perfomance analysis of polynomial triple key pre ... assistant professor, rvs college of engineering...

SSRG International Journal of Electronics and Communication Engineering - (ICET-2017) - Special Issue - March 2017

ISSN : 2348 - 8549 www.internationaljournalssrg.org Page 92

Perfomance Analysis of Polynomial Triple Key Pre-Distribution Scheme for Secured Communication in

Wireless Mesh Networks Chitralekha.T, Assistant Professor, RVS College of Engineering and Technology, Coimbatore

Ramamoorthy.P, Professor, Adithya Institute of Technology, Coimbatore

ABSTRACT: In recent works Wireless Mesh Networks (WMN) suggest capable communication scenarios at the same time it provide secure information when compared to wireless systems. In WMN, security in information sharing is performed via the creation of the group which is collection of nodes. To support such a type of secure communication between mobile nodes, multicast routing is used. So , there is a necessitate to design secure and reliable multicast routing schema for WMNs toward guarantee enhanced packet delivery ratio (PDR), lower delays and high security.The Polynomial Triple Key Pre-Distribution Scheme(PTKPS) is designed by using the well-known system of threshold secret sharing, and secure alongside a collusion of up to an assured number of nodes. PTKPS key generation methods allow each pair of group member to create a pair wise key without disturbing group controller and also reduces the communication cost for the group controller. Simulations results are carryout to examine the system performance. INDEX TERMS: Wireless Mesh Network (WMN),Security, Pairwise keys, Polynomial-Based Key Management (PBKM), Polynomial Triple Key Pre-distribution Scheme (PTKPS),Group communication

1. INTRODUCTION

Wireless Mesh Network (WMNs) environment faces many types of attacks in their communication. The WMNs security is frequently forecasted on the accessibility of proficient key management methods. Though the standard features of key management is: (1) it has lack of a centralized authority, (2) dynamic scenery of WMNs, signify foremost difficulties to provided that secure, effectual and competent key management. The issue in WMNs secure routing [1] is that, cryptographic keys require to be founded prior to communication between nodes. The solution of above issue is standard key exchange solutions for example Station-to-Station protocol, but is not suitable as: (1) they need the nodes to interrelate and (2) they depend on a few form of a Public Key Infrastructure (PKI) and which is not frequently available in WMN’s environment. In WMN the solution is permits nodes to establish pair wise keys for without the need of a PKI and without communicating. In Matrix Threshold Key Pre-distribution (MTKP) the results are based on two well-known techniques such as Blom's key pre-distribution and threshold secret sharing. Then the Polynomial Threshold Key Pre-distribution (PTKP) is using a polynomial for

employs threshold secret sharing. In both MTKP and PTKP, first a node joins in WMN and getting a secret token from t (security parameter) various nodes.

In this paper, PTKPS (Polynomial Triple Key pre-distribution Scheme), for WMNs is proposed. PTKPS scheme consists of following phases such as: 1) Mesh formation through the Route Request (RR) packets and Route Reply (RP) packets and 2) for selecting SFNs to finding steady routes between source to destination by using link stability metric and 3) mesh preservation and handling link failures. In PTKPS, the group members obtain spins acting as group coordinator to compute and allocate middle key materials to group members. The group key is locally computed by every group members in a dispersed manner. For secure communication in WMN first distinct the following terms, that is used in expanding Polynomial Triple Key pre-distribution Scheme.

NG is the Node Group and is the group of Mobile Station in a local WMN having the similar polynomial distributors which obtains its keying matter.

AHN is an ad hoc node in the Mobile Station which belongs to .

Here Base Station(BS) is the Polynomial distributor (PD) that acts as a polynomial supplier to an .PD will be called founder PD when it is involved in process of generation of key in the beginning.

While generating of key, the trusted authority is PD for Mobile Stations(MS).

Both PD and MSs together gives the outcome about the key (i.e., each MS should have its own the polynomial) which should be passed to their own AHNs particularly.

The rest of this paper is structured as follows. Section II of this paper discusses some of the existing group key management techniques. Section III describes proposed method of polynomial triple key pre distribution based simple and efficient group key management protocol for WMNs. Section IV explains the performance evaluation of the proposed approach and section V concludes the paper with fewer discussions.

2. RELATED WORK To achieve the fault tolerances in WMN, two multicast

tree are constructed for improving the effectiveness and preserves it in a parallel fashion. In Wu.B&Fernandez et



al(2007).proposed Secure and Efficient Key Management (SEKM) model and its multicast tree are classified as a blue tree and a red tree. Then coordinator only maintains the multicast connection. The coordinator is grouping the all member’s computation and allocation of intermediates keying materials by use of original tree links. In WMN each group member i.e. mobile node have the common group key, and these group keys participates in a share of a final common group key and it is updated sporadically.

In Boneh et al(2004) proposed Group signatures are provide secrecy for signers. Here the group of any member can sign the messages but the ensuing signature maintains the identity of the signer secret. Wang et al. (2007) proposed a key management for secure group communication in WMNs. For secure group communications in WMNs, the key management exemplifies a hierarchical key management scheme (HKMS). For the security reason, in this scheme of packet is encrypted by twice.

Kong et al., (2006) proposed a distributed Multicast Group Security Architecture for Mobile Ad Hoc Networks. In this method the group key management distributed to distributed mobile nodes. A cluster head is dynamically selected in each k-hop neighborhood. In first phase, presumes that there are definite candidate Group Controller Key Server (GCKS) nodes.

Huihua Zhou et al.(2011) proposed the two-layered WMNs model and explained the group key establishment scheme. In this method, the nodes are divided in the group and the groups are divided into two parties such as cell group and control group. The cell group is consisting of group members and a centralized key establishment is employed.

Yang et al.(2012) proposed an Identity Based Broadcast Encryption (IBBE) methodology of communication efficient group key distribution scheme. To establish a group key from this scheme no message exchange is required. Through the broadcaster the group members’ identities are known. The high performance of this scheme is that communication overhead ruins unchanged as group size increases. Bilinear pairing computation is required for the group member to attain his/her session key.

3. BUILDING BLOCKS AND PROPOSED POLYNOMIAL BASED TRIPLE KEY SCHEME

In recent work, Wang et al (2008) developed a polynomial-based inter-group key sharing schema to perform group communication between users. In this schema make use of a group controller to allocate personal key shares designed for inter-group communication. As shown in Figure 1, an l-degree polynomial is created through the controller in is second-hand to distribute a secret group key to and members of be able to share and exchanges data between users via secret key.

Piao et al. (2013) developed an advanced version of security schema based on such that each member is able to create by her/himself. They also develop a polynomial F(x) for intra-group key distribution such with the purpose of all group members is able to proficiently recover the intra-group key from the broadcast message sent through the controller.One of the most important difficulties is that this scheme might not prevent a group member to attain other members’ secret keys shared through the controller. To solve this problem in this work proposed a Polynomial Triple Key pre-distribution Scheme, namely PTKPS for secure communication in WMN.

Figure 1: An example of Wang et al.’s inter-group key sharing: a member S in G1 sends message to all of

members in both G2 and G3.

The notation used in the rest of the paper is summarized as follows :

size of the network nodes network identity

: the k-th group : the intra-group key for members of : Pre-distributed secret key shared among the group

controller and a member s in the equivalent group the polynomial function in a finite field

second-hand for deriving intra-group key , where is a large prime Let be a finite field.

For example consider a polynomial symmetric key sharing system is employed through a central server. At initial stage of the work the central server chooses a polynomial function and keeps it safely . The selected polynomial function assure the property

. The polynomial is able to be estimate through , where is the individuality of the node. Instead of sharing the original polynomial value, the authorized server strongly broadcast the towards



the equivalent node consequently with the intention of node has no information about of the original polynomial. For instance, node having a polynomial key and node j having a polynomial key be able to determine

and , correspondingly. Let P(x, y) be a symmetric polynomial of degree c with coefficients in GF(q).

So, P(x, y) = P(y, x) Node receives the polynomial Node receives the polynomial Common key between i and j is For example consider , q=7, coefficients in Z7, P(x, y)=x2+y2+5xy, Let there be 7

nodes.

P(x,2) = x2+4+10x

n2 = x2+10x+4

p(x,6) = x2+36+36x

n6 = x2+36x+36

For instance, n2 and n6 wishing to communicate securely, first they calculate the common key n2(6) = x2+10x+4

= 36+60+4

= 100 mod 7 = 2

n6(2) = x2+36x+36

= 4+72+36

=100 mod 7 = 2

In other words, it promises the grouping key confidentiality. The group member is able to simply securely communicate with the group controller inter group communication only. Alternatively, it might be numerous local WMNs in the region of adjacent group controller. Consequently, the group key creation needs to be a decentralized procedure, which involves each and every one group controller with the purpose of group member in a WMN are attached, rather than a single group controller. 3.1. Multicast mesh creation

Multicast mesh formation consists of two phases namely a request stage and a reply stage. Request stages call up a route discovery procedure to discover routes toward the multicast group. Diverse routes to the multicast group are setup throughout the reply phase. There are two types of nodes such as group members and non-group members. Group members comprise each and every one multicast sources, receivers and that of non-group members comprise in-between nodes to help to generate multicast

routes beginning source to receivers. Non-group members help out in forwarding the data packets. In the following work we describe the procedure of request phase, reply phase with the intention of help out in creating multicast mesh. 1) Request Phase: A base station node discovers the multicast routes toward its receivers through the use of RR packets. Several numbers of steps are carryout during this process which is specified as follows

1) Base station node arranges a RR packet through position the following information: IP address, source address, destination address, set RR =1, preceding node address as its address, communication power. 2) Transmit RR packet in the direction of neighbors. 3) A node receiving RR packet determination abandons it if it is previously received. 4) If RR packet is not a reproduction, revise the Mesh Routing Information (MRI) and connection constancy database such as route used for multicast address / source address, if obtainable and the sequence number of RR packet is larger than the MRI sequence number then modernize the next hop designed for multicast address / source address as earlier node address through innovative sequence number. 5) Rebroadcast the RR packet to its neighbors. 6) Repeat the steps 3 to 5 until the destination node is reached. 7) If destination nodes are not reached inside certain hops, send RE packet to source.

2) Reply Phase: Multicast receiver begins the reply phase. In reply phase, RP packet is created on a multicast receiver following getting a RR packet. During this phase the following steps is carryout. 1) Receiver arrange RP packet through situate the subsequent information in the packet: destination address, source address, formulate RR=0, increase sequence number, modify preceding node address as next hop address. 2) Send RP packet towards its neighbor’s equivalent to grouping id/source address in MRI. 3) The node receiving RP packet evaluate sequence number and next hop address corresponding to group id / destination address with the respective values in MRI, if presented 4) If series number of the arrived RP packet is larger than the series number in MRI, than alter the next hop in MRI and then append the route for destination address through next hop with RP packet has arrived. 5) Keep informed the link stability database and constancy feature in MRI. 6) If next hop address in RP packet equivalent through node address subsequently position FW flag as 01 representing it as individual of the forwarding nodes. 7) Modernize the preceding node address in RP packet toward the equivalent next hop address for group id/ source address 8) Send RP packet toward its neighbors equivalent to group id/foundation address in MRI 9) Perform steps 3 to 8 until source is reached.

A forwarding node ensure for higher value of constancy factor in its MRI used for next hops equivalent to group id / destination address. Forwarding



Node choose one of the next hops as SFN and selected SFN FW flag determination be position to 10 in its MRIC.

3.2. PROPOSED POLYNOMIAL BASED TRIPLE KEY SCHEME

In the initial stage of the key creation, make use of a triple key scheme for group-based polynomial distribution among the Polynomial Distributors (PDs). Each of the nodes is a PD of a Node Group and each node Group in WMN is set to An ad hoc node (AHN). Localized WMN includes of group of nodes related through multiple PDs concerned in group based schema. In this work indicate a participating group of nodes (AHNs) through and the polynomial distributor of through where is the number of PDs. In a group through n members, presume with the intention of each member have pre-shared a secret key through the group controller all the way through a protected channel. If the group controller desires to allocate the intra-group key to each and every one member for a secure group communication, the controller has to carry out the following procedures. At this stage, every one selects a function with three variables x, y, and z, and

. The variables and symbolize the group of members and x specifies the variables connected among PDs. The greatest degree of this polynomial is ‘t’ in every one variable. Every independently formed a t-degree symmetric polynomial as,

(1)

where each coefficient is indiscriminately chosen from a finite field , and is a large prime number. The random chosen of make sure coefficients to exist self-determining, not including some association among them. After selection of the polynomial sends to . Each now find the polynomial as follows

(2)

In the above polynomial distribution the sends through polynomial after the evaluation of

secret key between each PD identifier k. This makes sure that each PD has no information regarding the original polynomial and the polynomial related with others. Earlier than participating in the k-th group every nodes in the AHN be supposed to have strongly registered through the group controller through subsequent a typical registration

procedure. During the process of registration, the group members and group controller equally validate each other. During the process of registration, the group controller creates a shared key such as used for group members node . This shared key allows exchange of secure information between the group controller and the group members. When a calculates from Equation (2), it additional it evaluates of every of its group member

as

(3) is the common key, be the individual node key.

From this encrypted message is computed as , be the message. This key is

sended via to . The transmitted keying is created from polynomial coefficients following the assessment of AHN identifier. For example instead of sharing the original polynomial key value shares a key value of group members a, which is the . Consequently, every group member (i.e., ) might not be familiar with the polynomial in the PD . Beginning Eq. (3), it is well-known with the purpose of the polynomial function broadcasted to AHN is symmetric key function. Because the variables include be alternate through the identifier of the group member. Appropriate to individuality of the group member identifier, each group member might not contain the information of the polynomial of further group members. The communication among the PD and the

is protected through using their shared key . The PD sends each MS the ID-related polynomial consequently with the intention of every group member be able to calculate the pairwise key through some other group member in the localized WMN. In this work secure key is generated using the triple key schema. For example consider

Let q=7, coefficients in Z7 p(x,y,z) = x2+y2+z2+4xy+4yz+4zx+x+y+z+1 For instance, First nodes N1, N2 and N3 can calculate their individual key then calculate common triple key K123 Individual key generation Node N1: X=3, Y=3 N1 : p(x,y,1) =x2+y2+4xy+5x+5y+3 =32+32+4(3)(3)+5(3)+5(3)+3 =9+9+36+15+15+3 =87 Mod 7 N1 =3 Common key generation algorithm 1 Input: k>0, P=(x,y) , (x,y) -> Base station Location Output: Ck If k=0 or x=0 then output(0,0) Set k = (kl-1,kl-2,…,k0)2 Set x1=x, x2=x2+b/x2 For (i = l-2 to 0)



Set t=x1/(x1+x2) If ki=1 x1=x+t2+t, x2= +b/ Else x1= +b/ , x2=x+t2+t r1=x1+x, r2=x2+x y1=r1(r1r2+x2+y)/x+y Return Ck=(x1,y1) In order to carry out pair wise key generation procedure among group members in the equivalent group the node

basically reserve the ID of the other node used for and the ID of the other node’s PD used for y. For example consider that there are two PDs through IDs and j and two group members related through these group controller by IDs a and b. Thus, a receives the subsequent polynomial coefficients and build the polynomial: (4)

(5)

In a group through n members, presume that all members have pre-shared a secret key through the group controller throughout a protected channel by above mentioned process. If the group controller desires towards distribute the intra-group key to each and every one members designed for a secure group communication, the group controller needs to perform the above mentioned procedures.

4. RESULTS AND DISCUSSION

In the recent work the security of the group configuration method depends exclusively on the pairwise key used toward encrypt the group formation messages, focus on the examination of proposed PTKPS key distribution scheme with triple keys. The security strength of the pairwise keys principally relies upon the inherent security of PTKPS key allocation system. In the development of group-based polynomial connections amongst PDs, make use of a “triple -secure” polynomial for each PD. Table 1 demonstrates the conditions required the security analysis of PTKPS scheme for successful attack detection. Table 1 demonstrates that the is improved and might improve the robustness of the security key. The maximal be able to be the maximum number of PDs. If the is higher than the number of PDs, that improves the security of the schema for all group members. Subsequently, judge a brute force attack with the purpose of

unknowns in the polynomial Consequently, to carry out a bruteforce attack, each and every one these values include to be guessed. Consider that field of size of the polynomial coefficients is , the attack complexity is .

Table 1: Security analysis of PTKPS scheme with the ‘entity type’ column representing colluding entities

Entity type Compromise conditions

Compromised polynomial

Same grou

p m PDs - m AHNs - m AHNs Yes a PDs and b AHNs

No

The proposed decentralized PTKPS key distribution scheme have two major advantages in terms of effectiveness: (i) Each and every one the computation used for the group member is linear combination; (ii) it has no communication among the group member in the key creation. The major objective of this examination is to estimate the proposed PTKPS key distribution scheme in terms of message and latency overhead.. The experimentation work of proposed PTKPS key distribution scheme is simulated in NS-2. The usage nodes during experimentation are varied from 30 to 70 and node group size is varied from 0 to 20.The experimentation work is carried out under 1000m × 1000m simulation area through a communication radius of each node as 200 m. Predetermined the speed of the nodes at 10 m/s.

0200400600800

1000120014001600

0 5 10 15 20

Num

ber o

f rou

ting

pack

ets

Group size

PTKPS MPBKMPBKM

Figure 2. Routing overhead in key exchange

Figure.2 shows the results of Routing overhead with different NG sizes during the key exchange process. The experimentation work is carried out to NG size of 5 with 70 numbers of nodes; the number of routing messages is extremely elevated The results of the proposed PTKPS are compared with Polynomial-based key management (PBKM), modified PBKM (MPBKM) [20] schemas.



0

5

10

15

20

25

30

0 2 4 6 8 10 12 14Late

ncy

in o

btai

ning

all

shar

es

(Sec

)

Thershold values

PBKM MPBKM PTKPS

Figure 3. Average latency during the initial key exchange process

In Figure. 3 , if the results of network latency are increases if the threshold values (t) become increases. On the other hand, the rise in the network latency values is considerable designed for a larger network.

Packet Delivery Ratio (PDR)

This is the ratio of total number of packets effectively received from source to destination node all the way through the simulation.

PDR = no. of packets effectively received no. of sent packets If the value of PDR is high it designates with the intention of a large amount of the packets is being distributed to the higher layers and is a good quality indicator of the protocol performance.

020406080

100120

0 5 10 15 20

Pack

et d

eliv

ery r

atio

(PDR

)

Group size

PBKM MPBKM PTKPS

Figure 4. PDR results as a function of group size

Figure 4 demonstrates that the increasing number of Group size, the PDR of proposed PTKPS schema is higher and relatively compare to existing schemas such as PBKM and MPBKM. Normalized Routing Load (NRL)

NRL is calculated as the ratio between the numbers of routing packets transmitted to the number of data packets essentially received.

NRL = no.of routing packets sent number of data packets essentially received.

NRL approximate how well-organized a routing

protocol. Larger NRL demonstrates that higher routing overhead and thus results lower effectiveness of the protocol.

010203040506070

0 5 10 15 20

Nor

mal

ized

Rou

ting

load

(pac

kets)

Group size

PBKM MPBKM PTKPS

Figure 5. NRL results as a function of group size

Figure 5 demonstrates that the NRL of the proposed PTKPS schema is running under DSR protocol, it achieves higher NRL results when compare to existing MPBKM and PBKM schemas. If the number of group size increases that DSR need more routing packets towards preserve unicast connections between group members. For example if the network group size is 5, NRL results of PTKPS, MPBKM and PBKM are 59.8 packets, 52.369 and 0.735 packets respectively.

5. CONCLUSION AND FUTURE WORK

Key management in WMN is a difficult issue regarding the safety of the group communication. In this paper presents a novel Polynomial Triple Key Predistribution Schema (PTKPS) for secure group communication in WMN. This PTKPS scheme, attain the objectives of together perfect forward and backward secrecy. The experimental results of the key distribution schemas are measured in terms of routing overhead, network latency, NRL and PDR, results demonstrates that the proposed PTKPS schema outperforms than existing methods. Extend the PTKPS scheme by employing swarm agents toward perform mesh formation and stable route selection, which be able to enhance the scalability, flexibility in terms of bandwidth restricted routing, delay restricted routing, cost function restricted routing and customization services for multicasting.

REFERENCES

1.Y. Cheng and D. P. Agrawal, “An improved key distribution mechanism for large-scale hierarchical wireless sensor networks,” Ad Hoc Networks, vol. 5, no. 1, pp. 35-48, 2007. 8.M. Eltoweissy, M. Moharram, R. Mukkamala, Dynamic key management in sensor networks, in: IEEE Communications, April 2006



3.Luo Junhai, Ye Danxia, Xue Liu, and Fan Mingyu ”A Survey of Multicast Routing Protocols for Mobile Ad-Hoc Networks”, IEEE Computer Communications Surveys and Tutorials Vol. 11, No. 1, First Quarter 2009, pp. 78-91. 4.Wu, B., Wu, J., Fernandez, E., Ilyas, M. and Magliveras, S., “Secure and Efficient key Management in mobile ad hoc networks”, Network and Computer Applications, Vol. 30, pp. 937-954, 2007. 5.D. Boneh, X. Boyen, and H. Shacham, “Short group signatures,” in Advances in Cryptology–Crypto’04, Lecture Notes in Computer Science, vol. 3152, 2004, pp. 41–55. 6.Nen-Chung Wang, and Shian-Zhang Fang, “A hierarchical key management scheme for secure group communications in mobile ad hoc networks,” Journal of Systems and Software, vol. 80, no. 10, pp. 1667-1677, 2007. 7.H. Zhou, M. Zheng and T. Wang, “A Novel Group Key Scheme for WMNs”, Advanced in control Engineering and Information Science, Procedia Engineering, (2011), pp. 3388-3395 8.Yang, Yang. "A communication efficient group key distribution scheme for WMNs." Network and System Security. Springer Berlin Heidelberg, 2012. 361-372 9.Y. Piao, J. Kim, U. Tariq, and M. Hong, “Polynomial-based key management for secure intra-group and inter-group communication,” Computers and Mathematics with Applications, vol. 65, no. 9, pp. 1300-1309, 2013. 10.Chang, C. C., Harn, L., & Cheng, T. F. (2014). Notes on “Polynomial-based Key Management for Secure Intra- Group and Inter-Group Communication”. International Journal of Network Security, 16(2), 143-148.

perfomance analysis of polynomial triple key pre ... assistant professor, rvs college of engineering...

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