Grid-Based Key Pre-Distributionin Wireless Sensor NetworksSource: KSII Transactions On Internet And Information Systems Vol. 3, No. 2, April 2009Authors: Abedelaziz Mohaisen, DaeHun Nyang, YoungJae Maeng, KyungHee Lee, Dowon HongPresenter: Hsing-Lei WangDate: 2010/11/26

1

OutlineIntroductionRelated WorksThe Proposed Scheme

Grid-Based Key Pre-Distribution in WSN (3D)AnalysisConclusionsComment

2

Introduction

3

A Grid-Based Key Pre-Distribution Scheme (3D) Goal: Improve the connectivity and resiliency

Y-Plat

Z-Plat

X-Plat

Related Works (Blundo et al. scheme, 1993)

4

Polynomial-Based Key Pre-Distribution Scheme

, 0

Setup Server randomly generates a bivariate degree polynomial:

, ,where , , .

Computes the polynomial share , for each node .

Each node has a unique .

Node compute

ti j

iji j

t

f x y a x y f x y f y x

f i y i

ID

i

s , by evaluating , at point

Node computes , by evaluating , at point

, , the common key for both nodes.

f i j f i y j

j f j i f j y i

f i j f j i

Grid-Based Key Pre-Distribution Scheme (1/2)

Related Works (Liu et al. scheme, 2003)

5

2

, 0,......, 1

Assume network size . Constructs a grid.Generates 2 polynomials

, , ,

Assign the sensor nodes and polynomials to the grid as figure.

Each node has a uniq

Setup:

c ri j i j m

N mm mm

f x y f x y

ue , or ,

Each node stores: , , , ,c ri j

ID i j c r

ID f j y f i y

6

Grid-Based Key Pre-Distribution Scheme (2/2)

Suppose node , want to establish

a pair-wise key with node , .

Node checks whether: or

If equal, they have a common polynomial:

Polynomial share Discove

, or

ry:

i i

i i

j j

i j i j

cc r

i c r

j c r

ic c r r

f x y f

,

Use the polynomial share to compute common key.

r x y

Related Works (Liu et al. scheme, 2003)

The Proposed Scheme

7

3D Grid-Based Key Pre-Distribution Scheme (1/11)

3

0 1 1

0 1 1

0 1 1

Assume network size . Constructs a 3D-grid.Let , , be three axes

, ,...,

, ,...,

, ,...,

Grid Structure:

m

m

m

N mm m m

X Y ZX c c c

Y r r r

Z h h h

8

The Proposed Scheme 3D Grid-Based Key Pre-Distribution

Scheme (2/11)

Assign the sensors to the grid.

Each node has a unique , ,

Node has the identif

Sensors

ier structure

|| ||

Assignment:

x y z

i

xi yi zi

ID c r h

S

i c r h

9

The Proposed Scheme 3D Grid-Based Key Pre-Distribution Scheme

(3/11)

, constant, x z

, , constantx y

constant, ,y z

The plat is the virtual shape confined by all possible values for two variable axes and a constant v

Definition o

alue in the

f The Pl

third a

at:

xis.

X-Plat

Z-Plat

Y-Plat

10

The Proposed Scheme 3D Grid-Based Key Pre-Distribution Scheme

(4/11)

, , 0,......, 1

Generates 3 polynomials

, , , , ,

Assign the polynomials to the gridAll

Key Mater

nodes in

ial Assignm

the same plat have the same

e

polynomia .

nt:

l

cx ry hz

x y z m

m

f x y f x y f x y

1 ,cf x y 0 ,cf x y 2 ,cf x y

0 , ,c y z1, ,c y z2 , ,c y z

11

The Proposed Scheme 3D Grid-Based Key Pre-Distribution Scheme

(5/11)

0, , x r z

1, , x r z

2, , x r z 1 ,rf x y 2 ,rf x y 0 ,rf x y

, , 0,......, 1

Generates 3 polynomials

, , , , ,

Assign the polynomials to the gridAll

Key Mater

nodes in

ial Assignm

the same plat have the same

e

polynomia .

nt:

l

cx ry hz

x y z m

m

f x y f x y f x y

12

2, , x y h

0, , x y h

1, , x y h

2 ,hf x y

1 ,hf x y

0 ,hf x y

The Proposed Scheme 3D Grid-Based Key Pre-Distribution

Scheme (6/11)

, , 0,......, 1

Generates 3 polynomials

, , , , ,

Assign the polynomials to the gridAll

Key Mater

nodes in

ial Assignm

the same plat have the same

e

polynomia .

nt:

l

cx ry hz

x y z m

m

f x y f x y f x y

13

The Proposed Scheme 3D Grid-Based Key Pre-Distribution Scheme

(7/11)

Each node with identifier || || was assigned to

three polynomial , , , and ,For each node , t

Polynom

he serv

ial shares:

er computes the polynomial shares:

yixi zi

xi x

i xi yi zi

rc h

i

c c

S i c r h

f x y f x y f x yS

g f

,

,

,

Each node will stores: identifier , , ,

i

yi yi

zi zi

yixi zi

r r

h h

rc hi

i y

g f i y

g f i y

S i g g g

14

The Proposed Scheme 3D Grid-Based Key Pre-Distribution

Scheme (8/11)Suppose two nodes and want to communicate.

with identifier || ||

with identifier || ||

Two nodes exchange their identifier.If o

Direct Key Establishmen

r

t:

i j

i xi yi zi

j xj yj zj

xi xj y

S S

S i c r h

S j c r h

c c r

or ,

The two nodes compute common key by the polynomial share.

i yj zi zjr h h

15

The Proposed Scheme 3D Grid-Based Key Pre-Distribution Scheme

(9/11)

2 2

2 2

2

2

:

The two nodes belong to -plat,

computes , by evaluating , with identifier

computes

Direct Key Establishm

, by evaluating , with identi

ent

fier

The c m n

:

om o

zi zj

h hi

h hj

Exampleh h h

h

S f i j f i y j

S f j i f j y i

2 2key , ,h hijk f i j f j i

2, , x y h

2 ,hf x y

iS

jS

ijk

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The Proposed Scheme 3D Grid-Based Key Pre-Distribution

Scheme (10/11)

If the two nodes and do not belong to the same plat

Let is a intermediate node with identifier . must satisfied one of the

Indirect Key Establishme

following condition:

a.

t

a

n :

i j

x x

S S

S

c i c

nd or

b. and or

c. and or

y y z z

y y x x z z

z z x x y y

r j r h j h

r i r c j c h j h

h i h c j c r j r

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The Proposed Scheme 3D Grid-Based Key Pre-Distribution

Scheme (11/11)

: and

and

generate indirect keys wi

Indirect Key Establishment

th :

, ,

, ,

:

x x z z

i j

cx cxi

hz hzj

Examplec i c h j h

S S

S

k f i f i

k f j f j

2,2,2 jS

0,1,0iS

S

AnalysisConnectivity

18

AnalysisResiliency

19

Comparison

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ConclusionsOriginal contribution:

Introduce a grid-based key pre-distribution scheme that utilizes the notion of plats on grid

Plat-based polynomial assignmentThe advantages of the proposed scheme

Guarantees higher connectivityMore possible intermediate nodes, better

resiliency

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CommentIn the Key Establishment phase, the authors

do not describe how the sensor node find the intermediate node for indirect key establishment.

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