A Key Management Scheme for Wireless Sensor Networks Using

Deployment KnowledgeWenliang Du et al.

Outline

• Introduction• Modeling deployment knowledge• Key pre-distribution using deployment

knowledge • Performance evaluation• Conclusion

Introduction

• Problem– Key pre-distribution in sensor network

• Previous work– Random key pre-distribution scheme– Improvement to random scheme

• q-composite scheme• Polynomial-based scheme

• Common assumption– No deployment knowledge is available

New assumption• In many practical scenarios

– Certain deployment knowledge may be available• What is deployment knowledge

– How are sensors deployed?– Are they uniformly randomly distributed?

• Deployment method– Uniformly randomly distributed

• No deployment knowledge– Non-uniform distribution

• Deployed by groups• Possible to know where a node is more likely to reside

• Useful– Most communications are between neighbors– Deployment knowledge helps us to know which nodes are more likely to

be neighbors for each node

Modeling deployment knowledge

• Probability density function (pdf)• General Deployment Model

– Deployment area• 2-dimensional rectangular area X x Y

– pdf for the location of node i, i = 1,…,N• fi(x,y), • Existing key pre-distribution schemes assume

– fi(x,y) = 1/XY– All sensor nodes are uniformly distributed over the deployment

region

],0[ Xx ],0[ Yy

Modeling deployment knowledge (Cont’d)

• Group-based Deployment Model– N sensor nodes are divided into t x n groups

• Probability node is in a certain group is (1 / tn)– Group Gi,j is deployed from the point (xi,yj)– The resident point of node k in group Gi,j follow the pdf

• Example of pdf f(x,y): 2-dimensional Guassian distribution)|,( , jiGkyxf

Deployment Points

Modeling deployment knowledge (Cont’d)

• Deployment distribution used in paper– 2-dimensional Gaussian distribution for each group

– Overall distribution over the entire deployment region

Modeling deployment knowledge (Cont’d)

• Why use group-based model– Easy to determine which nodes are more likely to be close to

each other• Distance between two deployment points increases Probability for

two nodes from these two groups become neighbors decreases– Different groups can use different key pools

• Key pool size is smaller better connectivity• Two groups are far away overlap between their key pools

becomes smaller

• Notations– Si,j: key pool used by group Gi,j,

– |Sc|: size of Si,j , njtiSS ji ..1,,...1,,

Key Pre-distribution Scheme

• Step 1: Key pre-distribution– Divide the key pool S into t x n key pools Si,j

• Si,j corresponding to deployment group Gi,j

• | Si,j | = | Sc|, for any i, j• Nearby key pools share more key• Far away key pools share less or no key

– Two horizontally or vertically neighboring key pools share exactly a|Sc| key spaces, 0 <= a <= 0.25

– Two diagonally neighboring key pools share exactly b|Sc| key spaces, 0 <= b <= 0.25

– Two non-neighboring key pools share no key spaces

Key Pre-distribution Scheme

• Key sharing among key poolsHorizontal

Vertical Diagonal

a

a b

b

b b

b

A C

F

H I

D

G

aa aa

B

Key Pre-distribution Scheme

• Determining |Sc|– Given key pool |S|, overlapping factor a, b– Si,j

– Determine

bnttnantntnSSc

)1(2)2(||||

njtiSS ji ..1,,...1,,

Key Pre-distribution Scheme

• Select keys for each key pool Si,j

– Global key pool S – Overlapping factor a

and b

Global Key Pool S

1 1-a 1-a 1-a1-(a+b) 1-2(a+b) 1-2(a+b) 1-(2a+b)1-(a+b) 1-2(a+b) 1-2(a+b) 1-(2a+b)1-(a+b) 1-2(a+b) 1-2(a+b) 1-(2a+b)

|Sc| keys

a|Sc| keys1-a|Sc| keys

a|Sc| keys b|Sc| keys

1-(a+b)|Sc| keys

t = 4, n = 4

Key Pre-distribution Scheme

• Effects of the Overlapping Factors– Best overlapping factors

• Combination of a and b that maximizes the local connectivity

Key Pre-distribution Scheme

• Step 2: Shared-key discovery– After deployment, every node will find out

whether it shares keys with its neighbors• Step 3: Path-key establishment

– Two neighboring nodes cannot find any common key

– Use secure channels that have already been established

Performance Evaluation• Performance metrics:

– Local connectivity plocal• The prob. of any two neighboring nodes sharing at least one

key– Resilience against node capture

• The fraction of additional communications (communications among uncaptured nodes) that an adversary can compromise based on the information retrieve from x captured nodes

– Communication overhead• When two neighboring nodes cannot find a common key• ph(l): prob. That the smallest number of hops needed to

connect two neighboring nodes is l

Performance Evaluation

• Local connectivity

Performance Evaluation

• Resilience against node capture

Performance Evaluation

• Communication overhead

Conclusion

• Use pdf to model deployment knowledge• Propose a key pre-distribution scheme

using deployment knowledge– Sensors carry less key– Achieves same level of connectivity– Improves network’s resilience against node

capture