Grid-Based Key Pre-Distribution in Wireless Sensor Networks
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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
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OutlineIntroductionRelated WorksThe Proposed Scheme
Grid-Based Key Pre-Distribution in WSN (3D)AnalysisConclusionsComment
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Introduction
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A Grid-Based Key Pre-Distribution Scheme (3D) Goal: Improve the connectivity and resiliency
Y-Plat
Z-Plat
X-Plat
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Related Works (Blundo et al. scheme, 1993)
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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
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Grid-Based Key Pre-Distribution Scheme (1/2)
Related Works (Liu et al. scheme, 2003)
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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
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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)
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The Proposed Scheme
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3D Grid-Based Key Pre-Distribution Scheme (1/11)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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AnalysisConnectivity
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AnalysisResiliency
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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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