1

Epidemic Data Survivability Epidemic Data Survivability in UWSNsin UWSNs

{dipietro,nverde}@mat.uniroma3.it

ACM WiSec 20112

RoadMapRoadMap

• Introduction to UWSNs• Information Survivability• The SIS Model• Modeling Information Survivability in UWSNs• Epidemic Data Survivability

– Full Visibility– Geometrical model

• Experimental results• Conclusions

ACM WiSec 20113

Unattended WSNsUnattended WSNs

• Sporadic presence of the sink• Sensors upload info as soon as the sink comes

around• Applications:

– Hostile environmentsmonitoring

– Pipelines monitoring

ACM WiSec 20114

Information SurvivabilityInformation 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

ACM WiSec 20115

Epidemic ModelsEpidemic 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

ACM WiSec 20116

SISSIS

• Solution:

S IInfectedSusceptibles

SI

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• Using i(t) it is possible to predict the number of sick individuals at time t

ACM WiSec 20117

Steady StatesSteady 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

ACM WiSec 20118

Modeling the Information Spread Modeling the Information Spread with epidemic modelswith 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

ACM WiSec 20119

Modeling the Information Spread Modeling the Information Spread with epidemic models (2)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

ACM WiSec 201110

Modeling the Information SpreadModeling 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

it possesing sensors of fraction theis )(

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Have infoS

Do not have info

ACM WiSec 201111

Modeling the Information SpreadModeling 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

ACM WiSec 201112

Modeling the Information SpreadModeling 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

ACM WiSec 201113

Epidemic Data SurvivabilityEpidemic 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

ACM WiSec 201114

Full VisibilityFull 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:

si

ns

in

11

i

Therefore, the SIS model with parameters α and β can be used to predict the behavior of such a network

ACM WiSec 201115

SIS Prediction Vs. SimulationsSIS Prediction Vs. Simulations

The SIS model is not always accurate(In the Simulation α=0.95)

ACM WiSec 201116

SIS Prediction Vs. SimulationsSIS 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

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Video Information LostVideo Information Lost

Start video

ACM WiSec 201118

A probabilistic lower bound on A probabilistic lower bound on the data survivabilitythe data survivability

THEOREMOnce 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

ACM WiSec 201120

Trade-Off between Energy Consumption, Trade-Off between Energy Consumption, Data Survivability and Collecting TimeData Survivability and Collecting Time

TRADE-OFF THEOREMOnce 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:

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

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Video Probabilistic BoundVideo Probabilistic Bound

Start video

ACM WiSec 201122

Geometrical ModelGeometrical 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

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Steady States:

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ACM WiSec 201123

Video Information Lost – Video Information Lost – Geometrical caseGeometrical case

Start video

ACM WiSec 201125

Extending the results for the Extending the results for the geometrical modelsgeometrical models

TRADE-OFF THEOREMIn 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:

1.In each round the expected number of sent messages is less than nπrn2/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 (nγπrs2 (1- β/ ( απrn

2)))-1

ACM WiSec 201126

Geometrical model: Geometrical model: experimental resultsexperimental results

Information Survivability

Sent Messages

Collecting Time

Theoretical prediction Vs.

Experimental results

ACM WiSec 201128

Video Probabilistic Bound – Video Probabilistic Bound – Geometrical caseGeometrical case

Start video

ACM WiSec 201129

ConclusionsConclusions

• 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 WorkWhat if the UWSN becomes a mobile WSN?

ACM WiSec 201130

Questions?Questions?

Thank you!

ACM WiSec 201131

Related Work (some) 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.