CHAPTER 4 SECURED MODEL USING RSA CRT -...

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CHAPTER 4

SECURED MODEL USING RSA – CRT

4.1 Secured Wireless Network using RSA Algorithm

The solution for critical issues due to the inherent limitations of

computational capacity, storage capacity and power usage, security in

Wireless Networks (WN) is focused on this chapter. Packets are dropped or

discarded completely, or selectively forwarded by an anonymous party, the

network is flooded with global suspicious broadcasts are the few kinds of

attacks are countered using multipath and authenticated broadcasts, which has

to be facilitated by the underlying key management architecture.

Key management only makes sure the communicating nodes

possess the necessary keys (Liang et al, 2011), at the same time protecting the

confidentiality, integrity and authenticity of the communicated data. In this

chapter, the analysis of existing methodology of the different security

approaches and various key management schemes available for authenticated

broadcast in the wireless mobile networks indicating their advantages,

drawbacks and weaknesses.

It is difficult to identify the suitable cryptography for WNs because

of its inherent limitations. Most previous schemes available for mobile

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network security have used symmetric cryptography than asymmetric

cryptography as asymmetric keys are used for key generation. In this chapter,

a broader analysis of the well-known security issues in WNs is carried out and

the study of the various asymmetric key or public key algorithms which are

used for key distribution as well as encryption/decryption in ad hoc network

for authenticated message broadcast is taken into account.

Based on the analysis, this chapter further proposed a new method

which improves the performance of an existing RSA algorithm by using

Chinese Remainder Theorem (CRT) in decryption phase which reduces

computation time through Montgomery multiplication. The improved RSA

with CRT algorithm is proposed for efficient key management and

encryption/decryption of broadcast message authentication.

4.2 Introduction to Security Mechanism in Wireless Network

Security mechanisms in WN are developed in view of certain

constraints and are classified into two types. One is security needed for

operations and another is security of information. The objectives of these

securities are, first the network should continue its function even when some

of its components attacked and CIA of information should never be disclosed

respectively. In the second objective the information security can be achieved

with cryptography, the following two facts that influences and make it difficult

in achieving CIA in WNs because

As ad hoc nodes operate unattended, they are potentially accessible

to any malicious user.

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Ad hoc nodes communicate through open medium.

4.2.1 Issues and challenges in WN security

The security in WNs is critical issue due to the inherent hardware

limitations and constraints:

Energy efficiency: The requirement for energy efficiency suggests

that in most cases, computation is favoured over communication, as

communication is three orders of magnitude more expensive than

computation (Wander, 2005). The requirement also suggests that

security should never be overdone. More computationally intensive

algorithms not used to incorporate security due to energy

considerations.

No public-key cryptography: Public-key algorithms remain

prohibitively expensive on mobile nodes in both terms of storage

and energy (Carman et al, 2000). No security schemes should rely

on public-key cryptography. However, it has been shown that

authentication and key exchange protocols using optimized

software implementations of public-key cryptography is very much

viable for smaller networks (Wander, 2005).

Physically tamper able: Since mobile nodes are low-cost hardware

that is not built with tamper-resistance in mind (Chan et al, 2003),

their strength has to lie in their number. Even if a few nodes go

down, the network survives (Yang et al, 2004). The network should

instead be resilient to attacks.

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Multiple layers of defence: Security becomes an important concern

because attacks can occur in different layers of a networking stack.

Naturally, it is evident that a multiple layer of defence is required,

i.e. a separate defence (Yang et al, 2004) for each layer.

4.2.2 Security requirements

Availability: Since the wireless mobile networks are vulnerable to

various attacks, there is a risk of no availability of information. The

following facts will have an impact on the availability of

information.

i. If no energy exists, the data will not be available.

ii. Additional communication consumes more power and results

in conflict or interference.

iii. A single point failure in central scheme (e.g. Sink or

gateway) will greatly affect the availability.

Confidentiality: Confidentiality, integrity and authentication

security services are required to thwart the attacks from adversaries.

These security services are achieved by cryptographic primitives as

the building blocks. Confidentiality means that unauthorized third

parties are not authorized to access the information between two

communicating parties. Ad hoc network should not leak mobile

readings to its neighbours. In many applications, nodes

communicate highly sensitive data, e.g., key distribution; therefore

it is extremely important to build a secure channel in a wireless ad

hoc network.

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Integrity and authenticity: Confidentiality only ensures that the

data are not accessible for reading by the third party, but it does not

guarantee that data is unaltered or unchanged. Integrity means the

message one receives is exactly what was sent and it was unaltered

by unauthorized third parties or damaged during transmission.

Wireless ad hoc networks are more vulnerable to eavesdropping and

message alteration. Measures for protecting integrity are needed to

detect message alteration and to reject the injected message.

Authentication: Authentication ensures that the contents of the

message have not been altered since in ad hoc network an adversary

can easily inject a message. It is essential that each node and base

station should verify the correctness of data and trusted sender.

Authentication for the broadcast message requires stronger trusted

assumptions on the network nodes. SPIN (Perigg et al, 2002) and

LEAP (Zhu and Lui, 2003).

Security Management: Issues like key distribution from base

station to nodes for establishing encryption and routing information

need the secure management.

Data freshness: Data freshness means that the data is recent and

any old data has not been replayed. Data freshness criteria are a

must in case of shared- key cryptography where the key needs to be

refreshed over a period of time. An attacker may replay an old

message to compromise the key.

Quality of service: Since the Wireless Ad hoc networks are having

many limitations, the objective of achieving QoS becomes more

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difficult. Performance and quality in ad hoc networks involve timely

delivery of data to prevent the loss of critical data, accuracy.

Self organization: Due to the ad-hoc nature of WNs it should be

flexible, resilient, adaptive and corrective in regards to security

measures.

4.3 Analysis of Types of Threats and Attacks in WN

Security attacks in ad hoc networks can be broadly classified into

Passive attacks and Active attacks. Passive attacks are in the nature of

eavesdropping on, or monitoring of, transmissions. The motive of the attacker

is to obtain information that is being transmitted. Basically, this thesis mainly

looking at two types of protection: protection from Denial-of-Service (DoS)

attacks, and protection of the secrecy of information.

4.3.1 Physical Layer

DoS attacks on the physical layer are radio jamming. Well-known

countermeasures to radio jamming include adaptive antenna systems, spread

spectrum modulations, error correcting codes and cryptography.

4.3.2 Data Link Layer

The data link layer defines how the data are encoded and decoded,

how errors are detected and corrected, the addressing scheme as well as the

medium access scheme. According to results in link-layer jamming smart

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jammers can take advantage of the data link layer to achieve energy-efficient

jamming. Thus link-layer jamming is more energy efficient for the attackers

as compared to radio-jamming in physical layer. TDMA protocols like LMAC

have better anti-jam properties.

4.3.3 Network Layer

The network layer “provides functional and procedural means to

exchange network service data units between two transport entities over a

network connection depending upon parameters such as latency or energy. It

provides transport entities with independence from routing and switching

considerations.”

Neglect: Packets are dropped or discarded completely, or

selectively forwarded by an anonymous party. This attack is

countered using multipath routing (Ganesan et al, 2002)

Flooding: The network is flooded with global suspicious

broadcasts. This attack is countered using authenticated broadcasts,

which has to be facilitated by the underlying key management

architecture.

Sybil attack/Misdirection/Homing: Some mobile nodes in the

network are misguided into believing that nodes that either are

multiple hops away, or that do not exist at all are their neighbours.

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Wormholes: A considerable amount of the network traffic is

tunnelled from one place in the network to another distant place of

the network, depriving other parts of the network that under normal

circumstances would have received the traffic themselves. This is

called a wormhole attack. This tunnelling or retransmitting of bits

can be done selectively.

Black holes: In flooding based protocols, the attacker listens to

requests for routes then replies to the target nodes that it contains

the high quality or shortest path to the base station. Thus it attracts

a large portion of traffic and acts as a black hole in the network.

This is called a sink hole or black hole attack. This attack can be

facilitated by the wormhole attack.

Looping: Some routes form loops or detours. These attacks are

sophisticated forms of DoS attacks. Among these attacks, This

thesis ignores the last one because this is not a significant value for

the attackers in it - causing loops is not more efficient than just

dropping or discarding packets; causing detours is an inefficient

way of wasting the mobile node‟s energy.

Sybil, wormhole and sinkhole attacks require the attackers to

manipulate packets (Proano and Lazos, 2012). To prevent this, key

management architecture is required. In particular, Sybil attacks can be

countered using random key pre-distribution schemes, to be discussed later.

Against wormhole attacks and hence sinkhole attacks, so far there is no

resource-lean and energy-efficient countermeasure, i.e. with or without key

management, wormholes and sinkhole attacks are still an open issue.

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Table 4.1 Different types of attacks and mode of defence in Network layer

of ad hoc network

Main

Security

Concern

Available Modes of defence Best optional

choice Mode Strength Weakness

Hello-

flooding Nil Nil Nil

Authenticated

Broadcast &

Efficient Key

management

Neglect

/discard Nil Nil Nil

Multipath

routing

Black holes

or sink hole

Key

Management

Schemes

Nil Nil REWARD

algorithm

Sybil

Radio-resource

testing, Random

Key pre-

distribution

Nil Nil

Key

management

Architecture

Wormholes TIK

Implements

Temporal

leashes

Requires

synchronize on

computational

expensive

TIK based upon

symmetric

cryptography

In general, the above strategy is not effective against wormhole and

sinkhole attacks, but the data link layer is easier to DoS attack than the

network layer, so if the security of the network is somewhat relaxed, then data

link layer should at least be made as resistant to DoS attacks as possible. In

ID-based routing, it is recommended to use (Hu and Perrig, 2004), an

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improved version of Ariadne (Buttyan and Hubaux , 2003), because it is

probably more secure against an attacker with a single compromised key and a

single compromised node.

However, it does not support multipath routing. Furthermore, the

corresponding key management architecture has to support node-specific key

pre-distribution (i.e. every node has to share one key with every other node in

the network), in addition to authenticate broadcasts. These two issues, 1)

Multipath routing support and 2) Node specific key pre-distribution support

should be well analysed and a new efficient key management scheme to be

proposed.

Table 3.1 summarizes the different types of attacks in Network

layer and the mode of defence availability with their strength and weakness.

4.4. Analysis of Key Management Schemes

Key management is the process in which cryptographic keys are

generated, stored, protected, transferred, loaded, used, and destroyed. There

are four principal concerns in a key management framework are given below

and the major advantages and drawbacks of different key distribution and

management schemes are summarized in Table 3.2.

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Table 4.2 Comparison of Various key management schemes in WNs

Key

Management

schemes

Advantage Drawback

Network Wide

Shared Key

A symmetric key is used by

every node.

An adversary can extract by

capturing a single node.

Master Key and

Link Keys

Every node is preconfigured

and loaded with a master key

and a set of link keys for each

communication link to

others.

Resilient to a single node

compromise attack, addition of new

node is not possible and the link

keys cannot be securely transmitted

over the network.

Public Key

Cryptography

Very good solution for key

management and distribution

in traditional WN.

The memory, energy and

processing constraints rule out the

possibility for using this scheme.

Preconfigured

Symmetric Keys

Every node in the network is

preconfigured with a set of

link keys

This is not scalable as every node

has to store n(n-1)/2 keys, where n

is the number of nodes. Needs large

space to store keys.

One way key

chain

Very efficient to verify since

it can compute one way

function only in milliseconds.

It would require a long time to

generate or verify the traditional

signature up to minutes.

Bootstrapping

Keys

Allows an on-demand key

generation for a secure

connection established

between the nodes.

Suffers from a single point of

failure as base station has to

maintain a database for the link

keys.

Random pre

distributed keys

Allows a node to be mobile

and countering Sybil attacks.

Yet to establish secure connections

with neighbours, although with

reduced connectivity.

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Key deployment/pre-distribution: Method to find the number of

keys and methods required to distribute the keys before the nodes

are deployed.

Key Establishment: Establish the secure session between any pair

or group of mobile nodes or between node to cluster head and in

turn to base station.

Member/ Node Addition: Method for a node to be added to the

network such that it be able to establish secure sessions with

existing nodes in the network, while not being able to decipher past

traffic in the network.

Member / Node Deletion: Method for a node to be evicted from

the network such that it will not again be able to establish secure

sessions with any of the existing nodes in the network, and not be

able to decipher future traffic in the network.

4.4.1 Key Establishment

Establishment of keys in ad hoc networks can also be realized with

protocols where the nodes set up a shared secret key after deployment, either

through key transport or key agreement. The advantage of key agreement over

key transport is that no entity can predetermine the resulting key as it depends

on the input of all participants.

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There are three types of general key agreement schemes:

i. Trusted-server schemes,

ii. Self-enforcing scheme, and

iii. Key pre-distribution scheme.

First the Trusted server scheme depends on a trusted server for key

agreement between nodes (e.g. Kerberos) is not suited for WNs because there

is no trusted infrastructure in WNs. Second, Self-enforcing scheme depends on

asymmetric cryptography using public key algorithms for key agreement

(Diffie-Hellman, RSA) which needs the high computation capability and

energy which limits its use. The third type is key pre-distribution scheme

where all keys are pre distributed to all mobile nodes prior to deployment.

In our proposed method takes the advantages of the public key

algorithm scheme and third key pre distribution scheme are combined together

to achieve an efficient key management scheme which will reduce the energy

consumption and communication overheads even with limited resources.

4.4.2 Various Keys used in ad hoc network

There are various communication patterns in ad hoc networks. The

following types of keys are used in WNs:

Network key: A key that is shared by all nodes in the network and

is used to encrypt and decrypt global messages. It cannot be used

for message authentication.

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Cluster keys: A key shared by a cluster head node and its

neighbour nodes to encrypt and decrypt local broadcast messages.

It cannot be used for message authentication

Link keys: A key shared by two neighbour nodes (two mobile

nodes or mobile and base station) it provides protection for uni-cast

messages between neighbouring nodes. They can be used for

encryption, message authentication, and integrity protection. They

can also be used to set up other keys between neighbouring nodes (

e.g. Cluster keys)

Node keys: A key that is shared by the mobile node and the base

station. It is used to protect unicast messages exchanged between

the mobile node base stations that do not need in-networking

processing.

4.5 Proposed RSA-CRT Algorithm

It is difficult to identify the suitable cryptography for WNs because

of its inherent limitations in terms of energy, computational power and storage

capacity. Most previous schemes proposed for WNs security have used

symmetric cryptography (DES, AES, RC4) than asymmetric cryptography

(RSA, ELGAMAL, ECC) as asymmetric keys are used for key generation.

Table 4.3 is summarizes the advantages and disadvantages of a

symmetric over symmetric keys. In this thesis, an effort made to analysis

various asymmetric key algorithms ELGAMAL, RSA (Rivest Shamir

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Adelman), Public Key Encryption (PKE), Public Key Cryptography (PKC),

Elliptic Curve Cryptography (ECC) which are used for key distribution as well

as encryption/decryption in ad hoc network for authenticated message

broadcast.

The analysis shows that RSA is better than ELGAMAL and PKE.

But comparing ECC the effort needed for RSA is rather too much and so ECC

is better than RSA for security in WNs. This thesis proposed a method to

enhance and improve the performance of RSA by applying Chinese

Remainder Theorem (CRT) in the decryption phase of RSA. This concept of

applying CRT in the decryption phase of RSA is utilized in Hardware fault

attacks and shows better performance.

Table 4.3 Comparison of symmetric and asymmetric keys

Symmetric Asymmetric

Single key approach WN need to store n-1

keys in mobile node for network size n.

Complicated one way key chain

Two key approach one public, one private

key. Also reduced key storage.

Large computations required more energy. Less computation, so less energy

Need key distribution. No need for n-1 key pre distribution. Since

Secrete key is private, inverse calculation

is not possible, so more secure.

Fixed key length. The variable key length provides data CIA,

and supports group key management

Complicated, needs key sharing No pairwise key sharing, More flexible and

simple interface suitable for WN

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This concept has been tested in hardware like CPU, RAM, EPROM,

Smart card processors fault attacks and shows improvement in speed and

reduced computational time and space for the RSA cryptography algorithm.

The same concept of applying CRT in the decryption phase of RSA algorithm

used for message authentication in WN will give advantages over the methods

studied (ELGAMAL, RSA, PKE) with respect to energy, computation time,

storage space, speed of processing in turn reduces the communication

overheads.

RSA operations are modular exponentiations of large integers with

a typical size of 512 to 2048 bits. RSA encryption, generates a cipher text C

from a message M based on a modular exponentiation using equation 4.1 and

Decryption regenerates the message by computing using equation 4.2

C = Me mod n (4.1)

M = Cd

mod n (4.2)

Among the several techniques that are used to accelerate RSA [Ko

et al, 1994]. In this thesis, specifically focused on those applicable under the

constraints of mobile nodes.

The RSA private-key operations, namely decryption and signature

generation, can be accelerated using the Chinese Remainder Theorem (CRT).

RSA chooses the modulus n as the product of two primes p and q, where p and

q are on the order of √n (e.g. for a 1024-bit n, p and q are on average 512 bits

long).

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Using the CRT, a modular exponentiation for decryption is using

equation 4.3 can be decomposed into two modular exponentiations are

showing in the equations 4.4 and 4.5

M = Cd

mod n (4.3)

M1 = C1d1

modp (4.4)

And M2 = C2d2

mod q, (4.5)

The message (M) in the existing RSA is one word in the length of

actual message; it is divided in the proposed method as M1 and M2 in the

word length of half of the actual message. In order to test the performance, the

proposed method further divides the M into four pattern of each M/4 size, i.e.

M1 to M4 and then into eight pattern of each M/8 size, i.e. M1 to M8, the

result of the various proposed key pattern and the subsequence performance is

represented in the table 3.4 to 3.12.

In which, when the number of sub-division is increased then there

are many advantages like better storage complexity and optimal energy

efficiency, also there are few pit-falls like time consumption and key

management. In order to optimize better performance in all aspects like

storage complexity, energy consumption, time complexity, and key

management, a trade off condition is required. Therefore, the number of sub-

division of M is fixed as 2, of size M/2 which is [log2(n)]/2; modular

multiplications can be computed in roughly 1/4 of the time as m-bit modular

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multiplications. Thus the CRT reduces computation time through Montgomery

multiplication by nearly 3/4 resulting in up to a 4x speedup.

4.6 Result and Performance Analysis

The proposed RSA-CRT is implemented in the network simulator

(NS2), and the performance of proposed algorithm is compared with existing

algorithm. The configuration of internal mobile and data sheet of mobile node

which used in our simulation environment are given here under.

The orientation range of the internal mobile is 360°; accelerometer

range is ± 5; A/D resolution is 16bits; orientation accuracy is ± 0.5°in static

mode and ± 2.0° in dynamic mode. The output modes are acceleration, angular

rate, magnetic field, Euler angles and clock info. The mobile node has

standard (USB and RS232) interface and the supply voltage are 16 to 32V.

The weight of the mobile is 23 gram which will operate in the -40°C to +65°

C.

The result of performance comparison based on storage space

requirement, energy consumption and time consumption are listed in the table

4.4, 4.5 and 4.6. The performance of proposed algorithm and the comparison

with existing algorithm are also shown in figure 4.3 to 4.6. In table 4.4, the

storage space requirements of existing and proposed methodologies are

shown.

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The ELGAMAL is using large control packets whereas the PKC is

using lesser control packets. To improve the authentication, RSA is better than

ELGAMAL and PKC. But the control packet size is higher than PKC. The

proposed methodology is using RSA for encryption and CRT for decryption.

Therefore the size of the control packet and number of key requirement are

reduced in the proposed RSA-CRT.

Table 4.4 Storage Space Required (in MB) in ‘M/2’ pattern

No of Nodes ELGAMAL RSA PKC Proposed

20 0.30 0.20 0.10 0.15

40 0.39 0.26 0.13 0.20

60 0.51 0.34 0.17 0.25

80 0.63 0.42 0.21 0.32

100 0.79 0.53 0.26 0.40

120 0.99 0.66 0.33 0.50

140 1.19 0.79 0.40 0.59

160 1.43 0.95 0.48 0.71

180 1.71 1.14 0.57 0.86

200 1.88 1.25 0.63 0.94

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Table 4.5 Time Consumption (in ms) in ‘M/2’ pattern

The scalability of the proposed algorithm also proved using

experimental result which is shown in the table 4.5; in all existing methods,

the time consumption of the concern method is increased much more when

number of nodes incremented, whereas in the proposed system it is less than a

minutes.

If the time consumption of the algorithm increases more than a

second, then it may be treated as data lost or sleep mode. Therefore in the

ELGAMAL, more than 200nodes is not wise architecture; in the PKC, more

than 890nodes is not wise architecture; in the RSA, more than 1200nodes is

not wise architecture; but in the proposed method, more than 2000 nodes is

supported without any loss.


200 1120 273.8 412.3 102.7

400 1321.60 350.46 527.74 126.32

600 1559.49 448.59 675.51 155.37

800 1840.20 574.20 864.66 191.11

1000 2355.45 734.98 1106.76 235.07

1200 3014.98 940.77 1416.65 289.13

1400 3859.17 1204.19 1813.31 355.63

1600 5132.70 1541.36 2321.04 437.43

1800 6826.49 1972.94 2970.93 538.04

2000 9079.23 2525.36 3802.80 661.78

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Table 4.6 Time Consumption for Key Exchange in client and server side

(in bits) in ‘M/2’ pattern

Key

Size (in

bits)

Time Consumption for Key

Exchange in Server

Time Consumption for Key Exchange

in Client

ELGAMAL RSA PKC Proposed ELGAMAL RSA PKC Proposed

160 3 3 4 3 1.32 1.23 1.78 1.11

256 9 7 11 8 4.80 4.30 5.20 4.06

512 17 16 18 15 8.28 7.37 8.62 7.01

1024 26 22 28 19 11.76 10.44 12.04 9.96

2048 161 166 178 122 15.24 13.51 15.46 12.91



20 0.24 0.16 0.08 0.12

40 0.31 0.21 0.10 0.16

60 0.40 0.27 0.13 0.20

80 0.50 0.33 0.17 0.25

100 0.62 0.42 0.21 0.32

120 0.78 0.52 0.26 0.39

140 0.94 0.62 0.32 0.47

160 1.13 0.75 0.38 0.56

180 1.35 0.90 0.45 0.68

200 1.48 0.99 0.50 0.74

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200 1251 306 460 115

400 1476 391 589 141

600 1742 501 754 174

800 2055 641 966 213

1000 2631 821 1236 263

1200 3367 1051 1582 323

1400 4310 1345 2025 397

1600 5733 1722 2592 489

1800 7624 2204 3318 601

2000 10141 2821 4247 739


20 0.23 0.15 0.08 0.12

40 0.30 0.20 0.10 0.15

60 0.39 0.26 0.13 0.19

80 0.48 0.32 0.16 0.25

100 0.61 0.41 0.20 0.31

120 0.76 0.51 0.25 0.38

140 0.91 0.61 0.31 0.45

160 1.10 0.73 0.37 0.55

180 1.31 0.88 0.44 0.66

200 1.45 0.96 0.48 0.72

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Figure 4.3. Comparison of Storage Space Requirement between

(ELGAMAL, RSA, PKC) vs Proposed System


200 1397 342 514 128

400 1649 437 658 158

600 1945 560 843 194

800 2296 716 1079 238

1000 2938 917 1381 293

1200 3761 1174 1767 361

1400 4814 1502 2262 444

1600 6403 1923 2895 546

1800 8516 2461 3706 671

2000 11326 3150 4744 826

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Figure 4.4. Comparison of Energy Consumption between

(ELGAMAL, RSA, PKC) vs Proposed System

Figure 4.5 Comparison of Time Consumption for key exchange in

server side between (ELGAMAL, RSA, PKC) vs Proposed System

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Figure 4.6 Comparison of Time Consumption for key exchange in client

side between (ELGAMAL, RSA, PKC) vs Proposed System in bits

Figure 4.7 Storage Requirement of Proposed System with exponential

trend line in MB

4.7 Conclusion

WN security is a very important issue motivated towards ensuring

security under strict constraints. While analyzing the various attacks in the

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network layer of WNs there are two issues multi path routing support and

node specific key pre-distribution support is taken in consideration in this

thesis. These are the two possible countermeasures identified for the attacks

like Neglect, Hallo-flooding, Sybil attack in the network layer of WNs and a

new key management scheme need to be implemented.

In this view, this thesis proposed a new, efficient key management

scheme RSA-CRT algorithm to support both multi path and node specific key

pre-distribution for authentication of message broadcast on Wireless Networks

(WNs). The proposed method takes the advantages of the self-enforcing

scheme ie., public key algorithm and key pre distribution scheme and are

combined together to further improve the key management scheme which will

reduce the energy consumption and communication overheads even with

limited resources than a popular key management scheme for WNs.

Further, the proposed algorithm RSA-CRT enhances the

performance of RSA, which can be used for the encryption (RSA) and

decryption (CRT) for authenticated message broadcast on wireless ad hoc

networks along with key pre distribution.

The simulated results and the output graphs indicate that our

proposed RSA-CRT algorithm compared with the existing algorithms shows

better performance, scalability and reduced communications overheads.

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