Epidemic Data Survivability in UWSNs

1. Epidemic Data Survivability in UWSNs Roberto Di Pietro, Nino Vincenzo Verde {dipietro,nverde}@mat.uniroma3.it Universita’ di Roma Tre

2. RoadMap • Introduction to UWSNs • Information Survivability • The SIS Model • Modeling Information Survivability in UWSNs • Epidemic Data Survivability • Full Visibility • Geometrical model • Experimental results • Conclusions

3. Unattended WSNs • Sporadic presence of the sink • Sensors upload info as soon as the sink comes around • Applications: • Hostile environments monitoring • Pipelines monitoring

4. Information Survivability • 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. Epidemic Models • 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. S I Infected Susceptibles SIS • Solution: • Using i(t) it is possible to predict the number of sick individuals at time t

7. Steady States • 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: • STEADY0: i(t)=0 • STEADY1: i(t)=1-β/α STEADY1 is Asymptotically Stable: Perturbing the system will not produce any long term effect

8. Modeling the Information Spread with epidemic models • 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. Modeling the Information Spread with epidemic models (2) • 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. Modeling the Information Spread 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 S I S I Infected Have info Susceptibles Do not have info

11. Modeling the Information Spread 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. Modeling the Information Spread 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. Epidemic Data Survivability • 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. Full Visibility • 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 αandβ can be used to predict the behavior of such a network

15. SIS Prediction Vs. Simulations The SIS model is not always accurate (In the Simulation α=0.95)

16. SIS Prediction Vs. Simulations • Not accurate when β is close to α -> that means STEADY1 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. Video Information Lost Start video

18. A probabilistic lower bound on the data survivability THEOREM Once reached Steady1, if α>β/(1- ε) , the probability to loose the datum is less than or equal to exp(-ε2n/2) The proof is based on the Method of Bounded Differences

19. Trade-Off between Energy Consumption, Data Survivability and Collecting Time • The following result assures at the same time: • Data survivability • An optimal usage of sensors resources • And a fast and predictable collecting time • TRADE-OFF THEOREM • Once reached Steady1, 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: • In each round the expected number of sent messages is less than n/x • the probability to loose the datum is less than or equal to exp(-ε2n/2) • The expected collecting time will be equal to (nγ(1- β/α))-1

20. Video Probabilistic Bound Start video

21. Geometrical Model • 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:

22. Video Information Lost – Geometrical case Start video

23. Extending the results for the geometrical models • TRADE-OFF THEOREM • In the geometrical model, once reached Steady1, considering a itinerant intermittent sink, and full visibility among sensors, if β/(πrn2(1- ε) )<α< β/(πrn2)+(1/x), with 1<x<n, the following three conditions will hold: • In each round the expected number of sent messages is less than nπrn2/x • the probability to loose the datum is less than or equal to exp(-ε2n/2) • The expected collecting time will be equal to (nγπrs2 (1- β/ ( απrn2)))-1

24. Geometrical model: experimental results Sent Messages Theoretical prediction Vs. Experimental results Collecting Time Information Survivability

25. Video Probabilistic Bound – Geometrical case Start video

26. Conclusions • Future Work What if the UWSN becomes a mobile WSN? 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

27. Questions? Thank you!

28. 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 6th 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.