A cluster-based countermeasure against blackhole attacks in MANETs

Abstract

Mobile ad hoc networks (MANETs) become more and more popular and significant in many fields. However, the important applications of MANETs make them very attractive to attackers. The deployment scenarios, the functionality requirements, and the limited capabilities of these types of networks make them vulnerable to a large group of attacks, e.g., blackhole attacks. In this paper, we propose a cluster-based scheme for the purpose of preventing blackhole attacks in MANETs. In our scheme, we firstly present a novel algorithm that employs a powerful analytic hierarchy process (AHP) methodology to elect clusterheads (CHs). Then CHs are required to implement the blackhole attacks prevention scheme to not only detect the existence of blackhole attacks but also identify the blackhole nodes. Simulation results show that our scheme is feasible and efficient in preventing blackhole attacks.

Appendix

Part 1:

Let’s assume the second level criteria factor’s weight. For example, if we consider the criterion S _r is moderately more important than the criterion C _v , we can assign “3” to $a_{S_{r} C_{v}}$. If we consider the criterion S _r is extremely more important than the criterion C _d , we can assign “9” to $a_{S_{r} R_{f}}$. If we consider the criterion C _v is strongly more important than the criterion C _d , we can assign “6” to $a_{C_{d} R_{f}}$. Hence, the A matrix is shown as follows in Eq. (20):

$$\begin{aligned} A =& [ a_{ij} ] \\ =& \left [ \begin{array}{c} S _{r}\\ C_{v}\\ C_{d} \end{array} \right ] \left [ \begin{array}{c@{\quad}c@{\quad}c} S _{r} & C_{v} & C_{d} \end{array} \right ] \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} a_{S_r S_r} & a_{S_r C_v} & a_{S_r C_d}\\ \frac{1}{a_{S_r C_v}} & a_{C_v C_v} & a_{C_v C_d}\\ \frac{1}{a_{S_r C_d}} & \frac{1}{a_{C_v C_d}} & a_{C_d C_d} \end{array} \right ] \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} 1 & a_{S_r C_v} & a_{S_r C_d}\\ \frac{1}{a_{S_r C_v}} & 1 & a_{C v C d}\\ \frac{1}{a_{S_r C_d}} & \frac{1}{a_{C_v C_d}} & 1 \end{array} \right ] \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} 1 & 3 & 9\\ \frac{1}{3} & 1 & 6\\ \frac{1}{9} & \frac{1}{6} & 1 \end{array} \right ] \end{aligned}$$

(20)

By aforementioned Eq. (6), the A matrix can be standardized to a normalized A ^norm, as shown in Eq. (21).

$$\begin{aligned} A^{\mathrm{norm}} =& \left [ \begin{array}{c@{\quad}c@{\quad}c} a_{S_r S_r}^{\mathrm{norm}} & a_{S_r C_v}^{\mathrm{norm}} & a_{S_r C_d}^{\mathrm{norm}}\\ a_{C_v S_r}^{\mathrm{norm}} & a_{C_v C_v}^{\mathrm{norm}} & a_{C_v C_d}^{\mathrm{norm}}\\ a_{C_d S_r}^{\mathrm{norm}} & a_{C_d C_v}^{\mathrm{norm}} & a_{C_d C_d}^{\mathrm{norm}} \end{array} \right ] \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} 0.6923 & 0.7200 & 0.5625\\ 0.2308 & 0.2400 & 0.3750\\ 0.0769 & 0.0400 & 0.0625 \end{array} \right ] \end{aligned}$$

(21)

where $a_{S_{r} C_{v}}^{\mathrm{norm}} = \frac{a_{S_{r} C_{v}}}{a_{S_{r} C_{v}} + a_{C_{v} C_{v}} + \frac{1}{a_{C_{v} C_{d}}}} = \frac{3}{3+1+ \frac{1}{6}} =0.7200$, for instance.

Then by Eq. (7), the weight of each criterion can be calculated.

• The weight of S _r :

  $$\begin{aligned} W_{S_r} =& \frac{a_{S_r S_r}^{\mathrm{norm}} + a_{S_r C_v}^{\mathrm{norm}} + a_{S_r C_d}^{\mathrm{norm}}}{3}\\ =& \frac{ ( 0.6923+0.7200+0.5625 )}{3} =0.6583 \end{aligned}$$

• The weight of C _v :

  $$\begin{aligned} W_{C_v} =& \frac{a_{C_v S_r}^{\mathrm{norm}} + a_{C_v C_v}^{\mathrm{norm}} + a_{C_v C_d}^{\mathrm{norm}}}{3}\\ =& \frac{ ( 0.2308+0.2400+0.3750 )}{3} =0.2819 \end{aligned}$$

• The weight of C _d :

  $$\begin{aligned} W_{C_d} =& \frac{a_{\mathrm{R} \mathrm{f} S_r}^{\mathrm{norm}} + a_{C_d C_v}^{\mathrm{norm}} + a_{C_d C_d}^{\mathrm{norm}}}{3}\\ =& \frac{ ( 0.0769+0.0400+0.0625 )}{3} =0.0598 \end{aligned}$$

Hence, by Eq. (5), the vector of weight of each criterion $W_{i}^{T}$ can be calculated as shown in Eq. (22).

$$\begin{aligned} W_{i}^{T} =& \frac{1}{k} \sum _{j =1}^{k} \biggl( \frac{a_{ij}}{ ( \sum_{i=1}^{\mathrm{k}} a_{ij} )} \biggr) \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} W_{S r} & W_{C v} & W_{C d} \end{array} \right ] \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} 0.6583 & 0.2819 & 0.0598 \end{array} \right ] \end{aligned}$$

(22)

Then we should consider the consistency problem. Hence, the CI should be calculated so as to measure the weight of each criterion above, i.e., $W_{S_{r}}$, $W_{C_{v}}$ and $W_{R_{f}}$, is consistent or not. By Eq. (10), the consistency vector μ _i can be calculated as shown in the following Eq. (23).

$$\begin{aligned} \mu_{i} =& \left [ \begin{array}{c} { ( W_{S_r} \cdot a_{S_r S_r} + W_{C_v} \cdot a_{S_r C_v} + W_{\mathrm{R} \mathrm{f}} \cdot a_{S_r C_d} )} / {W_{S_r}}\\ { ( W_{S_r} \cdot \frac{1}{a_{S_r C_v}} + W_{C_d} \cdot a_{C_v C_v} + W_{\mathrm{R} \mathrm{f}} \cdot a_{C_v C_d} )} / {W_{C_v}}\\ { ( W_{S_r} \cdot \frac{1}{a_{S_r C_d}} + W_{C_v} \cdot \frac{1}{a_{C_v C_d}} + W_{\mathrm{R} \mathrm{f}} \cdot a_{C_d C_d} )} / {W_{\mathrm{R} \mathrm{f}}} \end{array} \right ] \\ =& \left [ \begin{array}{c} { ( 0.6853 \cdot 1+ 0.2819 \cdot 3+ 0.0598 \cdot 9 )} / {0.6853}\\ { ( 0.6853 \cdot \frac{1}{3} + 0.2819 \cdot 1+ 0.0598 \cdot 6 )} / {0.2819}\\ { ( 0.6853 \cdot \frac{1}{9} + 0.2819 \cdot \frac{1}{6} + 0.0598 \cdot 1 )} / {0.0598} \end{array} \right ] \\ =& \left [ \begin{array}{c} 3.1025\\ 3.0512\\ 3.0086 \end{array} \right ] \end{aligned}$$

(23)

Then by Eq. (9), we can calculate the value of λ as shown in the following Eq. (24).

$$ \lambda= \frac{\sum_{i=1}^{n} \mu_{i}}{ n} = \frac{3.1025+3.0512+3.0086}{3} =3.0541 $$

(24)

By Eq. (8), we can calculate the value of CI by the following Eq. (25).

$$ \mathrm{CI}= \frac{\lambda-n}{n-1} = \frac{3.0541-3}{3-1} =0.0270 $$

(25)

From Table 3, we can obtain the RI based on the value of n which is 3. Finally, we can calculate the value of CR. As shown in the following Eq. (26), the CR is smaller than 0.1, so the consistency is acceptable.

$$ \mathrm{CR}= \frac{\mathrm{CI}}{\mathrm{RI}} = \frac{0.0270}{0.58} =0.0466 <0.1 $$

(26)

where RI is equal to 0.58 obtained from the Table 3, since the n is equal to 3.

Part 2:

To make a clear and intuitive explanation, we assume there are only three nodes in the vicinity, i.e., node 1(n ₁), node 2(n ₂), and node 3(n ₃).

First, let’s calculate $A_{S_{r}}$, which is based on the criterion S _r . For example, if we consider node 2’s is relative stability value is slightly larger than node 1, we can assign “1/2” to $a_{n_{1} n_{2}}^{S_{r}}$. If we consider node 3’s is relative stability value is very very strongly larger than node 1, we can assign “1/8” to $a_{n_{1} n_{3}}^{S _{r}}$. If we consider node 3’s is relative stability value is strongly larger than node 2, we can assign “1/5” to $a_{n_{2} n_{3}}^{S _{r}}$. Hence, the $A_{S_{r}}$ matrix is as follows in Eq. (27):

$$ A_{S_r} = \bigl[ a_{ij}^{S _{r}} \bigr] = \left [ \begin{array}{c@{\quad}c@{\quad}c} a_{n_1 n_1}^{S _{r}} & a_{n_1 n_2}^{S _{r}} & a_{n_1 n_3}^{S _{r}}\\ \frac{1}{a_{n_1 n_2}^{S _{r}}} & a_{n_2 n_2}^{S _{r}} & a_{n_2 n_3}^{S _{r}}\\ \frac{1}{a_{n_1 n_3}^{S _{r}}} & \frac{1}{a_{n_2 n_3}^{S _{r}}} & a_{n_3 n_3}^{S _{r}} \end{array} \right ] = \left [ \begin{array}{c@{\quad}c@{\quad}c} 1 & \frac{1}{2} & \frac{1}{8}\\ 2 & 1 & \frac{1}{5}\\ 8 & 5 & 1 \end{array} \right ] $$

(27)

By the similarity assumption, we can obtain $A_{C_{v}}$ and $A_{R_{f}}$, in the following Eqs. (28) and (29).

$$\begin{aligned} &{A_{C_v} = \bigl[ a_{ij}^{C_{v}} \bigr] = \left [ \begin{array}{c@{\quad}c@{\quad}c} 1 & 1 & 6\\ 1 & 1 & 3\\ \frac{1}{6} & \frac{1}{3} & 1 \end{array} \right ]} \end{aligned}$$

(28)

$$\begin{aligned} &{A_{R_f} = \bigl[ a_{ij}^{C_{d}} \bigr] = \left [ \begin{array}{c@{\quad}c@{\quad}c} 1 & \frac{1}{8} & \frac{1}{3}\\ 8 & 1 & 3\\ 3 & \frac{1}{3} & 1 \end{array} \right ]} \end{aligned}$$

(29)

By using the similar process of calculation of $W_{i}^{T}$, we can obtain every node’s weight factor on the corresponding criterion as follows in Eq. (30):

$$\begin{aligned} \propto =& [ \propto_{ij} ] \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} \propto_{n_1}^{S _{r}} & \propto_{n_2}^{S _{r}} & \propto_{n_3}^{S _{r}}\\ \propto_{n_1}^{C_{v}} & \propto_{n_2}^{C_{v}} & \propto_{n_3}^{C_{v}}\\ \propto_{n_1}^{C_{d}} & \propto_{n_2}^{C_{d}} & \propto_{n_3}^{C_{d}} \end{array} \right ] \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} 0.0874 & 0.1622 & 0.7504\\ 0.4967 & 0.3967 & 0.1066\\ 0.082 & 0.6816 & 0.2364 \end{array} \right ] \end{aligned}$$

(30)

where the $\propto_{n_{1}}^{S _{r}}$ stands for if only the criterion S _r is considered, the weight of node 1 is 0.0874.

$$ W_{i} = \sum_{j =1}^{n} w_{j } \cdot \propto_{ij} $$

(31)

The global weight of a mobile node is achieved through multiplying its local weight by its corresponding parent weights. Hence, finally by Eq. (31), we can obtain the global weight vector as follows in Eq. (32):

$$\begin{aligned} W_{i} =& \left [ \begin{array}{c@{\quad}c@{\quad}c} W_{n_1} & W_{n_2} & W_{n_3} \end{array} \right ] \\ =& \left [ \begin{array}{c@{\quad}c@{\quad}c} 0.2025 & 0.2594 & 0.5382 \end{array} \right ] \end{aligned}$$

(32)

where $W_{n_{1}}$ is the weight of node 1 by considering all of the criteria, i.e., S _r , C _v and $C_{d}. W_{n_{1}} = W_{S_{r}} \cdot \propto_{n_{1}}^{S _{r}} + W_{C_{v}} \cdot \propto_{n_{1}}^{C_{v}} + W_{C_{d}} \cdot \propto_{n_{1}}^{C_{d}} =0.6583 \cdot 0.0874+0.2819 \cdot 0.4967+0.0598 \cdot 0.082=0.2025$, for instance.

In our example, the node 3 has the largest weight value, i.e., 0.5382, as shown in Eq. (32). Therefore, node 3 is elected as the CH to take care of the nodes in the vicinity.