1. CODE RED WORM PROPAGATION MODELING AND ANALYSIS Cliff Changchun Zou, Weibo Gong, Don Towsley

2. Introduction  The Code Red worm incident of July 2001 has stimulated activities to model and analyze Internet worm propagation.  Previous works didn’t consider two factors affecting Code Red propagation  Dynamic countermeasures taken by ISPs and users  The slowed down worm infection rate  Two factor worm model

3. Background on Code Red Worm  Code Red worm exploited Windows IIS vulnerability on Windows 2000  Each worm copy generated 100 threads  99 threads randomly chose one IP address to attack  Timeout: 21 seconds

4. Background on Code Red Worm

7. Using Epidemic Models to Model Code Red Worm Propagation  Computer viruses and worms are similar to biological viruses on their self-replicating and propagation behavior  Introduce two classical epidemic models as the bases of the two-factor internet worm model  Classical simple epidemic model  Kermack-Mckendrick model

8. Classical Simple Epidemic Model J(t): the number of infected hosts at time t : infection rate S(t): the number of susceptible hosts at time t N: size of population  At t=0: J(0) hosts are infected and other N-J(0) hosts are all susceptible

9. Classical Simple Epidemic Model  Let, dividing both sides by N^2 where

10. Classical Simple Epidemic Model  The classical epidemic model can match the beginning phase of Code Red spreading, it can’t explain the later part of Code Red propagation: during the last five hours from 20:00 to 00:00 UTC, the worm scans kept decreasing

11. Kermack-Mckendrick Model  Considers the removal process of infectious hosts  Once a host recovers from the disease, it will be immune to the disease forever – “removed” state I(t): the number of infections hosts at time t R(t): the number of removed hosts from previously infectious hosts at time t

12. Kermack-Mckendrick Model  Base on the simple epidemic model, Kermack-Mckendrick Model is: J(t): the number of infected hosts at time t : removal rate of infectious hosts : infection rate N: size of population

13. Kermack-Mckendrick Model  Define  If the initial number of susceptible hosts is smaller than some critical value, there will be no epidemic and outbreak

14. Kermack-Mckendrick Model  The Kermack-Mckendrick model improves the classical simple epidemic model by considering that some infectious hosts either recover or die after some time, but still not suitable for modeling Internet worm propagation  Removal only from the infectious hosts  Assume infection rate to be constant

15. A NEWINTERNET WORMMODEL: TWO-FACTOR WORM MODEL  Two factors affecting Code Red worm propagation  Human countermeasures  Decreased infection rate

16. A NEWINTERNET WORMMODEL: TWO-FACTOR WORM MODEL  According to the same principle in deriving the Kermack-Mckendrick Model:  In order to solve the equation, we have to know the dynamic properties of, and

17. A NEWINTERNET WORMMODEL: TWO-FACTOR WORM MODEL  Use the same assumption as what Kermack- McKendrick model uses:  The removal process from susceptible hosts looks similar to a typical epidemic propagation:

18. A NEWINTERNET WORMMODEL: TWO-FACTOR WORM MODEL  Last, we model the decrease infection rate by the equation: : initial infection rate : used to adjust the infection rate sensitivity to the number of infection hosts

19. A NEWINTERNET WORMMODEL: TWO-FACTOR WORM MODEL  For parameters N=1000000, I(0)=1, =3, r=0.05, u=0.06/N, =0.8/N

20. Simulation

23. Conclusion  Considering human countermeasures taken by ISPs and users and the slowed down worm infection rate, two-factor worm model match the observed data better than previous models do  The two-factor worm model is a general Internet worm model for modeling worms by adjusting different parameters