Reconfiguration time and complexity minimized trust-based clustering scheme for MANETs

Abstract

A trust management mechanism for mobile ad hoc networks (MANETs) is proposed to cope with security issues that MANETs face due to time constraints as well as resource constraints in bandwidth, computational power, battery life, and unique wireless characteristics. The trust-based reputation scheme GlobalTrust is a reliable trust management mechanism. In this paper, a clustering algorithm is applied to the GlobalTrust scheme (named Cluster-based GlobalTrust (CGTrust)) to find the optimal group size to minimize the configuration time, which consists of trust information computational time and complexity, while having to satisfy the trust reliability requirements. The optimal number of clusters is derived from the minimizing point of the computation complexity function. Simulation results show that the computational time and complexity of CGTrust are controllable and can be used effectively in time critical network operations that require trust analysis.

1 Introduction

Mobile ad hoc networks (MANETs) consist of distributed wireless mobile nodes. In MANETs, it is critical to make a decision of assessing the trustworthiness of participating nodes accurately by a trust authority. Trust evaluations are made on node reputation, which is the perception of a node evaluated by other nodes. A node’s reputation is evaluated based on the collection of trust evaluations made on that node by other nodes [1, 2]. Cho et al. [1] analyzed the concepts and properties of trust. In addition, they surveyed MANET trust management schemes for secure routing, authentication, and intrusion detection, etc. Aberer and Despotovic [3] proposed a trust-based reputation management scheme. The authors of [4, 5] proposed distributed methods for reputation management. However, results in [3–5] are vulnerable to collusive attacks. Reputation management schemes in [6–9] subjectively evaluate reputation using direct observation that disturbs the global view. Quorum-based reputation management schemes are proposed based on k-out-of-n threshold signatures [10, 11]. The k-means-based reputation scheme is presented in [12, 13], which does not consider conflicting recommendation attacks. Chen et al. [2] proposed GlobalTrust for accurate decision-making of a trusted authority (TA) under various attacks, which shows an outstanding performance in trust on MANETs. The TA needs to collect trust-related data and compute trust values and set up optimal routing paths, which is a very computationally burdening task. Thus, a common issue would be the time constraints and required computing resources of the TA and MANET nodes. The computational time delay and complexity of GlobalTrust significantly increases as the number of nodes in the MANET increases. In addition, in a MANET, communicating nodes are mobile. Therefore, route reconfiguration may need to be conducted frequently. As a result, reconfiguration time minimization would be necessary. In this paper, a Cluster-based GlobalTrust (CGTrust) scheme is proposed with the objective to minimize the computational complexity and reconfiguration time delay experienced by a TA while supporting the required trust reliability requirements. CGTrust consists of the following three unique features.

• CGTrust evaluates trust at cluster heads (CHs) and at the TA in contrast to GlobalTrust that focuses on the TA. This approach has the benefit of requiring less time and uses less computing resources at the TA in the network.

• CGTrust provides a computational complexity minimized mechanism to form MANET clustering, where the complexity considers both intra and inter cluster computations. This algorithm helps to drastically reduce the complexity associated with the trust evaluation and computation.

• CGTrust provides a mechanism to evaluate the trust of both non-CH nodes and CHs to prevent false trustworthiness decisions of non-CH nodes by a non-trustworthy CH and minimize the setup and reconfiguration time.

2 CGTrust

The proposed scheme is for MANETs that use the GlobalTrust trust-based reputation scheme [2]. It is assumed that MANETs consist of multiple nodes communicating via multiple hops. The objective of CGTrust is to provide a trust-based clustering algorithm that derives the optimal number of clusters k (i.e., k _optimal ) to minimized network setup and reconfiguration time delay based on the constraints of the required trust level that needs to be satisfied. CGTrust forms clusters by using a trust-based reputation algorithm, where the TA makes decisions based on trust values. The TA is a system that can determine the trust level of all nodes in the network and manage the security and performance of the network [2]. Therefore, it is assumed that the TA does not perform the role of a node in the network, rather the TA exists independently and manages the network because the TA requires a large amount of resources to perform the trustworthiness evaluation functions. The TA collects evidence periodically to assess the trust of participating nodes through CHs and makes a trustworthy decision. In the initial setup stage, if no CHs have been preselected, then the TA will select CHs and provide initial cluster information (where this initial formation may not be an optimal setting). If The number of nodes changes, the TA recomputes the optimal number of clusters, and then reassigns CHs among the nodes with the highest reputation values. Figure 1 is a diagram that illustrates the operations of CGTrust. The CGTrust process is described in the following steps (Fig. 2).

Fig. 1

CGTrust network operations

Fig. 2

CGTrust algorithm

Step 1: Non-CH nodes that belong to the ith cluster transmit local trust opinions (LTOs) of their neighbor nodes to the local CH. LTO _w,u is node w’s trust opinion towards node u based on direct observations. LTO _w,u is calculated as below

$$\begin{array}{@{}rcl@{}} \text{LTO}_{w,u} = \frac{p_{w,u}}{p_{w,u}+n_{w,u}} \end{array} $$

(1)

where p _w,u and n _w,u are respectively the total number of positive events and the total number of negative events. If there are no events between node w and node u, the LTO is null. The sum of positive and negative events (p _w,u +n _w,u ) is the sum of the number of events sent by node w to node u. Positive events represented by p _w,u are events that node w is determined that a packet was transmitted well to node u. Negative events represented by n _w,u are events that node w is determined that a packet was not delivered to node u for some reasons (noise, wrong decision, intentional packet drop, etc.). The transmission can be determined by an acknowledgement packet, etc. As can be seen from Eq. (1), the higher the positive events, the closer to 1 the LTO and the closer to 0 the negative events become. The higher the LTO, the trust opinion of node u approaches the reputation of an honest node.

An honest node correctly sends a packet to a predefined route when it receives a packet from another node, except for errors that occur during the transmission process. In addition, when the LTO is reported to the TA or CH, the reporting of the LTO is performed without distortion.

A malicious node may drop a packet when it is received from another node, or intentionally send a packet to a different route. In addition, information may be distorted during the transmission and reporting process of the LTO to the TA or CH.

The ith CH (CH _i ) aggregates trust-related evidences and computes the subjective reputation (SR) of node u as it is assessed by node w (SR _w,u ) using

$$\begin{array}{@{}rcl@{}} \text{SR}_{w,u} = \sum_{j \in S_{u}} \text{LTO}_{j,u}\frac{\text{HR}_{j} \text{Sim}(w,j)}{\sum_{j \in S_{u}}\text{HR}_{j} \text{Sim}(w,j)} \end{array} $$

(2)

where Sim(w,j) is the cosine similarity of the LTOs between node w and node j, S _u is the set of nodes that have non-null LTOs over node u (including w if w has one), and HR _j is the hierarchical rank of node j. HR _j can specify that administrators have different values, or they can all have the same value, depending on how trustworthy the node’s opinion is [2]. The TA should have a hierarchy rank higher than that of any CH or node, because the TA’s opinion is more strongly reflected than the CHs or nodes as it is where the reputation judgment is made. In this paper, the hierarchy rank is designated as TA = 3, CH = 2, and node = 1.

After calculating the SR, CH _i makes a SR matrix. The SR tuple in node w’s view is denoted as a vector. CH _i compares all SR tuples, and merges the two SR tuples with the least difference based on the agglomerative hierarchical clustering technique [2]. CHs use this technique to form its trusted quorum (D _CH ). The process of finding the trusted quorum ends when the set having the largest number of nodes has more than half of the total number of network nodes. When the total number of nodes is N, the number of nodes belonging to the trusted quorum may have a value between [N/2, N], depending on how it is calculated. Since all SR tuples are compared and a trusted quorum is found, the complexity does not change depending on the size of the trusted quorum.

Based on the trusted quorum, CH _i obtains the behavioral reputation (BR) of node u ($\phantom {\dot {i}\!}\text {BR}_{\text {CH}_{i,u}}$). $\phantom {\dot {i}\!}\text {BR}_{\text {CH}_{i,u}}$, reflecting how CH _i views node u’s network behavior, is computed by averaging the SR tuples using (3).

$$\begin{array}{@{}rcl@{}} \text{BR}_{\text{CH}_{i,u}} = \frac{\sum_{w \in D} \text{SR}_{w,u}}{|D_{CH}|} \end{array} $$

(3)

Then CH _i computes the credibility reputation (CR) of node u ($\phantom {\dot {i}\!}\text {CR}_{\text {CH}_{i,u}}$) using (4). $\phantom {\dot {i}\!}\text {CR}_{\text {CH}_{i,u}}$ indicates how trustworthy u’s reported LTOs are. This is computed based on the difference between u’s reported LTOs and BRs of the nodes that node u has reported LTOs over.

$$\begin{array}{*{20}l} &\text{CR}_{\text{CH}_{i,u}} = \\ & 1 - \sqrt{\frac{\sum_{j \in \left\{\text{LTO}_{u,j} \neq \text{null}\right\}}\left(\text{LTO}_{u,j}-\text{BR}_{\text{CH}_{i,j}}\right)^{2}}{|j \in \{\text{LTO}_{u,j} \neq \text{null}\}|}} \end{array} $$

(4)

Next CH _i computes the global reputation (GR) of node u ($\phantom {\dot {i}\!}\text {GR}_{\text {CH}_{i,u}}$) using the normalized factor γ selected from the range in [0,1].

$$\begin{array}{@{}rcl@{}} \text{GR}_{\text{CH}_{i,u}} = \gamma \text{BR}_{\text{CH}_{i,u}} + (1-\gamma)\text{CR}_{\text{CH}_{i,u}} \end{array} $$

(5)

Step 2: Once a CH computes all GRs of its cluster’s nodes, it sends the result information to the TA. The TA computes the SR from GR based on the resultant data as in (6). The cosine similarity (Sim(CH _i ,CH _k )) in Eq. (6) is calculated on the basis of the LTO between the CH communication. This allows the TA to determine if a CH is infected and can make a final decision. Step 2 is performed when the number of clusters is two or more. If the network is not divided into clusters, the TA directly makes all trust decisions of all nodes in the network.

$$\begin{array}{*{20}l} &\text{SR}_{\text{CH}_{i,u}} = \\ & \sum_{\text{CH}_{k} \in S'_{u}} \text{GR}_{\text{CH}_{k},u}\frac{\text{HR}_{\text{CH}_{k}} \text{Sim}(\text{CH}_{i},\text{CH}_{k})}{\sum_{\text{CH}_{k} \in S'_{u}}\text{HR}_{\text{CH}_{k}} \text{Sim}(\text{CH}_{i},\text{CH}_{k})} \end{array} $$

(6)

After (6), the TA calculates the BR of node u in (7), and the CR of node u (i.e., CR_TA,u ) in (8).

$$\begin{array}{@{}rcl@{}} \text{BR}_{\text{TA},u} = \frac{\sum_{\text{CH}_{i} \in D} \text{SR}_{\text{CH}_{i,u}}}{|D_{\text{TA}}|} \end{array} $$

(7)

$$\begin{array}{*{20}l} &\text{CR}_{\text{TA},u} = \\ & 1-\sqrt{\frac{\sum_{u \in \{\text{GR}_{\text{CH}_{i,u}} \neq \text{null}\}} \left(\text{GR}_{\text{CH}_{i,u}}-\text{BR}_{\text{TA},u}\right)^{2}}{|u \in \{\text{GR}_{\text{CH}_{i,u}} \neq \text{null}\}|}} \end{array} $$

(8)

Then the TA computes the GR of node u (i.e., GR_TA,u ) using

$$\begin{array}{@{}rcl@{}} \text{GR}_{\text{TA},u} = \gamma' \text{BR}_{\text{TA},u} + (1-\gamma')\text{CR}_{\text{TA},u} \end{array} $$

(9)

Step 3: After the TA computes the GR, the TA decides the trustworthiness of each node using

$$\begin{array}{*{20}l} &\text{Decision}(u) = \\ & \left\{ \begin{array}{ll} \text{unknown}&\text{if}~ \text{GR}_{\text{TA},u} = \text{unknown}\\ \text{honest}&\text{if}~ \text{GR}_{\text{TA},u} \geq \theta\\ \text{malicious}&\text{if}~ \text{GR}_{\text{TA},u} < \theta \end{array} \right. \end{array} $$

(10)

where θ is a decision factor selected from the range in [0, 1]. The detection errors can be reduced by selecting the most appropriate θ value.

The TA evaluates each CH’s trustworthiness using direct trust computation, which can be conducted using the encrypted packet mode, which encrypts packets exchanged between non-CH nodes and the TA. In this mode, non-CH nodes send (encrypted) information packets to their CH and the CH forwards these packets to the TA without trust computation. Using the encrypted packet mode, the TA computes the CHs’ trustworthy level periodically considering β, which is the ratio of nodes that use encrypted packet mode in the cluster. In this computation process, β is a variable that represents the possibility that a CH is a malicious node. As the value of β increases, the number of nodes that the TA needs to directly compute increases, making it difficult to reduce the computational complexity. Considering the computational complexity of trust computation and the worst case where the majority of CHs are infected, the suitable value of β is [0, 0.5].

3 Cluster-based network analysis

3.1 Computational complexity analysis

The proposed scheme computes the GR of each node based on GlobalTrust that uses a trusted quorum D. GlobalTrust uses the agglomerative hierarchical clustering technique to find a minimum dominating cluster [2].

For an accurate complexity analysis, the method of [14] is applied to CGTrust, where the complexity of the pseudocode steps is computed. Each cluster has N/k nodes. Every node will collect the SRs of all other nodes in its cluster, which are ((N/k)-1) SRs. Two nodes in a cluster will pair up and compare their collected SRs, but will exclude the SR of the paired node in this comparison process. Therefore, ((N/k)-2) SRs will be compared by the node pair. In addition, since there are $\binom {N/k}{2}$ combinations of possible node pairs in each cluster, the computational complexity of one cluster is O[((N/k)- 2)(N/k)((N/k)-1)/2] = O((N/k)³) (step 3).

In case of inter-clusters, the TA uses ((1−β)k+β N−1) SRs for each node since the TA computes the GR directly at the rate of β. The minimum pair complexity becomes O (((1−β)k+β N−1)²). The computational complexity for all steps is O (((1−β)k+β N−1)((1−β)k+β N−2)/2)) and based on this the computational complexity of each node is O (((1−β)k+β N−1)²)+O(((1−β)k+β N−1)((1−β)k+β N−2)/2)). Therefore, to compute the TA’s trusted quorum the required complexity is O [((1−β)k+β N−1)²+((1−β)k+β N−1)((1−β)k+β N−2)/2)(1−β)k+β N] (step 9). After organizing the terms, the computational complexity can be expressed as O((1- β)³ k ³ + (β N)³). In CGTrust, the complexity of both intra-cluster and inter-clusters are considered. Therefore, the total computational complexity (C _total) becomes

$$\begin{array}{@{}rcl@{}} C_{\text{total}} = O\left((N/k)^{3} + (1-\beta)^{3} k^{3} + (\beta N)^{3}\right) \end{array} $$

(11)

3.2 Trust information computation time

In order to minimize the time required to evaluate the trust profile of a large MANET, the optimal cluster size (k _optimal) that minimizes the computational complexity used in evaluating the trust profile of all nodes in the network is derived. As shown in Fig. 3, the computational complexity is directly proportional to the computational time required in evaluating the trust profile of all nodes of the MANET.

Fig. 3

Relation of computational complexity and time

3.3 Minimization of computational complexity

The main objective of the CGTrust scheme is to minimize the computational complexity that results in a minimized network reconfiguration time delay. The optimization statement and constraints are established as below.

$$\begin{aligned} & \underset{k}{\text{minimize}} & & C_{\text{total}}(k) \\ & \text{subject to} & & 0 \leq \beta \leq 0.5, \\ &&& N,k \in \mathbb{Z}_{>0}. \end{aligned} $$

The total computational complexity in the TA is a function of k in the form of C _total, where the computational complexity minimizing optimal number of clusters can be obtained from

$$\begin{array}{*{20}l} k'&=\text{arg}\left[\frac{\partial C_{\text{total}}(k)}{\partial k}=0 \right]\\ &=\text{arg}\left[-\frac{3\left(N^{3}+(\beta-1)^{3} k^{6}\right)}{k^{4}}=0 \right] \end{array} $$

(12)

which results in the following candidate solutions.

$$\begin{array}{*{20}l} k' = \left\{ \begin{array}{ccc} \frac{\sqrt{N(1-\beta)}}{1-\beta},&\frac{-\sqrt{N(1-\beta)}}{1-\beta},&-\sqrt{\frac{N(i\sqrt{3}+1)}{2(1-\beta)}},\\ \sqrt{\frac{N\left(i\sqrt{3}+1\right)}{2(1-\beta)}},&-\sqrt{\frac{N\left(i\sqrt{3}-1\right)}{2(1-\beta)}},&\sqrt{\frac{N\left(i\sqrt{3}-1\right)}{2(1-\beta)}} \end{array} \right\} \end{array} $$

(13)

There are 6 solutions of (13), where N is a positive number and the range of β is [0, 0.5]. Considering the fact that k needs to be a positive integer, the only feasible solution is $\frac {\sqrt {N(1-\beta)}}{1-\beta }$ which is a positive real number. In addition, the second derivative of the objective function is

$$\begin{array}{@{}rcl@{}} \frac{\partial^{2}}{\partial k^{2}}C_{\text{total}}(k)=\frac{12N^{3}}{k^{5}}+6(1-\beta)^{3} k \end{array} $$

(14)

in which $k'=\frac {\sqrt {N(1-\beta)}}{1-\beta }$ results in a positive value of the convex objective function C _total(k). The optimal number of clusters (k _optimal) has to be a positive integer, and therefore, the nearest integer function (i.e., Nint(·)) is applied to result in (15).

$$\begin{array}{@{}rcl@{}} k_{\text{optimal}} = Nint\left(\frac{\sqrt{N(1-\beta)}}{1-\beta}\right) \end{array} $$

(15)

Figure 4 presents the C _total profile and the k _optimal values for the range of interest based on N and k.

Fig. 4

Minimum points of C _total (k _optimal) according to N and k

4 Performance evaluation

Malicious attack patterns investigated for the FN and FP performance evaluation include the following five attack patterns [2].

• Naive malicious attack (NMA): a malicious node provide improper services with probability α. However, it reports its LTOs honestly.

• Collusive rumor attack (CRA): In addition to providing improper services with probability α, malicious nodes collude to report false LTOs. Malicious nodes report LTOs of 1 to malicious node and LTOs of 0 to honest nodes.

• Non-collusive rumor attack (NRA): a malicious node can report a false LTO that is opposite to the observed evidence. For example, if an LTO is evaluated as p, the malicious node may report (1−p) as the LTO.

• Malicious spy attack (MSA): some malicious nodes misbehave with probability α. Other malicious nodes behave honestly. These malicious nodes may collude and report LTOs of 1 to malicious node and LTOs of 0 to honest nodes to confuse the trust and reputation system.

• Conflicting behavior attack (CBA): malicious nodes can collude to confuse the trust and reputation system such as CRA and MSA. However, they misbehave only to some of honest nodes, and report LTOs of 1 to malicious node and LTOs of 0 to honest nodes to confuse the trust and reputation system. This attack causes LTO disagreement among honest nodes, which makes it difficult to find malicious nodes.

CBA is considered the most demanding type of attack because it makes it difficult to distinguish malicious nodes by confusing LTO information of honest nodes with respect to other nodes. For the above reasons, CBA was selected and evaluated.

The simulation based performance analysis of CGTrust and GlobalTrust was conducted using Matlab with N nodes randomly distributed with a uniform density in a 2×2 km² square area. Simulation parameters were set same to the experiments in [2], where the ratio of malicious nodes was set to 0.3 and every node randomly requests of its neighbor nodes to send a packet (which is multihop relayed) 100 times per minute, and β is in the range in [0, 0.5]. Honest nodes were made to drop packets based on a 0.05 packet error rate (PER) and the detection error probability of the monitoring system was set to 0.05. Each node was made to transmit trust data packets every 30 s and the TA computes the GRs based on the accumulated data of the past 30 min.

In addition, the probability that a malicious node drops a packet was set to 0.5, γ = 0.7, θ = 0.7, and the upper bound probability of FN and FP were set to 0.1 as used in [2].

In the simulation, the TA is not a target of a malicious node. If the TA is infected, trust decisions on network nodes will not be correct. It is assumed that CH and other nodes can be malicious nodes, based on the restriction that the malicious ratio is not more than 0.5. If the malicious node ratio is greater than 0.5, the malicious nodes can take control of all the opinions in the network and the trust decision cannot be determined correctly. Although it is assumed that the overall ratio of malicious nodes is less than 0.5, the proportion of malicious nodes in a cluster is not limited. Therefore, in some clusters, malicious nodes may not properly report to the TA because they have taken control of the cluster.

Figure 5 compares C _total of GlobalTrust and CGTrust based on β, where it can be observed that C _total of CGTrust decreases to less than 1/1000 compared to GlobalTrust. The results show that CGTrust can significantly reduce the required computations and thereby reduce the network’s trust evaluation time. Figure 6 shows the detection error probability of FN and FP for CGTrust, where for the number of nodes of interest (i.e., 100≤N≤1000), the probability of FN and FP are always lower than the upper bound 0.1. More significantly, the FN probability is always below 0.00012. In addition to being much faster than GlobalTrust, having a very low FN probability is a very advantageous feature of CGTrust because (compared to FP) FN is a significantly more critical security problem due to the fact that FN represents the probability that a malicious node has been not detected and still remains operational in the network. On the other hand, an erroneous FP decision on a node can be easily corrected by additional checking of the node. Figure 7 investigates influence of changes in malicious node ratios, where the results show that the FN probability of CGTrust is an approximate 0.1 times lower compared to GlobalTrust, while the FP probability of the two are similar. Abrupt changes in the performance can be observed in Figs. 4 and 5, which are due to the positive integer rounding effect applied to k _optimal.

Fig. 5

C _total comparison of GlobalTrust and CGTrust based on N and β

Fig. 6

Detection error probability (FN and FP) of CGTrust

Fig. 7

Detection error probability (FN and FP) comparison of GlobalTrust and CGTrust based on various malicious node ratios

5 Conclusion

Mission supportive MANETs require fast updates on node conditions in order to properly support command and control operations. To support this objective, CGTrust was designed to minimize the time required to evaluate the trust profile of a MANET through optimal cluster size control applied to GlobalTrust. The simulation results show that for the number of nodes and malicious node ratios of practical interest (based on β = 0.1 and 0.5), CGTrust can be approximately 1000 and 10 times faster compared to GlobalTrust, respectively. In addition, the results also show that the FN probability is approximately 0.1 times lower when CGTrust is used instead of GlobalTrust for the malicious node ratio range of 0.05 to 0.5.