A Trust Evaluation Model for Cloud Computing

The entities are divided into Cloud Server Provider (CSP) and Cloud User (CU) in cloud computing. Trust evaluation depends on interactions evidences between the CSP and the CU. The interaction evidence is dynamic. And it has fine timeliness. Below we present our trust evaluation model.

2.1. The timeliness of interaction evidence and sliding window

In cloud computing, CUs send service requests to CSPs, and then CSPs provide the corresponding services for CUs. Entities rate each other after each interaction, as in the E-commerce System. Here, we don't consider the cooperation among CSPs and among CUs. For trust evaluating, the interaction and assessment between CSPs and CUs are evidence information.

In this paper, the evidence set E is defined as follows.

\(E = \{E_1,E_2,...,E_i,...,E_k\}\)

Where, \(k \in N\), N is a natural number. \(E_i(1 \leq i \leq k)\) is defined by 5-tuple.

\(E_i = \{time,cspid,cuid,csp \_ eva,cu \_ eva\}\)

Where, each attribute of evidence \(E_i\) is described as follows:

The interaction evidence would keep on increasing with the realization of interactions by time. And it is basis for trust computing. In addition, the importance of evidence information would decay over time. The importance of negative evidence would decay more slowly than positive evidence. In order to evaluate reasonably trust of entities based on the evidence information, we employ sliding windows to describe the timeliness of evidence information.

The direct interaction is divided into three categories: positive interaction, negative interaction and uncertain interaction. Accordingly, we set three time windows: positive interaction window \((Wp)\), negative interaction window \((Wn)\) and uncertain interaction window \((Wu)\). \(Wp\) is used to sift the positive interaction evidence. \(Wn\) is used to sift the negative interaction evidence. \(Wu\) is used to sift the uncertain interaction evidence. Sliding window mechanism is shown in Fig 1.

Fig. 1. Sliding window mechanism

Here, t_curr expresses the current time; t_pos, t_neg and t_unc are the critical time. Separately, we denote every time window size as \(S_p\), \(S_n\) and \(S_u\) \((S_p \leq S_u \leq S_n)\) for Wp ,Wn and Wu. There exists follow quantitative relationship:

\(\left\{\begin{array}{l}

\mid t_­ \text {curr }-t_­ \text {pos } \mid=S_{p} \\

\mid t_­ \text {curr }-t_­ \text {unc } \mid=S_{u} \\

\mid t_­ \text {curr }-t_­ \text {neg } \mid=S_{n}

\end{array}\right.\)

After introducing Sliding windows, the interaction evidences only inside the windows are valid. Supposed there is positive interaction evidence \(E_k\) at time \(t\). If \(|t\_curr = t| \leq S_p , E_k\) is valid; otherwise, it is invalid. This is similar for negative and uncertain interaction evidence. In the process of trust computing, only valid interaction evidences affect the trust degree of entities. In this way, the trust degree of entities would not be increased or decreased by over-ranging interaction evidence. In addition, negative interaction window is bigger than positive interaction window. So negative interaction evidences can affect the trust of entities for longer time. It is in keeping with law of nature.

2.2. Direct Trust

Each interaction is considered as evidence. By querying the evidence set \(E\), we can count up the number of valid interactions in time windows. Suppose that positive interaction evidence is marked as \(\alpha\), negative interaction evidence is \(\beta\), and uncertain interaction evidence is \(\gamma\). At time \(t\), the number of every kind of valid direct interaction between entity \(i\) and entity \(j\) can be marked as \(\alpha_{i,j}^t,\beta_{i,j}^t,\) and \(\gamma_{i, j}^t\). In \(t = t_0\), there is no interaction between entity \(i\) and entity \(j\) so \(\alpha_{i,j}^0 = \beta_{i,j}^0 = \gamma_{i,j}^0 = 0\). Direct trust between entity \(i\) and entity \(j\) is computed by direct interactions. Here, we compute direct trust between entities using D-S evidence theory, because D-S evidence theory can express the uncertainty of practical problems with a probability range.

We set the trust distinguish framework \(\Omega = \{T, -T\}\), so \(2^{\Omega} = \{f, \{T\}, \{-T\},\{T, -T\}\}\). Here, \(\{T\}, \{-T\}, \{T, -T\}, f\) respectively represent trust, distrust, uncertain and impossibility. We denote the direct trust as dt. In time \(t\), entity \(i\) evaluates the direct trust degree on the entity \(j\), which is expressed as \(dt_{i,j}^t = (dm_{i,j}^t(\{T\}), dm_{i,j}^t(\{-T\}), dm_{i,j}^t(\{T, -T\}))\).

Where, if \(t=t_0 , dt_{i,j}^0 = ( 0,0,1)\). And the BPA (basic probability assignment) function \(dm_{i,j}^t(\{ \cdot \})\) is defined as follows: 

\(\left\{\begin{array}{l}

d m_{i, j}^{t}(\{T\})=u \times d m_{i, j}^{t-1}(\{T\})+(1-u) \times \frac{\alpha_{i, j}^{t}}{\alpha_{i, j}^{t}+\beta_{i, j}^{t}+\gamma_{i, j}^{t}} \\

d m_{i, j}^{t}(\{-T\})=u \times d m_{i, j}^{t-1}(\{-T\})+(1-u) \times \frac{\beta_{i, j}^{t}}{\alpha_{i, j}^{t}+\beta_{i, j}^{t}+\gamma_{i, j}^{t}} \\

d m_{i, j}^{t}(\{T,-T\})=1-d m_{i, j}^{t}(\{T\})-d m_{i, j}^{t}(\{-T\})

\end{array}\right.\)

Here, \(u \in\) is a weight factor. After setting the sliding windows as Figure 2, interactions beyond the window size are regarded as invalid evidence. And the invalid evidence would not be cited in trust computing. However, the invalid evidence still is behavior of entities ever, and the effect of the invalid evidence can not be dispelled suddenly, but rather gradually. By introducing the weight factor u and \(dm_{i,j}^{t-1} (\{ \cdot \})\), the past interactions can affect the trust degree of entities to some extent. Of course, its effect will disappear gradually. We can control the influence of the past interactions by adjusting the weight factor \(u\).

2.3. Reputation

The entity obtains the recommendation information from other entities which have ever interacted with the evaluated entity. If the entity has no direct interaction with the evaluated entity, its recommendation information will not be considered. And we do not consider recommendation's iteration. So it avoids large recommendation chains.

Suppose entity s has direct interaction with entity \(j\). Entity \(i\) can gain the recommendation information about entity \(j\) from entity \(s\) according to direct trust from entity \(s\) to entity \(j\), which is denoted as \(r t t_{s, j}^{t}=\left(r m_{s, j}^{t}(\{T\}), r m_{s, j}^{t}(\{-T\}), r m_{s, j}^{t}(\{T,-T\})\right)\). Here, \(r m_{s, j}^{t}(\cdot)\) is the corresponding BPA function. And we take the direct trust value \(d t_{s, j}^{t}\) as the recommendation trust value \(r t_{s, j}^{t}\) for entity \(i\), so \(r t_{s, j}^{t}=d t_{s, j}^{t}\) and \(r m_{s, j}^{t}(\cdot)=d m_{s, j}^{t}(\cdot)\).

In the trust network, there exists more than one recommendation information from different entities. Based on Dempster rule, we can combine these recommendations. However, the conclusion may be inconsistent with the evidence if there is serious conflict among recommendations. Referring to fusion approach for conflicting evidence in reference, we compute the weight of every recommendation, which is denoted as \(\omega_{s}\). According to \(\omega_{s}\), the BPA function \(r m_{i, j}^{t}(\{\cdot\})\) of the recommendation trust \(r t_{s, j}^{t}\) is revised as follows.

\(\left\{\begin{array}{l}

r m_{s, j}^{t}(\{T\})=\omega_{s} \times r m_{s, j}^{t}(\{T\})=\omega_{s} \times d m_{s, j}^{t}(\{T\}) \\

r m_{s, j}^{t}(\{-T\})=\omega_{s} \times r m_{s, j}^{t}(\{-T\})=\omega_{s} \times d m_{s, j}^{t}(\{-T\}) \\

r m_{s, j}^{t}(\{T,-T\})=1-r m_{s, j}^{t}(\{T\})-r m_{s, j}^{t}(\{-T\})

\end{array}\right.\)

Finally, the combination of the all recommendation trusts form reputation of entities. Reputation of the entity \(j\) is represented by \(r t_{j}^{t}\) at time \(t\). It is calculated as follows according to Dempster's rule.

\(r t_{j}^{t}(A)=r t_{1, j}^{t}(A) \oplus r t_{2, j}^{t}(A) \oplus \cdots \oplus r t_{q, j}^{t}(A), q=1,2, \cdots, m ; \quad A \neq f, A \in 2^{\Omega}\)