical Journal B 67 (2009), 301-318.
36. [36] L. Shaughnessy. “The Internet: Frontline of the Next War?” Available online (http://www.cnn. com/2011/11/07/us/darpa/), November 7, 2011.
37. [37] V. Sood, T. Antal, and S. Redner. “Voter Models on Heterogeneous Networks.” Physical Review E 77:4 (2008), 1-13.
38. [38] S. Staniford, V. Paxson, and N. Weaver. “How to Own the Internet in Your Spare Time.” In Proceedings of the 11th USENIX Security Symposium, pp. 149-167, 2002.
39. [39] S. Staniford, D. Moore, V. Paxson, and N. Weaver. “The Top Speed of Flash Worms.” In Proceedings of the 2004 ACM Workshop on Rapid Malcode (WORM’04), pp. 33-42. ACM Press, 2004.
40. [40] P. Van Mieghem, J. Omic, and R. Kooij. “Virus Spread in Networks.” IEEE/ACM Trans. Netw. 17 (2009), 1-14.
41. [41] M. Vojnovic and A. Ganesh. “On the Race of Worms, Alerts, and Patches.” IEEE/ACM Trans. Netw. 16 (2008), 1066-1079.
42. [42] Y. Wang, D. Chakrabarti, C. Wang, and C. Faloutsos. “Epidemic Spreading in Real Networks: An Eigenvalue Viewpoint.” In Proc. of the 22nd IEEE Symposium on Reliable Distributed Systems (SRDS’03), pp. 25-34, 2003.
43. [43] N. Weaver and D. Ellis. “White Worms Don’t Work.”;login: (Usenix) 31 (2006), 33-38.
44. [44] H. S. N. Wire. “Active Cyber-Defense Strategy Best Deterrent against Cyber-Attacks.” Available online (http://www.homelandsecuritynewswire.com/ active-cyber-defense-strategy-best-deterrent-against-cyber-attacks), June 28, 2011.
45. [45] J. Wolf. “Update 2-U.S. Says Will Boost Its Cyber Arsenal.” Available online (http://www. reuters.com/article/2011/11/07/cyber-usa-offensive-idUSN1E7A61YQ20111107), November 7, 2011.
46. [46] S. Xu, W. Lu, and Z. Zhan. “A Stochastic Model of Multivirus Dynamics.” IEEE Trans. Dependable Sec. Comput. 9:1 (2012), 30-45.