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Network Flow Modeling of Jamming Attack
Radha PoovendranNetwork Security LabElectrical Engineering DepartmentUniversity of Washington, Seattle, WAhttp://www.ee.washington.edu/research/nsl
Bertinoro PhD. Summer School, July 2009
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Robust Ad‐Hoc Networking
2
Network Performance Requirements
Availability of Network Resources
Efficient Resource
Expenditure
Reliable Network
Performance
Restricted Network/Info
Access
Denial of Service
Resource Depletion
Performance Degradation
Crypto Attacks
How can we enable robust network performance in the presence of adversaries?
7/6/2009 www.ee.washington.edu/research/nsl
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Outline for the first part
• Viewing Jamming as a network flow problem
• Linear programming models for the impact of attacks with jamming succeeds with probability one
37/6/2009 www.ee.washington.edu/research/nsl
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Network Layer Impact of Jamming Attacks
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Interference + Noise
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Sender Receiver
Receiver can decode message if SINR ≥ τ
…
Physical layer
MAC/link layer
Network layer
Path Loss
Jamming Jamming decreases SINR, causes decoding failure and packet loss
Effects of jamming, a physical layer attack, can be captured in the network layer metric of goodput
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Jamming Network Flows
• Adversary goal: reduce network throughput via coordinated jamming– Constraints: finite energy, device capability, physical restrictions
• How should the jamming energy be allocated to best throttle the network flows?
www.ee.washington.edu/research/nsl7/6/2009
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Modeling Jamming Attacks
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Jamming Energy
Flow 1
Flow 2
Energy to jam flow 2
Energy to jam flow 1
Jammer
Note: we assume a single jamming transmission is required to jam each packet.
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Modeling Jamming Attacks
• For jammer j, flow f:– rf = data rate of f
– xjf = fraction of data in fjammed by j
• Assume: jamming succeeds w.p. 1
– cjf = jamming energy per‐unit data rate for flow f
– cj = total energy available to jammer j
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Constraint: Total flow
Constraint: Total energy
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Attack Evaluation Metrics
• F = Total number of flows
• Impact of attack– Average reduction in flow rate
• Attack Gain (Efficiency)– Average reduction in flow rate per energy expenditure per jammer
• Energy Variation– Relative variation in resource expenditure
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Attack Formulations
• Constrained optimization formulation– Assume allocation is done by centralized adversary
– Optimize with respect to evaluation metrics individually or jointly
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Maximize Jamming Impact
• Maximize impact I(x) and gain E(x)– First, constrain I(x)=1 and minimize energy expenditure (denominator of E(x))
– If no feasible solution, maximize impact I(x)
– Both I(x) and denominator of E(x) are linear in x, so each formulation is LP
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Maximize Jamming Gain
• Maximize gain E(x)– Inherently tries to maximize impact I(x), but makes tradeoffs for energy savings
– E(x) is rational in x, can be approximated by an LP to within an additive constant ε>0
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Minimize Variation
• Minimize variation V(x) with max I(x)– First, constrain I(x)=1 and minimize maximum energy expenditure
– If no feasible solution, maximize minimum energy expenditure
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Traffic Allocation using Portfolio Selection under Stochastic
Jamming Attacks
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Outline
• Overview
• Wireless Network model
• Dynamic jamming & Recursive Estimation
• Markowitz portfolio optimization
• NUM Optimization of traffic allocation
• Simulation & Results
• Contributions and future work
157/6/2009 www.ee.washington.edu/research/nsl
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Network Model
• Collection of wireless nodes.
• Source, destination, links, paths.
• Individual links have constant capacities.• Graph model: Vertex set � , edge‐set � , set of sources ���
Csi
Csk
Cin
Ckn
Cij
Ckm
Cnj
Cnm
Cjd
Cmd
SOURCE DESTINATION
i j
k m
ns d
7/6/2009 www.ee.washington.edu/research/nsl
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Routing
• Source Routing: – Source discovers path to destination.
– Stores path information.
– Intermediate nodes help in route maintenance.
• Multi‐path Routing:– Source maintains multiple paths to destination.
– Multiple paths are more robust to link failures.
– Paths are preferably diverse and disjoint.
7/6/2009 www.ee.washington.edu/research/nsl
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Csi
Csk
Cin
Ckn
Ckm
Cnj
Cnm
Cjd
Cmd
k m
ns d
Jamming• Deliberate transmission of radio signals to disrupt the communication in a wireless network by decreasing the signal‐to‐noise ratio (SNR).
• Several types: constant, deceptive, random, reactive. Emphasis on the impact, not the type
• Mobile/Reactive jammers have greater impact.
i jCij
7/6/2009 www.ee.washington.edu/research/nsl
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Anti‐jamming methods
• Physical Layer methods:– Direct Sequence Spread Spectrum (DSSS)
– Frequency Hopping Spread Spectrum (FHSS)
– Beam‐forming and Interference Rejection
• MAC and Network Layer methods:– Channel Switching
– Routing around jammed areas
– Spatial retreats
• Our approach: Multi‐path routing (spatial route diversity)7/6/2009 www.ee.washington.edu/research/nsl
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Effect of Jamming on Network Throughput
Jamming Packet errors Packet Retransmission
Decrease in Throughput
100 100
S D
X
Y
Z
15015050 25
7/6/2009 www.ee.washington.edu/research/nsl
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Impact of Jamming –Probabilistic View
• Analytical measurements are not possible– Jammer locations, signal power are unknown.
– We use Heuristics ‐‐ Packet Delivery Ratio (PDR)
• Packet Delivery Rates vary over time:– Dynamic jammer strategy.
– Mobility of jammer.
• Due to uncertainty from jamming, we model the PDR at a node as a random process.
7/6/2009 www.ee.washington.edu/research/nsl
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Include Jamming Impact into Network Flow
• Network flow formulation– Suppose flow of rate φ� is sent over a single source‐destination
path �� .
– Let �be the fraction of correctly received packets over link (,) i.e. packet success rate. Mean of � is μand variance is σ2 .
– �� is the fraction of φ� successfully received at destination d along path �� and is the product of the �’s on path �� . Mean of �� is γ� and variance is ω�
2.– �‘s for multiple paths are correlated due to overlapping links.
Path 1: S – A – D�� = �� * � �
Path 2: S – B – D��= ��� * ���
S
B
A
D
� �
���
��
���7/6/2009 www.ee.washington.edu/research/nsl
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Reviewing the Problem Setup
• The traffic allocation problem for a source:– Resources available: Multiple paths
– Performance metrics for each path: • Estimated mean end‐to‐end packet success rate
• Estimated var in end‐to‐end packet success rate
– Goal: Achieve optimal throughput performance• Maximize average throughput
• Minimize variance in the achieved throughput
– “Intelligent” traffic allocation among paths.
– What is the role of uncertainty on link weights?7/6/2009 www.ee.washington.edu/research/nsl
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Markowitz Portfolio Optimization
• Input: – Past performance of each asset
• Expected return for each asset.
• Risk involved in each asset.
• Correlation between assets.
• Output:– Set of portfolios giving:
• Highest returns for a given risk.
• Lowest risk for given returns.
• History projects the known past to an uncertain future, quantified into risk.7/6/2009 www.ee.washington.edu/research/nsl
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Correspondence between Portfolio Theory and Traffic Allocation
Principal to be invested Source Data to be sent
Investment options
Mean return for each asset
Overall mean return
Risk
Potential Paths
Mean packet delivery rate γ for each path
Mean throughput
Standard deviation of throughput
7/6/2009 www.ee.washington.edu/research/nsl
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Constraints
Non‐negative traffic rates φ� ≥ 0
Data generation rate at source
1�φ�≤ � �
Link Capacity constraint
All constraints are linear in φ�7/6/2009 www.ee.washington.edu/research/nsl
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Utility Functions
Analogous to Markowitz Portfolio Theory, for a given source �, we define utility function as:
��(φ�) = γ��φ� − ��φ��Ω�φ�
Mean Variance
�� = 0 gives max‐mean case ��> 0 gives optimal risk‐return case
7/6/2009 www.ee.washington.edu/research/nsl
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Optimization Problem Setup
• Considering the combined utility function and constraints for all sources � S, we get:
Optimal Jamming‐Aware Traffic Allocation
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Distributed Solution
• Centralized method is not suited for large multi‐source networks.
• Enable each source to compute φ�* independently.
• Links are used by multiple sources and hence the capacity constraints are coupled.
• Problem setup is similar to Network Utility Maximization (NUM).
• Use Lagrangian method for decomposition.[1]
7/6/2009 www.ee.washington.edu/research/nsl
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Distributed Solution
• Use link prices λto convert the link capacity constraints into a Lagrangian price term.
• At each iteration, sources use links based on their current price.
• Price is then updated based on link utilization and capacity.
Link capacity
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Reading list for the 2nd lecture
• From NSL Website– Throughput Optimization for Multipath UnicastRouting Under Probabilistic Jamming
– Linear Programming Models for Jamming Attacks on Network Traffic Flows
7/6/2009 www.ee.washington.edu/research/nsl
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Acknowledgements
• Collaborators: Profs. Jim Ritcey, Guevara Noubir; Students Patrick Tague, David Slater, Sid Nabar
• http://www.ee.washington.edu/research/nsl
7/6/2009 www.ee.washington.edu/research/nsl