Roberto Di Pietro,

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Introducing Epidemic Models for Data
Survivability in UWSNs

• Roberto Di Pietro,
• Nino Vincenzo Verde

dipietro,nverde_at_mat.uniroma3.it
Universita di Roma Tre
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RoadMap

• UWSNs
• Epidemic Models
• SIR
• SIS
• Epidemic Models for Information Survivability in
  UWSNs
• Modeling the problem
• Applications
• Results
• Conclusions

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Unattended WSNs

• Sporadic presence of the sink
• Sensors upload info as soon as the sink comes
  around
• Applications
• Hostile environment
• monitoring
• Pipeline monitoring

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Information Survivability

• Sink not always available
• More subject to malicious attacks than
  traditional WSN
• Our target

To provide a certain level of assurance about
Information Survivability
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Epidemic Models

• Stochastic approaches
• Accurately describe fluctuation
• Variation chance in exposure risk
• Very complex
• Laborious to set up

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Epidemic Models

• Deterministic approaches
• Describe the dynamic of a disease at the
  population scale
• Fits very large populations
• Not accurate with small populations

Are they accurate when trying to minimize energy
consumption?
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Deterministic Epidemic Models

• n individuals are partitioned into several
  compartment
• Transition probabilities between any two
  compartments are given
• The spreading of the disease is taken into
  consideration

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SIR
S
I
R
Susceptibles
Infected
Recovered

• It does not admit a generic analytic solution,
  but

Is the basic reproduction number if gt
1/s(0) then Epidemic outbreak
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SIS

• Solution

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

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Modeling the Information Spread

• n sensors, 1 sink, 1 attacker
• A secure routing protocol allows to exchange
  information between any pair of sensor
• Evolution time partitioned in rounds
• Both sensors and the attackers play their game

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Sensors Model

• Data is transmitted by replication
• Each sensor that stores the datum transmits it
  with probability to each neighbor
• Theorem

If i is the fraction of sensors possessing the
datum, and if each sensor forwards the datum with
probability a/n , the value sia is an
approximation of the probability that the datum
reaches a sensor that do not possess it.
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Proof
sia
?
a/n is close to 0 -gt using the binomial
approximation the above formula is equal to asi
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Attacker Model

• We consider 2 attackers
• ADVsimple
• It is able to destroy each sensors containing the
  datum with probability ß in each time step
• ADVstealth
• It is able to erase the datum without destroying
  the sensor
• It does not change the behavior of the sensor

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Epidemic models in UWSNs
ADVsimple
Replication a/n
SIR
ADVstealth
Replication a/n
SIS
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SIR Test

• a0.605
• ß0.5
• n100
• i(0)0.1

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SIS Test

• n100
• i(0)0.1

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Outcome

• Epidemic models can be used to forecast the
  behavior of an UWSNs
• It becomes easy to set-up the parameters
• It is possible to study the conditions that have
  to be satisfied to assure information
  survivability
• Problems?
• Energy Consumption it is needed to minimize the
  replication process

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Minimizing Energy Consumption

• In both the models energy consumption is
  minimized when i(t) is close to 0 for any t
• Statistical fluctuation can force the system to
  loose the datum

n100 i(0)0.01
n100 i(0)0.05
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Video Simulation SIS
n100 a0.22 ß0.2
Steady state when i(t)(1-ß/a)
Is the information survivability assured?
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Conclusions

• Deterministic epidemic models can be used to
  model information assurance in UWSNs
• The parameters that assure the survivability are
  easy to set up
• They fit very well large sensor networks
• Unlikely events can induce the loss of the datum
• It is needed to assess bounds on the probability
  of these events

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Questions?
Thank you!
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Some Related Work

• R. Di Pietro, and N. V. Verde. Epidemic data
  survivability in Unattended Wireless Sensor
  Networks. In Proceedings of the ACM Conference on
  Wireless Network Security (WiSec), Hamburg,
  Germany, June 2011.
• 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.
• 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.
• 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.