Keywords

1 Introduction

Internet of Vehicle (IoV) refers to the realization of all-round network connection in vehicles, vehicles and persons, vehicles and vehicles, vehicles and roads, vehicles and service platforms with help of new generation of information and communication technologies. It improves the level of intelligent vehicles and automatic driving ability and constructs new business form of automobile and traffic services. It improves traffic efficiency and driving experiences, and provide users with intelligent, comfortable, safe, energy-saving and efficient comprehensive services [1]. Internet of Vehicle is centered on “both ends – cloud”, supplemented by roadbed facilities, including intelligent networked cars, mobile intelligent terminals, car networking service platforms and other objects. It involves five communication scenarios: vehicle-cloud communication, vehicle-vehicle communication, vehicle-to-person communication, vehicle-road communication, and in-vehicle communication [2]. As shown in Fig. 1.

Fig. 1.
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Application scene of IoV

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Internet of Vehicle is an open network that is constantly changing. There are a large number of entities, such as floating cars and various types of drive test equipment. The effective way to ensure data security in network is to establish a trust mechanism, through the transmission and dissemination of trust. Calculating and measuring the credibility of the target entity, and selecting the data provided by the reliable entity as the object of processing is to ensure that the result is more accurate and close to the real data. At present, the trust model of Internet of Vehicle mainly has four problems: ① Lack of trust model to consider multi-application scenarios. ② Lack of trust calculation method to support dynamic update. ③ Lack of ability to adapt to a dynamic trust decision-making mechanism. ④ Lack of consideration for future communication environments.

2 Description of Trust Model

2.1 Basic Definitions

The multi-attributes-based trust model based on IoV [3, 4] is shown in Fig. 2.

Fig. 2.
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Trust model based on Internet of Vehicle

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Definition 1.

Multidimensional vector A: \( \overline{A} = [A_{1} ,A_{2} , \cdots ,A_{i} ] \), \( i \in N \). \( A_{i} \) represents the transaction trust of node A of IoV in terms of i.

Definition 2.

If node \( A_{\text{i}} \) in domain A is not the first transaction with node \( B_{\text{j}} \) in domain B, \( hdtv_{{B_{j} }}^{{A_{\text{i}} }} \) represents the last historical direct trust between \( A_{\text{i}} \) and \( B_{\text{j}} \). \( dtv_{{B_{j} }}^{{A_{\text{i}} }} \) represents the direct trust between \( A_{\text{i}} \) and \( B_{\text{j}} \).

Definition 3.

\( {\text{dt}}_{{A_{j} }}^{TA} \) represents the direct trust of domain agent to node \( A_{\text{j}} \).

Definition 4.

\( {\text{rtv}}_{{A_{i} }}^{A} \) represents the recommended trust of domain A to node \( A_{\text{i}} \).

Definition 5.

The recommended trust of domain A to domain B is defined as \( {\text{rtv}}_{B}^{A} \). \( {\text{rtv}}_{{B_{j} }}^{{A_{i} }} \) represents the recommended trust of node \( A_{\text{i}} \) and node \( B_{\text{j}} \).

Definition 6.

\( R\left( {A_{\text{i}} ,A_{\text{k}} } \right) \) represents the recommended trust factor of node \( A_{\text{i}} \) to node \( A_{\text{k}} \). Range of the value is [0, 1].

Definition 7.

Domain maintains two tables, one is the trust table in the domain. Each node in the domain maintains a value of trust, which is used to describe performance of nodes in services. It is defined as \( {\text{f}}_{{A - A_{\text{i}} }} \). It represents the trust value of the node \( A_{\text{i}} \) granted by the admin domain A.

Definition 8.

The number of successful transactions between nodes are defined as S.

Definition 9.

The number of unsuccessful transactions between nodes are defined as f.

2.2 Calculation of Trust

  1. (1)

    Initialization of Trust

For newly registered nodes, each domain agent is obliged to give them an appropriate initial trust value. If the trust value is too low, it will not meet the conditions of transactions between nodes. If the trust value is too high, some malicious nodes will use the method of re-registering node to improve their trust value, which will damage the programs of other nodes. Reference [5] sets the initial trust value of the newly joined node to 0.5, and then improves or reduces trust of the node according to its performance.

  1. (2)

    Calculation of Direct Trust

Direct trust refers to the direct transaction between two nodes in the past. Thus a direct trust relationship is established. The source of trust value is based on the transaction between two nodes.

Calculation of direct trust has the following two situations:

  • Node \( A_{\text{i}} \) and node \( B_{\text{j}} \) have ever traded. For both parties, current trust can be calculated by direct trust of the latest history. Considering the time decay factor, direct trust of current two nodes is as shown in the following formula:

    $$ dtv_{{B_{j} }}^{{A_{i} }} = {\text{h}}dtv_{{B_{j} }}^{{A_{i} }} *T(\Delta {\text{t}},\sigma ) $$
    (1)

In formula (1), \( T(\Delta {\text{t}},\sigma ) \) is time decay function, \( \Delta {\text{t}} \) is time difference between current time and the latest transaction, \( \sigma \) is type of transaction and it represents some kind of scientific calculation, data storage and file download. Time decay function is as follows:

$$ T(\Delta {\text{t}},\sigma ) = \frac{1}{\Delta {\text{t}} + 1} $$
(2)

  • When transaction between two nodes is completed, current trust between them needs to be calculated. Trust of a single service is shown in the following formula:

    $$ dtv_{{B_{j} }}^{{A_{\text{i}} }} { = }f(\sigma ,\omega ) = \sum\limits_{k = 1}^{n} {\gamma_{\text{k}} \omega_{\text{k}} } $$
    (3)

In formula (3) \( \omega \) represents dimension of service trust and \( \gamma_{\text{k}} \) represents the Kth dimension coefficient which satisfies the expression \( \sum\limits_{k = 1}^{n} {\gamma_{\text{k}} \omega_{\text{k}} } \). This expression is suitable for any case regardless of whether there has been a transaction between two nodes.

  1. (3)

    Calculation of Recommendation Trust in Domain

Recommendation trust in domain, that is indirect trust in domain, refers to the fact that there has never been a direct transaction between two nodes in same domain. Source of trust value is based on recommendation and evaluation of other nodes. Calculation of recommendation trust in domain can be divided into the following two cases:

  • Node \( A_{\text{i}} \) in domain needs to evaluate trust of another node \( A_{\text{j}} \) in another domain. Firstly, neighbors of node \( A_{\text{i}} \) are asked whether they have had direct transactions with node \( A_{\text{j}} \). If so, recommended trust between nodes is shown in the following formula:

    $$ {\text{rtv}}_{{A_{j} }}^{{A_{i} }}\,{ = }\,\frac{{\sum\limits_{k - 1}^{\text{n}} {{\text{rtv}}_{{A_{k} }}^{{A_{i} }} *R(A_{i} ,A_{k} )*dtv_{{A_{j} }}^{{A_{k} }} } }}{{\sum\limits_{k - 1}^{\text{n}} {{\text{rtv}}_{{A_{k} }}^{{A_{i} }} *R(A_{i} ,A_{k} )} }} $$
    (4)

  • If two transaction nodes belong to the same domain, they can directly ask domain agent TA (Trust Agent) of that domain. Nodes can trust domain agent completely, as shown in the following formula:

    $$ {\text{rtv}}_{{A_{j} }}^{{A_{i} }}\,{ = }\,dt_{{A_{\text{j}} }}^{TA} $$
    (5)
  1. (4)

    Calculation of Recommendation Trust Between Domains

Recommendation trust between domains refers to trust recommendation between trust agents when two nodes that do not belong to the same domain judge each other’s trust. If the neighbor node has a direct transaction with the target node, then the formula (4) and formula (5) can be used to calculate the trust. In contrary, if the neighbor node has no direct transaction with the target node (service provider), then the domain agent must find a recommended trust path. Here, we can abstract the trust relationship between domains into a directed graph. Each domain is represented by each node in the graph. The trust relationship between domains is represented by the edge of the graph. It is recorded as a directed graph G = (V, E). Nodes (service applicants) need to send requests of trust recommendation and basic information of target nodes to domain agents. Trust agent needs to find a recommendation path and calculate trust of target node. As shown in Fig. 3.

Fig. 3.
figure 3

Recommendation trust between domains

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Describe the above situation as G = (V, E). Here we use the method the shortest path maximum trust value to select the most suitable path. As shown in Fig. 3, there are three paths: TA2-TA3-TA4, TA5-TA6 and TA7-TA8. Firstly the shortest path is selected. We can see that TA5-TA6 and TA7-TA8 are the shortest path. Then we select the maximum value of trust from the two paths. The method of calculating trust value is as follows:

$$ {\text{rtv}}_{{B_{j} }}^{{A_{i} }} {\text{ = dt}}_{{B_{j} }}^{TA} *\mathop \Pi \limits_{k = m}^{n - 1} {\text{rtv}}_{{TA_{k + 1} }}^{{TA_{k} }} $$
(6)

2.3 Trust Updating

  1. (1)

    Trust Update of Nodes

After using services provided by node \( B_{j} \), node \( A_{\text{i}} \) needs to update its own direct trust table to reflect changes of trust relationship between them. If node \( A_{\text{i}} \) is satisfied with the service of node \( B_{j} \), it needs to improve the trust of node \( B_{j} \). In contrary it needs to reduce its trust. As shown in the following:

$$ {\text{hdtv}}_{{B_{j} }}^{{A_{i} }} {\text{ = dtv}}_{{B_{j} }}^{{A_{i} }} = f(\sigma ,\omega ) = \sum\limits_{k = 1}^{n} {\gamma_{k} \omega_{k} } $$
(7)

Formula (7) is also applicable to the case that two nodes belong to the same domain.

  1. (2)

    Updating of Trust in Domain

Trust tables in domain agents need to be updated after the transaction between two nodes. If the transaction is successful, trust value of corresponding nodes will increase. On the contrary it decreases. As shown in the following:

$$ \left\{ {\begin{array}{*{20}l} {f_{{A - A_{i} }} = H + \mu \times \varphi (s)\quad Transaction \, Successed} \hfill \\ {f_{{A - A_{i} }} = H - \mu \times \varphi (f){\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} Transaction \, Failed} \hfill \\ {\varphi (x) = e^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} x}} \right. \kern-0pt} x}}} } \hfill \\ \end{array} } \right. $$
(8)

In formula (8) \( \mu (0 < \mu < 1) \) represents updating coefficient, H represents the trust value before updating, s and f represent the number of success and failure respectively. Referring to Beth model, we define \( \varphi (x) = e^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} x}} \right. \kern-0pt} x}}} \) and make \( \varphi (x) \) increases with increases of x. Because of \( \mu (0 < \mu < 1) \), it can be concluded that the more number of success is, the faster trust value increases. On the contrary the faster trust value decreases. When total trust value of a node is reduced to certain value, if it is less than zero, the domain agent will kick the node out.

For updating coefficient, the data in reference [6] is used as the updating coefficient of success transaction when \( \mu_{1}\,{ = }\,0.01 \). And when \( \mu_{2}\,{ = }\,0.1 \) it is used as the updating coefficient for failure transaction. The purpose is to reduce the trust value of malicious nodes when they provide services that harm other nodes.

  1. (3)

    Updating of Trust Between Domains

Assuming that two nodes from different domains trade with each other, if the transaction succeeds, the trust value between domains involved in the recommendation increases and on the contrary decreases. For the specific value of increase or decrease, it should be based on the number of success or failure transactions between nodes. As shown in the following:

$$ \left\{ {\begin{array}{*{20}l} {{\text{rtv}}_{B}^{A} = H + \mu \times \varphi (s)\quad Transaction \, Successed} \hfill \\ {{\text{rtv}}_{B}^{A} = H - \mu \times \varphi (f)\quad Transaction \, Failed} \hfill \\ {\varphi (x) = e^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} x}} \right. \kern-0pt} x}}} } \hfill \\ \end{array} } \right. $$
(9)

3 Experiments

We demonstrate security and effectiveness of our algorithm through simulation experiments. The main verification contents are sensitivity and accuracy of our algorithm in describing the trust relationship between nodes of IoV.

The service providers of this experiment were randomly selected. The steps to provide the service are as follows: Firstly, we ensure that the first 30 services are of high quality, then provide 20 low quality services, at last provide 50 quality services. It can be known from experiments (as shown in Fig. 4) that through use of our calculation methods, the results of the experimental objects will change accordingly due to the quality of the service. Moreover, although the quality of service has risen to the previous level and the quantity provided has far exceeded the original level, its trust value cannot be restored to its original level. It can be seen that the algorithm can make rapid feedback on the situation of degraded service quality, thus effectively curbing the cheating trend of malicious nodes.

Fig. 4.
figure 4

Sensitivity and accuracy

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After completing the above experiment, 20% of the nodes were randomly selected as bad nodes, and 60% of them were normal nodes to provide good quality of service. In this experiment, the results calculated by model PathTrust show that the interest ratio between the normal node and the malicious node is almost the same (as shown in Fig. 5). It can be seen that the Path Trust algorithm has poor ability to constrain bad nodes, and the algorithm incorporates a penalty mechanism to control the benefits of bad nodes below 60%. Compared with the Path Trust algorithm, bad nodes have a higher cost in our algorithm.

Fig. 5.
figure 5

Containment of bad nodes

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4 Conclusion

In this paper the trust model of Internet of Vehicle is studied and analyzed. From aspects of trust initialization, trust calculation and trust updating, we propose a trust model for Internet of Vehicle. When evaluating the trust relationship between nodes, overall experiences of the evaluator are considered as the main reference content, which have a significant restraining effect on malicious behaviors of bad nodes. Moreover, our model combines heuristic algorithm and takes the previous trust evaluation as an important reference content. Thus accuracy of evaluation of trust relationship is improved and sensitivity of our algorithm on behaviors of nodes is enhanced.