Wireless Sensor Network, 2010, 2, 689-697
doi:10.4236/wsn.2010.29083 Published Online September 2010 (http://www.SciRP.org/journal/wsn)
An Adaptive Key Management Framework for the
Wireless Mesh and Sensor Networks
Mi Wen1, Zhi Yin1, Yu Long2, Yong Wang1
1department of Computer Science & Engineering; 2department of Computer Science & Engineering;
1Shanghai University of Electric Power; 2Shanghai Jiaotong University,
1Shanghai, China
Received June 30, 2010; revised July 31, 2010; accepted August 30, 2010
Abstract
Wireless sensor networks (WSNs) and wireless mesh networks (WMNs) are popular research subjects. The
interconnection of both network types enables next-generation applications and creates new optimization
opportunities. Currently, plenty of protocols are available on the security of either wireless sensor networks
or wireless mesh networks, an investigation in peer work underpins the fact that neither of these protocols is
adapt to the interconnection of these network types. The internal cause relies on the fact that they differ in
terms of complexity, scalability and network abstraction level. Therefore, in this article, we propose a unified
security framework with three key management protocols, MPKM, MGKM, and TKM which are able to
provide basic functionalities on the simplest devices and advanced functionalities on high performance nodes.
We perform a detailed performance evaluation on our protocols against some important metrics such as
scalability, key connectivity and compromise resilience, and we also compare our solution to the current
keying protocols for WSNs and WMNs.
Keywords: Wireless Mesh Sensor Network, Key Management, Adaptive Security, Group Key
1. Introduction
The success of wireless technologies today caused the
international wireless network research community to
have high hopes for the future. Wireless mesh sensor
network (WMSN) is a new architecture that merges ad-
vantages of wireless mesh networks (WMN) and wire-
less sensor networks (WSN), especially on scalability,
robustness and balanced energy dissipation [1]. Wireless
sensor networks and wireless mesh networks are popular
research subjects. The interconnection of both network
types enables next-generation applications and creates
new optimization opportunities [2]. Many application
scenarios could benefit from a successful and optimal
interconnection between WSNs and WMNs. For exam-
ple, a wireless mesh network can be used as a backbone
for collecting sensor data from remote sensor clusters, or,
resource intensive calculations with sensor data may be
performed on a mesh router instead on a sensor node.
Although plenty of research is available on all aspects of
either wireless sensor networks or wireless mesh net-
works, little information is available on the interconnec-
tion of these network types. Their difference between
WMNs and WSNs in wireless technologies, addressing
protocols, routing strategies and security mechanisms
make an effective interconnection be challenging.
Especially, WMSNs are always deployed in hostile
environments to track target, monitor battlefield, detect
intruder or do some scientific explorations and the open-
ness of the wireless environment makes security in
WMSNs a critical concern in the deployment of such
group applications. In wireless communication environ-
ments an adversary not only can eavesdrop the radio
traffic in a network, but also can intercept the exchanged
data. To prevent the malicious node impersonating good
nodes for spreading misleading data intentionally, secret
keys should be used to achieve data confidentiality, in-
tegrity and authentication between communicating par-
ties [3]. But in WMN networks, security and trust is most
often guaranteed using either pre-shared keys, or by re-
lying on certificate based encryption techniques [4]. Be-
cause of the limited capacities of sensor nodes, the secu-
rity approaches used in WMNs are not suitable for
WSNs [5]. Some sensor nodes might be unable to im-

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690
plement any certificate based security mechanism at all.
Therefore, the development of adaptive key management
protocols is a promising approach to enable low end de-
vices to participate in heterogeneous network architec-
tures securely.
Adaptive key management protocol is an effective
approach to provide efficient and secure interconnection,
while respecting the individual characteristics of each
network type. The main difficulty with adaptive key
management protocols is the creation of a basic key
management protocol version that can be deployed on a
very basic network node. Current popular key manage-
ment protocols in WMNs such as the [6-8] are relatively
complex. Even though the performance of sensor nodes
will increase over time, there will always remain a class
of devices that is unable to run these complex protocols.
Therefore, there is a need for novel, simple techniques
that are able to provide basic functionalities on the sim-
plest devices and at the same time they can be extended
to support advanced functionalities on high performance
nodes. Thus, an adaptive and modular key management
approach is needed.
In this paper we present a unified security framework
that embodies three key management protocols which
can provide adaptive security for WMSNs for the need of
the applications. The framework includes three key
management protocols: (a) the Matrix based Pairwise
Key Management (MPKM) protocol for sensor nodes
with limited resources. (b) the Matrix based Group Key
Management (MGKM) protocol for the network with
sinks or cluster heads except the sensor nodes; (c) the
Threshold Key Management (TKM) protocol for the
network with mesh nodes in addition. All of these three
protocols are interrelated elements: MGKM can be ex-
tended from MPKM, and TKM can be extended from
MGKM. Therefore, the accession of MGKM and TKM
in the WMSNs will not increase the storage or commu-
nication overhead of sensor nodes.
2. Related Works
Key Management is one of the main challenges in se-
curing wireless networks, and has been addressed by
many authors. In this section, we present an overview of
some approaches and protocols for keying management
in both WSNs and WMNs respectively.
2.1. Key Management in WSNs
To date, the key management protocols in sensor net-
works can be mainly classified into two types: pairwise
key management protocols and group key management
protocols. In pairwise key management protocols [9-14],
each pair of communication nodes should establish a
shared key. One attractive idea in the pairwise key man-
agement is key pre-distribution, i.e., pre-installing a lim-
ited number of secrets in sensor nodes prior to actual
deployment; after the deployment, if two neighboring
nodes have some common keys, they can setup a secure
link by the shared keys. While in the group key man-
agement protocols [15-17], the key idea is to broadcast
information that is useful only for trusted nodes. Com-
bined with its pre-distributed secrets, this broadcast in-
formation enables a trusted sensor node to reconstruct a
group key. Most pairwise key and group key manage-
ment protocols in WSNs are based on symmetric key
cryptography, such as Du’s [12] key Matrix based, Cam-
tepe’s [9] Combinatorial Design based, Liu’s [13] poly-
nomial based protocols. These solutions are designed to
sustain severe computation power, storage, mobility, and
energy constraints, and as a result have limited scalability
and robustness. Although some research [18] shows that
the right selection of algorithms and associated parameters
along with code optimization can make public key cryp-
tography feasible for sensor networks. For example, the
ECC and RSA based key management protocols. The
major shortcomings of them are the associated expensive
computation and the high probability of likely penetra-
tion by malicious agents. Also all current asymmetric
key related studies only support their feasibility for
WSN’s. Unfortunately, as we know, none of current
works propose complete key management infrastructure
compatible public and private key cryptography.
2.2. Key Management in WMNs
Secure group communication is a mature research area
and has a large body of research literature. The main
objective of a secure group communication protocol is to
ensure the data confidentiality against outsiders such that
only legitimate group members can recover the group
data. Existing solutions for wired networks [19-21] are
not well suited for WMNs as they fail to take into con-
sideration the multi-hop communication paradigm fea-
tured by WMNs, as well as the communication security
among mesh clients within the coverage of a mesh router.
These protocols also do not exploit unique features of
WMNs, such as the broadcast nature of wireless com-
munication. ARSA [7] proposes attack-resilient security
architecture for WMNs, which uses ID-based cryptogra-
phy (IBC). SeGrOM [8] propose a new protocol frame-
work for secure group overlay multicast in WMNs. LSSS
[6] presents an ideal linear multi-secret sharing protocol,
by using monotone span programs. Though, they achieve
efficient and secure group communication in WMNs.
They can not be employed in the WSNs due to their ex-

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691
pensive energy consumption and also they can not offer
modular security for WMSNs.
In general, none of the existing protocols considered
the unique features of WMSNs, such as coexistence of
resources constrained sensor nodes and powerful mesh
nodes, increasing scalability when remote cluster sensors
get interconnected thanks to the presence of a WMN, all
of which can be leveraged for designing more optimized
protocols. Our work tries to fill this gap by designing
such a complete key management infrastructure specially
for WMSNs based on our previously key management
protocols [14,17].We will take into account the diversity
of nodes’ ability and propose a unified key management
framework, which includes simple techniques that are
able to provide basic functionalities on the simplest sen-
sor devices and at the same time they can be extended to
support advanced functionalities on high performance
mesh nodes.
3. System Model and Assumptions
3.1. Network Model
Define our target network environment is the intercon-
nection of WSNs and WMNs, called WMSNs. The
WMNs include a set of static wireless routers, called
mesh nodes (MN), organized in a backbone network and
communicating through multi-hop wireless links. Mobile
clients (MC) connect to the wireless mesh through a lo-
cal access router, called access point (AP), and commu-
nicate with each other through the wireless mesh. While
the WSN has the hierarchical architecture consisting of
numerous sensor nodes (SN) grouped in clusters and
each cluster has a cluster head (CH), which is responsi-
ble collecting and merging local data from sensor nodes
and send it to mesh nodes. Clusters of sensors can be
formed based on various criteria such as location, com-
munication range, resource and energy capabilities, etc.
(See Figure 1). Resource intensive calculations with
sensed data may be performed on a MN. MN here can be
considered as an actuator node in WSNs and can take
immediate response when monitoring some abnormal
phenomena in WSNs. Many application scenarios could
benefit from successful and optimal WMSNs. For exam-
ple, the WMNs can be used as a backbone for collecting
sensor data from remote sensor clusters. For clarity, we
describe the terms in the scope of this article is specified
as follows:
Sensor nodes are network nodes with limited capabili-
ties in terms of processing power, memory capacity and
bandwidth, equipped with a sensor and/or actuator chip.
As such, a sensor node can be a source of data in a net-
work, but could as well be used as intermediate node to
forward data from one sensor device to another, or to a
data collection device, called a cluster head (see Figure
1 (ii)). Sensor nodes are small sized and limited in cost.
With WSN, all forms of wireless networks between sen-
sor devices are indicated [1]. These sensor networks are
self-forming, and are used to gather data in places where
the use of cabled sensors is hard, costly or undesired. No
restriction is made based on network size or topology:
both single hop networks between SNs and a CH, and
complex multi-hop networks with meshed topologies are
considered.
Mesh nodes are relatively powerful networked nodes,
equipped with relatively powerful wireless interfaces and
thus are able to transmit and receive at higher band-
widths than sensor nodes. With WMN or wireless mesh
networks, all forms of wireless networks between mesh
nodes are indicated. Again, there are no restrictions on
the topology. Mesh networks are often used as a wireless
backbone for the interconnection of end user devices.
WMNs might also offer additional functionality to the
client networks; for example, provide an uplink to the
Internet (see Figure 1(i)). Mesh networks are self-
forming and self-healing, and are therefore an ideal solu-
tion to provide connectivity in places where cabled net-
works cannot easily be installed. Furthermore, because of
their self-organizing character, mesh networks can be
rolled out fast, making them ideal candidates to be used
as emergency network infrastructure.
3.2. Definitions and Notations
In the following section, we give some definitions and
notations used in this paper unavoidable.
Figure 1. Wireless mesh and sensor network archi-
tecture example.

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692
4. Proposed Framework
In this section, we first describe MPKM, our basic key
management protocol handling the pairwise key estab-
lishment for the resource limited sensor nodes. We then
describe two additional protocols, (a) MGKM, a key
management protocol handling the group key of the
WSNs and (b) TKM, a key management protocol han-
dling the key sharing in WMN using the asymmetric
cryptography. All these protocols together can manage
the key establishments in WMSNs. Since MPKM and
MGKM are previously proposed in [14] and [17]. Here
we include them only to form the unified key manage-
men framework. Thus, we will focus on the TKM proto-
col in the latter of this paper. Due to the node resource
limitation, MPKM and MGKM are based on symmetric
key cryptography while TKM is based on asymmetric
key cryptography. All of these three protocols are inter-
related elements: MGKM can be extended from MPKM
and TKM can be extended from MGKM. (See Figure 2).
Therefore, the accession of MGKM and TKM in the
WMSNs will not increase the storage or communication
overhead of sensor nodes. This is one of the advantages
of our framework and it just satisfies the requirement of
key management technique in WMSNs, scalable and
lightweight.
4.1. The Matrix Based Pairwise Key
Management (MPKM) Protocol
In MPKM, each sensor node is programmed according to
the application requirements before network deployment.
As we all know, Blom proposed a key distribution ap-
proach [12], which allows any pair of nodes in a network
to be able to find a pairwise secret key. As long as no
more than nodes are compromised, the network is per-
fectly secure. For the sake of key updating, we modify
the Blom’s symmetric matrix construction in [14]. We
briefly describe how to use our modified version of
Blom's key distribution approach to establish paiwise
key as follows. Some used notations in this paper are
given in Table 1.
The base station (BS) in WSNs (acting as a trusted
server) first computes a*nnmatrix B over a finite field
GF(q), B is considered as the public information, q is a
prime, and nq

. One example of such a matrix is a
Vandermonde matrix whose element()mod
ji
ij
bg q,
where g is the primitive nonzero element of GF(q)
and
j
g
is the jth column seed. That means:
23
12131 1
111 1
() ()()
n
nnnnn
gg gg
B
gg gg
 



















Table 1. Table type styles.
Ni
A sensor node i (i=,1,…,n), where Nn is the trusted
dealer and it has more power than normal sensor node,
i.e. the cluster head in a cluster.
si Row seed of the matrix D; the row seed used in each row
i of matrix D should not bigger than si.
gi Column seed of matrix B
Kij The pairwise key between node Ni and Nj
KG The group key of the initial set N={ N1, N2, ..., Nn }
GIDi The group or cluster identity of cluster i
IDi The identity of sensor node i
KGi The group key of the sensor cluster i
sk The secret key to be shared by the mesh nodes
ski The secret key share of mesh node i
Figure 2. Overview of our k ey management framework.

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693
This construction requires that2()nq  i.e.,
21nq. Since B is a Vandermonde matrix, it can be
proved that the n columns are linearly independent when
23
,, ,
n
g
gg gare all distinct.
Next, the BS generates n row seeds 1,n
s
s,
where (1,..., )
i
s
in is the random prime number of
GF(q) and it is only known to the powerful node (Nn) in
the network, e.g., the cluster head of WSNs. And then
BS creates a random nn* symmetric matrix D over
GF(q). Each row of the D is composed of hash values of
the row seeds. Differing from the construction of matrix
B, the elements in symmetric matrix D are generated as
follows:
(1; ; )
(1; ;)
{()( );();}
ij
ijj iji
foriin i
forjjn j
ifijd HselsedHs
 
 

Where dij is the element in matrix D. An example of ma-
trix D with size 3*3 is shown as follows:
123
111
22 3
122
33 3
12 3
()() ()
() () ()
() () ()
HsH sHs
H
sHs Hs
H
sHs Hs






At last, the BS computes a *nn matrix A= (DB)T,
where T indicates a transposition of the matrix. The ele-
ments in matrix A denote asij a, where1
n
ijj i
adb




.
The matrix B is public while the matrix D is kept secret
by the base station. Since D is symmetric, the key matrix
K = AB can be written as:
() ()
TTTT TT
K
DBBBD BB DBABK
Thus K is also a symmetric matrix andij ji
K
K

,
where ij
K
is the element of K at ith row and jth column.
We take ij
K
(or
j
i
K
) as the pairwise key between
node Ni and node Nj. To carry out the above computation,
nodes Ni and Nj should be able to compute Kij and Kji
respectively. This can be easily achieved using the fol-
lowing key pre-distribution procedure, for node Ni:
(1) Store the ith row of matrix A at node Ni, denoted as
ri (A), i.e., i ij r(A) [a], (1,,jn).
(2) Store the ith column seed gi of matrix B at Ni.
After deployment, each node has a piece of secret in-
formation as described above. When nodes Ni and Nj
need to find the pairwise key between them, they first
exchange their column seeds of matrix B (since B is the
public information, it can be sent in plaintext). Then, by
using the preloaded secrets, they can compute ij
K
(or
j
i
K
) respectively as:1
n
iji j
K
ab




. It can be
proved that the above protocol is n-secure because all the
rows in D are linearly independent. And this property
guarantees the uniqueness of the pairwise keys in the
cluster.
4.2. The Matrix Based Group Key Management
(MGKM) Protocol
When nodes with better resources, named as CHs, are
deployed in the network, they can be used to collect and
merge local data from sensor nodes and send it to mesh
nodes. Mesh nodes then distribute the required informa-
tion to the end user clients. Now, we assumed that after
deploying the new nodes into the operating WSNs, the
clusters can be formed based on various criteria such as
capabilities, location, and communication range etc. [17].
Now, without loss of generality, let N = {N1, N2, ..., Nn}
be the initial set of participants in each cluster group that
want to generate a group key. Assume that there are n-1
sensor nodes and a powerful node Nn in a cluster (Nn may
be a CH). The detailed steps of the group distribution are
presented as follows.
Step 1: Initially, each node )11(


niNi is
pre-loaded a row ri(A) from matrix A and column seed gi
as described in Subsection 4.1. Then, after deployment,
each node pre-computes Kin, Kii (i.e, 1
n
iii i
K
ab


 
)
an 1
ii
K

. Ni sends the enciphered message (Ni,
()
in
iKii
CEK) to node Nn and keeps1
ii
K
in its local
memory. Kin is the pairwise key between node Ni and Nn.
|| stands for message concatenation.
Step 2: Node Nn computes Knn as above. Upon receiv-
ing eachi (N ,)(11)
i
Cin

, node Nn deciphers them
and computes xi=KnnKii. Next, node Nn com-
putes 1
1
n
Gnn i
i
K
Kx


. Finally, the powerful node Nn
broadcasts (Nn, x1... xn-1) to other nodes.
Step 3: On receiving the broadcast messages, each
node i
N
(1 1)in

 computes the common group
key 1
1
1
n
Gjjji
i
KxKx



.
Note that the client Ni may pre-compute 1
ii
K

to re-
duce the computational load. Until now, storage limita-
tion is becoming less of a concerning issue as many
add-on memory cards are widely available. And we can
prove that the proposed protocol is a contributory group
key agreement protocol. Reference [17] for detailed
prove process.
4.3. The Threshold Key Management (TKM)
Protocol
If a WMN is added to an already existing WSN to collect
the sensed messages, should any adjustments to the WSN
protocols be made? In general: the less adjustments are
to be made on either WSN or WMN protocols, the faster
an interconnection can be realized and the sooner an in-
terconnection strategy might be adopted. Moreover, us-
ing either a single symmetric key or by relying on cer-
tificate based encryption techniques to achieve key
management operations for the mesh nodes risks high

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694
probability of key leakage or creates a vulnerable point
in the network. Thus, based on the two former key man-
agement protocols, MPKM and MGKM, we design a
threshold key management protocol for mesh network. In
such a system, the group keys of the WSNs will be cal-
culated as a secret key shared by n mesh nodes. And the
secret key can be recovered by a coalition of t mesh
nodes.
4.3.1. Preliminaries of Threshold Secret Sharing
The proposed protocol is based on the (m, k) threshold
cryptography [22]. Generally speaking, threshold cryp-
tography is used for distribution of a secret value S based
on polynomial interpolation, and an (m, k) threshold
protocol allows m parties to perform cryptographic op-
erations, so that any k parties can jointly perform key
discovery whereas (k-1) parties cannot derive any infor-
mation even after collusion. The parameter k represents
the threshold. A sample threshold cryptography protocol
proposed by Shamir can be explained as follows:
Consider the secret S, we can store the secret about S
into n shares (s1, . . . , sm) via a randomly chosen k degree
polynomial f(x) = a0+a1x+…+ak−1x
k−1 where a0 = S. Se-
cret shares are obtained by si = f (i), i = 1 . . . m. The m
shares of secrets are simply {f (1), f(2),… , f(m)}. Given
k points from the above m shares, we can derive the co-
efficients of f(x) by interpolation and hence calculate the
secret S =1()(0)
k
i
ifiL 
, where Li(0) is the Lagrange coeffi-
cient such as







ij ji
ij j
ixx
xx
xL )(
)(
)(
Therefore, the above protocol is a (n, k) threshold
cryptography protocol.
4.3.2. The Proposed TKM Protocol
We assume that there is a Trusted Server (TS, the base
station in WSN also can act as a TS) which can calculate
the secret key and the key shares for bootstrapping the
mesh nodes. And we also assume that when a WMN
with m mesh nodes is added to an already existing WSN,
each mesh node is innocent and cannot be compromised
during the first several minutes after deployment since
compromising a node takes some time. Based on this, the
system initialization process is carried out in two phases:
secret key calculation and mesh nodes bootstrapping. In
the first phase, the TS will collect the group keys of the
sensor nodes and calculate the secret key to be shared by
the mesh nodes. Here, we assumed that the messages
delivered among sensor nodes and mesh nodes are al-
ways encrypted by their group keys, the collaboration of
t mesh nodes can decrypt them. In the second phase, the
TS creates an (m, k) sharing (sk1,sk2, . . . , skm) and pri-
vately distributes these shares to m mesh nodes where (m
< M) and M is the network size.
Secret key calculation phase ： We assume that before
the WMN is added, the WSNs are classed by t clusters,
and each cluster has a CH and several SNs. Also, the
keys in WSNs are already established by using MPKM
and MGKM protocols. Thus, in this phase, the TS
 Step 1: Broadcast a hello message {IDTS, hello}
to the sensor nodes in WSNs.
 Step 2: On receiving the hello message, each CH
or the SNs will reply a message which contains
its group keys {GIDi, KGi, IDCH}.
 Step 3: By distinguish the different group keys
KGi (i=1,…, t) from the WSNs. The TS calculate
the secret key SK for mesh nodes as following:
Sk = KG1 ⊕ KG2 ⊕ …… ⊕ KGt , where⊕represents XOR
operation.
Mesh nodes bootstrapping phase: In this phase, the TS
performs the following operations:
 Step1: Create a random polynomial of degree k− 1:
f (x) =sk + a1x+· · ·+ak−1xk−1(mod p) where p is a
large prime number and sk is the shared private key
of the mesh nodes.
 Step2: Calculate and send to each node i the corre-
sponding share of (sk): ski = f (i)(mod p). For sim-
plicity i is assumed to be an integer and nodes to be
initialized range from 1 . . . m.
 Step3: Calculate and store locally the decryption
supplementary keys Si for each sensor group as fol-
lows, and then deleted the KGi (i=1,…, t) perma-
nently.
Si = sk ⊕ KGi(i = 1,…, t)
When a mesh node j receives messages from sensor
nodes, it should broadcast a request to its neighbors. Af-
ter collecting k-1 valid shares from its neighbors, it com-
bines them with its share in order to issue the secret key
sk. If the WSN only have one group, then sk = KG1, the
requester mesh node j can use sk to decrypt the received
messages immediately. If the WSN have two or more
groups, the requester node j should ask the TS for help.
The TS replies with the group i’s decryption supplemen-
tary keys Si. Then, the mesh node j decrypt the received
messages by calculate sk ⊕ Si , where sk ⊕ Si = KG1.
5. Post Deployment Operations
Network post-deployment issues are critical factors in
determining the efficiency of any key management pro-
tocol for WMSN specific environment. Each protocols
working in correspondence to these issues is explained
against the following matrices.
Scalability: Each of the three protocols supports node

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695
additions after network deployment. In case of MPKM
and MPGM, when a new node ID(n+1) wants to join the
network, the BS will generate the key information for
node n+1 and the Real-Time generation (RTG) program
in [14] will be triggered to expand the key matrix. Thus,
all nodes in its cluster will establish new pairwise key
with this node. And periodically their group key also will
be updated according to reference [17].
In TKM, when a new sensor cluster wants to join the
existing WMSN, here we assume that the pairwise keys
and group key in this cluster have been established by
using the MPKM and MPGM protocols. The main issue
in this procedure is the secret key updating and the key
share information updating for existing mesh nodes.
There are two types of techniques can address this prob-
lem.
(1) Regeneration: in this approach, the TS first recal-
culate the secret key by XOR sk and the new cluster’s
group key, here we denote it as KGnew. So, the new secret
key for the mesh nodes in new mesh network is sk’=sk⊕
KGnew. Then, the TS recreates a random polynomial of
degree k−1: h (x) = sk’+ b1x+· · ·+bk−1xk−1 (mod p) and
resends the key share for mesh nodes. Finally, the mesh
nodes can establish new secret key to guarantee the net-
work security. The drawback of this approach is that it
introduces substantive communication and computation
overhead.
(2) Real-Time updating: This technique relies on the
following Homomorphic property. If (s1, . . . , sn) is an (n,
k) sharing of S and (s’1, . . . , s’n) is an (n, k) sharing of S’,
then(s1 ⊕ s’1, . . . , sn ⊕ s’n) is the an (n, k) sharing of
S ⊕ S’, if we set S’ = 0, then we get a new (n, k) sharing
of S.
Now, let (sk1,…,skm) be the (m, k) sharing of sk and
KGnew is the group key of the new cluster, the TS creates
a random polynomial of degree k − 1: p (x) =KGnew +
c1x+· · ·+ck−1xk−1(mod p) where p is a large prime number.
And then the TS calculates the corresponding share of
(KGnew): Ki = p (i) (mod p) and sends it to each node i.
Thus, the mesh nodes can get a new sharing (sk1’,…,skm’)
of sk’ where ski’= ski⊕Ki.
Key connectivity: Key connectivity is described as the
number of keys required to be stored on each node for
specified level of required network connectivity.
MPKM establishes a pairwise key for each pair of nodes
in the same cluster. Since the keying information of the
nodes in one cluster is coming from the same symmetric
key matrix, each pair of nodes in one cluster can estab-
lish a paiwise key. This provides 100% cluster wide
connectivity.
MPGM provides good key connectivity on frequent
broadcast basis. In a typical information gathering sce-
nario where the primary purpose of the nodes is to gather
data and forward it to BS or MN, nodes in one cluster
communicate with each other more frequently. Such
communication is ensured by a common cluster wide
group key. Hence, broadcast based cluster-wide key
connectivity is ensured.
In TKM, to encrypt the communication between the
sensor nodes and the mesh node needs the sensor’s group
key, which is established in MPGM. And the decryption
of the communication messages needs local collabora-
tion of the neighboring mesh nodes by using the thresh-
old cryptography. All these keys are established and se-
cure. Therefore, complete network-wide key connectivity
is ensured by using these three protocols.
6. Performance Analysis
6.1. Security Analysis
We have proposed an adaptive key management frame-
work for WMSNs in this paper. From simple MPKM to
complex TKM, they can provide modular security ser-
vices from basic functionalities to advanced functionalities
on kinds of nodes. For instance, they can establish both
pairwise key and group key for sensor nodes with the
same pre-distributed secrets and update their keys at the
same time. Meanwhile, the secret key of the mesh nodes
also can be established by extending the key manage-
ment of the group keys. Furthermore, our framework
satisfies the security requirements of both WSNs and
WMNs. In this section, we analyze the security of our
proposed key management framework.
Compromise resistance: In MPKM, since the paiwise
key of each sensor node in our protocol is different from
each other, the discovery of the captured keys cannot
give out any knowledge of the keys in the innocent nodes.
Moreover, any node's failure or compromise triggers a
key updating process and, thus, the keys shared by the
captured nodes and the innocent nodes are get rid of.
That means MPKM provides sufficient security, no mat-
ter how many sensors in the same cluster are compro-
mised MPKM can achieve perfect compromise resilience.
In MPGM, the group key is established by the collabora-
tion of all the nodes in the same cluster, no participant
can predetermine the common key and each node has the
same right to verify if its contribution is included in their
currently used group key. Also, the group key can be
updated periodically. Thus, MPGM has perfect group
fairness and compromise resilience. In TKM, any k
nodes can jointly perform key discovery whereas (k-1)
nodes cannot derive any information even after collusion.
Thus, it is k secure and has (k-1) resistance. Also, the
secret key can be updated when the group keys changed
or a new cluster wants to join the WMNs.
Group confidentiality: In MPGM, nodes that are not
the part of the group should not have access to any key

M. WEN ET AL.
696
that can decrypt any data broadcast to the group. For the
message, only the powerful node (such as BS or TS) can
decrypt the message to get the contributions of the client
nodes by using its pairwise key with the client nodes.
With the same reason, only the contributory nodes can
recover the group key by using their own contribution.
Therefore, the group key is group confidential.
6.2. Comparison with other Protocols
Now let us compare our protocols with the available key
management techniques for wireless sensor networks and
wireless mesh networks. Such as Du’s [12] key Matrix,
Camtepe’s [9] Combinatorial Design, Liu’s [13] poly-
nomial based protocols for WSN, ARSA [7], SeGrOM [8]
and LSSS [6] for secure WMN group communication.
For convenience, the following notations are used to
analyze the various properties: Y: Yes or has; N: No or
hasn’t; Inc.: will increase; Nor.: remain normal; λ: the
threshold, represents that if more than λ nodes be com-
promised, the protocol is not secure; little p: the protocol
only provides p connectivity; big P: the protocol pro-
vides 100% or strong key connectivity. Table 2 lists the
comparisons among our protocols and protocols only for
the WSN or WMNs.
We consider the performance comparisons in terms of
the scalability，compromise resistance，key connectivity，
nesh nodes security，modular security service. It is ob-
vious that only our protocols can be scalable when the
network size changes. If some nodes are compromised
by the adversary, protocols for WSN and WMN only
have a certain level of resistance, if the number of com-
promised nodes exceed the level, the network will not
secure any more. While our protocols can maintain 2P+λ
resistance, which mean MPKM and MPGM can maintain
perfect compromise resistance, only TKM has a thresh-
old λ. In terms of nodes security, only our protocols can
provide security protection for both sensor nodes and
mesh nodes and the storage for nodes will not increase
no matter other two protocols being included or not.
Thus, from the table we can see only the protocols pro-
posed in our framework can be adaptive for WMSNs.
7. Conclusions
The interconnection of heterogeneous WSN and WMN
networks is a pilot case which can be used to derive di-
rections for the research on future heterogeneous net-
work architectures. One of the major challenges for the
development of future network architectures is the crea-
tion of adaptive key management protocols for the diver-
sity of network nodes. In this paper we have presented an
adaptive key management framework for WMSNs. It
includes three possible keying implementations for dif-
ferent network nodes, i.e. pairwise key for sensor nodes,
group key for high and low level sensor nodes and secret
key shares through threshold cryptography for mesh
nodes. The results clearly show that they can adapt to the
different resource availability and achieve levels of secu-
rity. In short, no matter the addition of low end nodes or
high end devices to a secure environment might intro-
duce security risks. The design of our key management
framework can give simple but effective security solu-
tions for each level of devices. And as we know, our
framework is the first one which provides adaptive and
modular security service for WMSNs. This is extremely
important for the future generation of integrated net-
works.
Adaptive security is an interesting future research
track. It will remain a continuous challenge to integrate
low-end devices in future networking environments. In
our future work, we would like to investigate new keying
mechanism with better extension properties to provide
perfect security and robust continuity for future genera-
tion of integrated networks.
8. Acknowledgements
This work is supported by the National Natural Science
Foundation of China under Grant No.60903188,
60863001 and 60903189, the Innovation Program of
Shanghai Municipal Education Commission under Grant
No.10YZ157, the Shanghai university scientific selection
Table 2. Comparisons among our protocols and protocols only for the WSN or WMNs
Du’s Liu’s Camtepe’s ARSA SeGrOM LSSS Our’s
Scalability N N N N N N Y
Compromise resistance λ p p p p p 2P+λ
Key connectivity p p p P P P P
Node’s Storage overhead In. Inc. Inc. Nor. Inc. Inc. Nor.
Sensor security Y Y Y N N N Y
Mesh nodes security N N N Y Y Y Y
Modular security service N N N N N N Y

M. WEN ET AL.
697
and cultivation for outstanding young teachers in special
fund No.sdl09010.
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