Adaptive Random Key Distribution Schemes
for Wireless Sensor Networks
Shih

I Huang
Dept. of Comp. Sci. & Info. Eng.
National Chiao Tung University
WADIS’03
2
Outline
Introduction
Motivation
Related Work
Proposed Schemes
Analysis
Conclusion
3
Introduction
Wireless Sensor Networks (WSNs)
It consists of a set of small devices with sensing and
wireless communication capabilities
Those small devices are named
sensor nodes
, and are
deployed within a special area to monitor a physical
phenomenon.
Ex: Anthrax
Multifunctional
Depends on what sensors are attached
Features
Widely deployed. (100~1M↑)
Low communication bandwidth
Limited memory space and computation power
4
Motivation
A large WSN consists of thousands of nodes
Need shared communication keys to ensure secure peer

to

peer wireless communication
Limited memory storage (512 bytes ~ 4K)
To deliver data without being compromised, WSN
services rely on secure communication and key
distribution
5
Conventional Scheme
(Random Pair

wise)
A
E
D
G
B
C
F
K
1
K
2
K
3
K
4
K
5
K
6
K
7
K
2
K
3
K
4
K
5
K
6
K
7
K
1
K
3
K
4
K
5
K
6
K
7
K
1
K
2
K
4
K
5
K
6
K
7
K
1
K
2
K
3
K
5
K
6
K
7
K
1
K
2
K
3
K
4
K
6
K
7
K
1
K
2
K
3
K
4
K
5
K
7
K
1
K
2
K
3
K
4
K
5
K
6
* Requires a large storage space for
keys in a large WSN
6
Motivation
The existing key distribution solutions require a large
memory space in a large WSN
We propose two symmetric key distribution schemes
to minimize storage requirement
Adaptive Random Pre

distributed scheme
(
ARP
)
Unique Assigned One

way Hash Function scheme
(
UAO
)
7
Related Work
Platform
Cryptography
Feature
Disadvantage
Zhou and Haas
MANETs
Asymmetric
Use threshold scheme to
distribute CA’s
functionalities
Asymmetric cryptography is not
energy efficient for WSNs
Luo et al
Asymmetric
Hubaux et al
Asymmetric
Use a PGP

like scheme
Asokan and
Ginzboorg
Asymmetric
Use a multi

party key
exchange protocol
Yi and Kravets
Asymmetric
Use the threshold scheme
Carman et al
WSNs
Asymmetric
Based on group key and
ID

based cryptography
Asymmetric cryptography is not
energy efficient for WSNs
SPINS
Symmetric
Use a base station to
perform key exchange for
sensor nodes.
It must have base station involved.
Liu and Ning
Symmetric
Undercoffer et al
Symmetric
Eschenauer and Gligor
Symmetric
Based on Random Graph
theory
The memory storage requirement is
high in a huge WSN.
Chan et al
Symmetric
8
Random Graph Theory
A Random Graph
G(n, p)
is a graph of
n
nodes, and the
probability that a link exists between any two nodes is
p.
Given a desired probability
P
c
for the graph connectivity
ex:
P
c
=0.99999
to get a connected graph.
Then we can get a threshold of
p
to form a connected graph.
……. (1)
The expected degree of a node
….…(2)
n
P
n
p
c
))
ln(
ln(
)
ln(
n
P
n
n
n
p
d
c
)))
ln(
ln(
)
)(ln(
1
(
)
1
(
*
* The scheme only needs to select
d
keys to keep a
network connected under probability
p
9
Random Key Based Schemes
Basic Scheme
L. Eschenauer, V. D. Gligor, “A Key

Management Scheme for Distributed
Sensor Networks,”
9th ACM Conference on Computer and Communication
Security
, pp.41

47, November 2002. (CCS’02)
Each node randomly picks
r
keys from a unordered key pool
S
.
Use the common shared key to establish a secure link.
Relies on probabilistic key sharing among the nodes of a random graph.
1
K
1
K
2
K
2
K
Secure link
Sensor nodes
1
K
1
K
2
K
2
K
Communication keys
A
B
C
D
A
B
C
D
A
B
C
D
* Map Random Graph Theory to key selecting problem
10
Adaptive Random Pre

distributed Scheme
(ARP Scheme)
The features of ARP scheme
A Random Key based key distribution scheme for WSNs.
To minimize the memory requirement.
ARP scheme consists of
Two

Dimension Key Pool
Key Selecting Algorithm
11
Two

Dimension Key Pool
Use
t
one

way function
F
1
, F
2
,…,F
t
and t seed keys
K
1,0
, K
2,0
,…,K
t,0
to
generate
t
one

way key chains.
For a key chain
KC
i
, it consists of
K
i,0
, K
i,1
,…K
i,s

1
.
Where
K
i,j
=
F
i
(K
i,j

1
)
, and the length of
KC
i
is
s
.
The key pool size
= s * t
.
(a) The unordered key pool
(b) The TwoDimension key pool
s
t
12
s
t
s
t
KC
2
Key Selecting
Each node randomly choose a one

way key chain, and
memorized its one

way function
F
i
and its seed key
K
i,0
.
Randomly select
d

t
key chains
KC
t1
, KC
t2
,…,KC
t(d

t)
, from
the rest of key chains.
For each key chain
KC
tj
selected, randomly pick a key
K
tj,sj
from
KC
tj
and memorized
K
tj,sj
.
13
Unique Assigned One

way Hash Function
Scheme (UAO Scheme)
The features of UAO scheme
Provide node

to

node authentication.
Great resistance to node capture.
The maximum supported network size is greater than the
existing schemes.
The UAO scheme consists of
Key Decision Algorithm
Node

to

Node Authentication Protocol
14
Key Decision Algorithm
Suppose each sensor node
SN
i
has
a unique identity
ID
i
.
First, we assign a unique one

way
hash function
F
i
to each sensor
node
SN
i
.
Second,
SN
i
randomly selects
d
other sensor nodes.
Third, each selected node use
following formula to generate the
unique key for
SN
i
.
Finally,
SN
i
memorizes those
unique keys and the generating
identities.
SN
i
)
(
i
v
j
ID
F
K
j
SN
1
SN
2
SN
3
SN
4
SN
5
SN
6
SN
7
ID
i
F
i
K
2
ID
2
K
5
ID
5
K
7
ID
7
K
2
=
F
2
(
ID
i
)
K
5
=
F
5
(
ID
i
)
K
7
=
F
7
(
ID
i
)
15
Node

to

node Authentication Protocol
1.
SN
i
broadcasts its identity
2.
SN
j
verifies its key ring, if
ID
i
is combined with any key then
3.
SN
i
calculates the
K
s
=
F
i
(
ID
j
), and decrypts the message, then
sends the ACK and challenge message.
4.
SN
j
receives the challenge and sends the response
}
{
:
i
j
i
ID
SN
SN
]}
Message
Request
[

{
:
s
K
j
i
j
E
ID
SN
SN
]}
Message
Challenge
and
ACK
[
{
:
s
K
j
i
E
SN
SN
]}
Challenge
for the
Response
[
{
:
s
K
i
j
E
SN
SN
1
2
3
4
SN
j
SN
i
16
Analysis of ARP Scheme
We analyze the ARP scheme in following aspect:
Probability of connectivity.
Analyze the link probability of using Two

Dimension Key Pool.
The link probability is equal to
1
–
Pr
[
any two nodes do not share any key
]
17
Probability of Connectivity (1/2)
To calculate the probability that any two nodes
A
and
B
do not share any
common key:
A’s
one

way key chain does not match with
B’s
one

way key chain.
A’s
one

way key chain does not match with any
B’s
selected keys.
The probability of above two parts is equal to
A’s
selected keys do not match with
B’s
one

way key chain.
The probability is equal to
A’s
selected keys do not match with any
B’s
selected keys.
The probability is equal to
The link probability is equal to
……(3)
t
s
d
t
)
1
(
'
0
1
1
)
(
1
1
'
)
1
'
(
1
'
r
i
i
y
i
p
h
r
h
h
r
h
p
'
0
1
1
)
(
1
1
'
)
1
'
(
1
'
r
i
i
y
i
p
h
r
h
h
r
h
p
1
1
)
(
1
2
d
s
d
t
s
d
t
s
d
t
s
d
t
i
s
d
s
d
t
i
s
d
i
p
2
)
(
2
)
(
s
d
i
i
t
i
p
0
1
1
)
(
s
d
r
i
i
s
i
p
t
s
d
t
t
s
d
t
p
0
1
1
)
(
1
1
)
(
)
1
(
1
'
18
Probability of Connectivity (2/2)
n
P
n
p
c
))
ln(
ln(
)
ln(
Key pool size = 100,000
* ARP needs fewer keys to achieve the same connectivity probability
19
The link probability
p’
can be evaluate by
1
–
Pr.
[
two nodes do not have any key derived from the other’s one

way function
]
p’
is equal to
Substitute
p’
by a function of
d
:
Substitute
d
by a function of
n
:
Evaluate the root of the above equation:
Analysis of UAO Scheme
2
)
1
1
(
1
'
n
d
p
2
)
1
1
(
1
'
n
r
n
d
2
)
1
1
(
1
'
)))
ln(
ln(
)
)(ln(
1
(
n
r
n
n
P
n
n
c
)
'
)))
ln(
ln(
)
)(ln(
1
(
1
1
)(
1
(
n
n
P
n
n
n
r
c
r
: Key ring size
20
Evaluation of UAO Scheme
Key size = 128 bits
Pc=0.99999
21
Conclusion
Key distribution is a critical and fundamental issue for the security service
in WSNs.
The pre

distributed and symmetric cryptosystem based scheme is well
suitable for the resource constrained sensor networks.
We propose two schemes based on one

way function and Random Graph
theory to provide memory efficient key distribution for WSNs.
ARP scheme
Provide efficient trade

off between memory space and security strength.
UAO scheme
Provide node

to

node authentication.
Great resistant to node capture.
If there is enough memory space, we suggest using UAO scheme as the key
distribution scheme for WSNs.
Otherwise, we suggest using ARP scheme.
To achieve an efficient trade

off between memory space and security strength.
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