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Research Article

A New Key Predistribution Scheme for Multiphase Sensor

Networks Using a New Deployment Model

Boqing Zhou,

1,2

Jianxin Wang,

Sujun Li,

1,2

and Weiping Wang

Hunan University of Humanities, Science and Technology, Loudi, Hunan 417000, China

School of Information Science and Engineering, Central South University, Changsha, Hunan 410083, China

Correspondence should be addressed to Jianxin Wang; jxwang@mail.csu.edu.cn

Received  May ; Accepted  May ; Published  June 

Academic Editor: Athanasios V. Vasilakos

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

During the lifecycle of sensor networks, making use of the existing key predistribution schemes using deployment knowledge

for pairwise key establishment and authentication between nodes, a new challenge is elevated. Either the resilience against node

capture attacks or the global connectivity will signicantly decrease with time. In this paper, a new deployment model is developed

for multiphase deployment sensor networks, and then a new key management scheme is further proposed. Compared with the

existing schemes using deployment knowledge, our scheme has better performance in global connectivity, resilience against node

capture attacks throughout their lifecycle.

1. Introduction

Due to limited energy capacity of batteries and the possibility

of node capture, the functional lifetime of sensor networks

(SNs) generally is longer than the operational lifetime of

single node. To keep networks working eciently, multiple

deployments of nodes are needed. In the paper, multiphase

SNs (MSNs) are studied, in which new nodes are periodi-

cally redeployed with certain intervals, called multiphase, to

replace the dead or compromised nodes.

When SNs are deployed in a hostile environment, security

becomes extremely important as they are vulnerable to dif-

ferent types of malicious attacks [–]. Hence, it is important

to protect communications among sensor nodes to maintain

message condentiality and integrity. As one of the most

fundamental security services, pairwise key establishment

enables sensor nodes to communicate securely with each

other using cryptographic techniques.

Public-key operations (both soware and hardware

implementations), albeit computationally feasible [, ], con-

sume energy approximately three orders of magnitude higher

than symmetric key encryption []. erefore, in the last few

years, dierent key distribution schemes using symmetric key

algorithms have been developed for SNs [–].

However, the security issue is still not solved for MSNs

by using deployment knowledge. In the schemes [, ], a

fraction of keys known by an attacker increases with the

captureofnodesduetotherepeateduseofaxedkeypool.

As a result, network security signicantly declines with time.

When a certain number of these nodes are captured, the

adversary has enough keys to compromise a large number of

links making the network ineective. Addition of new nodes

to the network with keys from the same key pool will not

help because the keys in the new nodes are compromised. In

[], a multiphase key management scheme is proposed, in

which a multiphase deployment model is used. However, it

has the following shortcomings. () In a cell, only a few nodes

which are not captured are working in a long time. () Nodes

must know their location information. () e number of new

nodes added to the network is xed in every deployment,

which will give rise to the number of nodes uncaptured in

the network with time. Also, the key management scheme

proposed based on the deployment model has the following

shortcomings. () Nodes which reside in the same cell but are

deployed in dierent phases cannot communicate with each

other. As a result, the local connectivity is low. () e global

connectivity will signicantly decrease with time.

Hindawi Publishing Corporation

Journal of Sensors

Volume 2014, Article ID 573913, 10 pages

http://dx.doi.org/10.1155/2014/573913

 Journal of Sensors

1.1. Outline of Our Scheme. To sum up, the problem of

authentication and pairwise key establishment between

nodes is still not solved for MSNs. In this paper, the main

focus is twofold. () A new multiphase deployment model

is proposed for sensor networks. In the model, the deploy-

ment eld is divided into hexagonal cells, each cell has a

deployment point, and nodes which have the same point

form a group. When the proportion of uncaptured nodes

in a group is less than the threshold 

, new nodes are

needed to be added to the cell. () A new key management

scheme is proposed based on the deployment model. In our

scheme, network deployment includes phases. For a cell, a

disjoint and association phases’ key pool is created, which

is generated by two-dimension backward key chains []. Key

pool of each phase is divided into  equal size subkey pools.

And nodes deployed in the th phase and deployed in a cell

(,)pick keys from the th-phase key pool of the cell (,)

and key pools which are created by neighbors cells of the

cell (,).

1.2. Main Contributions. e main contributions of this

paper are summarized as follows.

() A multiphase deployment model is presented. e

model has the following two main advantages: () the

number of nodes which are not captured in a cell can

be controlled by adjusting the parameter 

; () nodes

do not need to know their location information.

() A new method to construct key pools is proposed and

a new key predistribution scheme is presented. e

scheme can provide good performances in local con-

nectivity, global connectivity, and resilience against

node capture.

1.3. Organization. e remainder of the paper is organized as

follows. e existing schemes are summarized in Section .

e model of deployment is introduced in Section .Our

approach is proposed in Section  and the analysis and

simulation results are provided in Section .Conclusionand

future work are given in Section .

2. Related Work

To improve the performance of key establishment, Du et

al. [] and Yu and Guan (YG scheme) []developeda

scheme using predeployment knowledge, respectively. In

[], the network area is divided into a grid and information

on the associated matrices is stored in the sensors based

on deployment knowledge. In [], the network area is

divided into hexagonal cells. Compared with [], the scheme

achieves a higher connectivity with a much lower memory

requirement and a shorter transmission range. In the two

schemes, all nodes choose their keys from the same key

pool. An attacker can easily obtain a large number of keys

by capturing a small fraction of nodes, which can make SNs

ineective. e addition of new nodes to the network with

keysfromthesamekeypoolwillnothelpbecausethekeys

in the new nodes are already compromised. erefore, for

MSNs, the above two schemes are ineective.

For MSNs, in [], a scheme (ESPK scheme) is proposed

using deployment knowledge, in which a multiphase deploy-

ment model is presented. In the model, the deployment eld

is divided into a grid. Each cell has a deployment point. Nodes

which have the same deployment point form a group. e

number of nodes in a group is .Anditissupposedthat

a new group of nodes are needed to be added to a cell only

when % of nodes in the cell are captured. e model has

the following shortcomings. () To know the number of nodes

in each cell, location information of nodes is needed. ()

If just % of nodes in a cell are captured, there are a few

nodes in the cell that are working in a long time. () e

number of new nodes added to the network is measured

in a group, and the number of nodes in a group is xed,

which will give rise to the number of nodes in the network

with time. On the other hand, the proposed key management

scheme can provide good resilience against node capture by

using disjoint key pools. However, nodes which come from

dierent phases but are deployed in the same cell cannot

establish shared keys. As a result, the local connectivity is low,

and the global connectivity decreases signicantly with time.

So,theproblemofsecureisstillnotsolvedforMSNsusing

deployment knowledge.

3. Deployment Knowledge and Threat Models

3.1. Multiphase Deployment Knowledge Model. As shown in

Figure , a target eld is partitioned into hexagon cells, and

each cell has a deployment point that resides in the center of

the cell. Node distribution follows two-dimensional Gaussian

distributions [] with the deployment point as center.

Nodes which are deployed in the same cell form a group.

And nodes deployed in the cell (,)are denoted by 

(𝑟,𝑐)

.e

number of nodes in 

(𝑟,𝑐)

is . 

(𝑟,𝑐)

is clustered into phases

according to the deployment time. e -phase subgroup of



(𝑟,𝑐)

is denoted by 

𝑖

(𝑟,𝑐)

.Inourscheme,SN

(𝑟,𝑐)

represents

the set of nodes whose deployment point locate in the cell

(,)and that are not captured, and |SN

(𝑟,𝑐)

|≤(several

schemes have been proposed to identify the compromised

sensors in prior studies, such as []). When 

(𝑟,𝑐)

is less than

the threshold 

,weshouldadd-SN

(𝑟,𝑐)

new nodes to the

cell. e 

(𝑟,𝑐)

can be calculated as follows:



(𝑟,𝑐)



(𝑟,𝑐)





()

In a deployment phase, if no new nodes are needed to

be added to a cell, then the number of deployment phase

of the cell remains unchanged. For example, in the second

deployment phase, no new nodes are needed to be added to

the cell (1,1); the number of recent deployment phase of the

cell is  not .

3.2. reat Model. Due to the short time period of the direct

key establishment phase, it is reasonable to believe that only

a limited number of sensor nodes may be compromised by

an attacker [, –]. We further assume that if an attacker

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