1. 1 Epidemic Data Survivability in UWSNs {dipietro,nverde}@mat.uniroma3.it

2. ACM WiSec 2011 2 Introduction to UWSNs Information Survivability The SIS Model Modeling Information Survivability in UWSNs Epidemic Data Survivability – Full Visibility – Geometrical model Experimental results Conclusions

3. ACM WiSec 2011 3 Sporadic presence of the sink Sensors upload info as soon as the sink comes around Applications: – Hostile environments monitoring – Pipelines monitoring

4. ACM WiSec 2011 4 Sink not always available: – UWSN More subject to malicious attacks than traditional WSN Our targets: To provide a certain level of assurance about INFORMATION SURVIVABILITY To predict the sink COLLECTING TIME To set up a TRADE-OFF between energy consumption, data survivability, and collecting time

5. ACM WiSec 2011 5 Epidemic Models – Describe the dynamic of a disease at the population scale – Fit very large populations General Approach: – n individuals are partitioned into several compartments – Transition probabilities between any two compartments are given – The spreading of the disease is taken into consideration

6. ACM WiSec 2011 6 Solution: SI Infected Susceptibles Using i(t) it is possible to predict the number of sick individuals at time t

7. ACM WiSec 2011 7 A steady state is reached when i‘(t)=0 – The rate of infected individual will remain indefinitely constant In the SIS model there are 2 steady states: – STEADY 0 : i(t)=0 – STEADY 1 : i(t)=1-β/α STEADY 1 is Asymptotically Stable: Perturbing the system will not produce any long term effect

8. ACM WiSec 2011 8 Data replication process can be modeled as the spreading of a disease in a finite population – No crypto needed – No additional overhead due to the reconstruction of the info We want to achieve: – Data survivability – Optimal usage of sensor resources – Predictable collecting time

9. ACM WiSec 2011 9 Contributions – Highlighting that the original SIS model may lead to lose the datum, in contrast with theoretical results provided in the literature ( This risk is particularly sensitive when trying to optimize sensor resources usage ) – Providing a probabilistic analysis highlighting the conditions to be satisfied to preserve the data survivability ( for both geometrical and full visibility model ) – Experimental results confirming the findings

10. ACM WiSec 2011 10 THE NETWORK MODEL UWSN with n sensors ( n large) Evolution time partitioned in rounds – Sensors, attacker and sink play their game in each round Data is transmitted by replication: – In each round, each sensor that stores the datum transmits it with probability α/n to each neighbor I Infected S Susceptibles I Have info S Do not have info

11. ACM WiSec 2011 11 THE ATTACKER MODEL Search and Erase mobile adversary: – He wants to prevent certain target data from reaching the sink without being detected He is able to move inside the monitored area He compromises the nodes erasing information He does not change sensors’ behavior or destroy them (it would be easily detectable) In each round the attacker compromises up to β percentage of nodes that currently store the target information

12. ACM WiSec 2011 12 THE SINK MODEL It is able to contact and to download data from γ percentage of nodes belonging to the network in each round We will consider two models: – Global Intermittent Sink – Itinerant Intermittent Sink

13. ACM WiSec 2011 13 The datum corresponds to a disease Each healthy subject (sensor) can contract the disease (datum) from a sick individual with a certain probability The adversary corresponds to the process of healing from the disease A healed subject can then re- contract the disease (datum) Search and Erase mobile adversary n sensor with replication α/n SIS

14. ACM WiSec 2011 14 Assuming full visibility among the sensors, in each round: – The prob that a sensor receives a “new” datum can be approximated by: – The prob that a sensor will be compromised is: Therefore, the SIS model with parameters α and β can be used to predict the behavior of such a network

15. ACM WiSec 2011 15 The SIS model is not always accurate (In the Simulation α=0.95)

16. ACM WiSec 2011 16 Not accurate when β is close to α -> that means STEADY 1 close to 0 It depends on statistical fluctuations of i(t) Unfortunately, that portion is the most interesting for us: we want to minimize energy consumption

17. 17 Start video

18. ACM WiSec 2011 18 THEOREM Once reached Steady 1, if α>β/(1- ε), the probability to loose the datum is less than or equal to exp(-ε 2 n/2) The proof is based on the Method of Bounded Differences

19. ACM WiSec 2011 19 THEOREM Once reached Steady 1, considering a global intermittent sink, if α≥β, the expected time before the sink collects a given datum is equal to (nγ(1- β/α )) -1 Start video

20. ACM WiSec 2011 20 TRADE-OFF THEOREM Once reached Steady 1, considering a global intermittent sink, and full visibility among sensors, if β/(1- ε) < α< β+(1/x), with 1<x<n, the following three conditions will hold: 1.In each round the expected number of sent messages is less than n/x 2.the probability to loose the datum is less than or equal to exp(-ε2n/2) 3.The expected collecting time will be equal to (nγ(1- β/α )) -1 The following result assures at the same time: Data survivability An optimal usage of sensors resources And a fast and predictable collecting time

21. 21 Start video

22. ACM WiSec 2011 22 Sensor A can communicate with sensor B if and only if B is inside A’s transmission range Is the SIS model still valid? YES, but we need to revise it Steady States:

23. ACM WiSec 2011 23 Start video

24. ACM WiSec 2011 24 THEOREM In the geometrical model, once reached Steady 1, if α>β/(πr n 2 (1- ε) ), the probability to loose the datum is less than or equal to exp(-ε 2 n/2)

25. ACM WiSec 2011 25 TRADE-OFF THEOREM In the geometrical model, once reached Steady 1, considering a itinerant intermittent sink, and full visibility among sensors, if β/(πr n 2 (1- ε) ) < α< β/(πr n 2 )+(1/x), with 1<x<n, the following three conditions will hold: 1.In each round the expected number of sent messages is less than n πr n 2 /x 2.the probability to loose the datum is less than or equal to exp(-ε 2 n/2) 3.The expected collecting time will be equal to (nγ πr s 2 (1- β/ ( απr n 2 ))) -1

26. ACM WiSec 2011 26 Information Survivability Sent Messages Collecting Time Theoretical prediction Vs. Experimental results

27. ACM WiSec 2011 27 Alfa =0.05 Beta = 0.02 Sink and sensor range=0.3 n=100 epsilon=0.22 Survivability simple SIS: alfa>=0.07 Survivability considering our theorem: – With alfa>= 0.09 it is greater 91%

28. ACM WiSec 2011 28 Start video

29. ACM WiSec 2011 29 Epidemic models can be used to forecast the behavior of large UWSNs Statistical fluctuation can cause the loss of the datum We provided a theoretically sound result that assures data survivability, minimizes resources consumption, provides a fast collecting time Future Work What if the UWSN becomes a mobile WSN?

30. ACM WiSec 2011 30 Questions? Thank you!

31. ACM WiSec 2011 31 Related Work (some) [1] Roberto Di Pietro, Luigi V. Mancini, Claudio Soriente, Angelo Spognardi, and Gene Tsudik. “Catch Me (If You Can): Data Survival in Unattended Sensor Networks”. In Proceedings of the 6 th IEEE International Conference on Pervasive Computing and Communications (PerCom 2008), pages 185-194, Hong Kong, March 17-21, 2008. [2] Michele Albano, Stefano Chessa, and Roberto Di Pietro. “A model with applications for data survivability in Critical Infrastructures”. In Journal of Information Assurance and Security, vol. 4(6), pages 629-639, June 2009. [3] Roberto Di Pietro, Luigi V. Mancini, Claudio Soriente, Angelo Spognardi, and Gene Tsudik. “Playing Hide-and-Seek with a Focused Mobile Adversary in Unattended Wireless Sensor Networks”. In Journal of Ad Hoc Networks (Elsevier) - Special Issue on Privacy and Security in Wireless Sensor and Ad Hoc Networks -, vol. 7(8), pages 1463-1475, November 2009. [4] D. Ma, C. Soriente and G. Tsudik. “ New Adversary and New Threats in Unattended Sensors Networks ”. IEEE Network, Vol. 23, No. 2, 2009. [5] R. Di Pietro, and N. V. Verde. “Introducing Epidemic Models for Data Survivability in Unattended Wireless Sensor Networks”. Second International Workshop on Data Security and PrivAcy in wireless Networks (D-SPAN 2011), Lucca, Italy.