# Quantitative Assessment and Grading of Hardware Trojan Threat Based on Rough Set Theory
## 4 Case Study
### Quantitative Assessment Results  
Using Algorithm 1, the weight of each attribute and whether it was a core attribute was established as shown in Table 2. The core attributes in the HT threat information system are _Abstraction Level_, _Activation Mechanism_, \(Effect\), and _Location_. According to Algorithm 1, the process of calculating the weight is as follows:  
\[I(A)=I(C)=1-\frac{15\times 1^{2}+6\times 2^{2}+4\times 3^{2}+2\times 4^{2}+6 ^{2}+9^{2}+11^{2}+16^{2}}{94^{2}}=0.929 \tag{18}\]  
\[\text{sig}_{C}(a_{1})=\text{sig}_{(C\cup\{a_{1}\})-\{a_{1}\}}(a_{1})  
\[sig_{A-\{a_{4}\}}(a_{4})=1-\frac{7^{2}+25^{2}+26^{2}+36^{2}}{94^{2}}=0.701 \tag{22}\]  
\[sig_{A-\{a_{5}\}}(a_{5})=1-\frac{29^{2}+2^{2}+6^{2}+4^{2}+1^{2}+52^{2}}{94^{2}}= 0.592 \tag{23}\]  
In order to verify the weight calculation method based on RST, we compared the results of the Entropy Weight Method (EWM) [23] with the results of the proposed method, as shown in Table 2. It can be seen that the weights for the five attributes of the two methods are in the same order, namely, \(Effect\), \(Activation\)\(Mechanism\), \(Location\), \(Abstraction\)\(Level\), and \(Insertion\)\(Phase\), ordered from highest to lowest. In terms of running time, RST requires 1.92 ms, while EWM requires 1.61 ms. In addition, the RST algorithm can be used for attribute reduction in order to simplify calculation. The \(Insertion\)\(Phase\) is a non-core attribute and its weight is zero, indicating that the \(Insertion\)\(Phase\) attribute is redundant. In the original data, the difference in the \(Insertion\)\(Phase\) was the smallest. This means that the discrimination of HT threat is small during the \(Insertion\)\(Phase\). From the attributes shown in Table 1, the values for the \(Insertion\)\(Phase\) are related to the \(Abstraction\)\(Level\) and \(Activation\)\(Mechanism\). All the HTs inserted in the fabrication phase are described at the layout level as well as being always activated, and vice versa. Therefore, there is a high positive correlation between \(Insertion\)\(Phase\) and both \(Abstraction\)\(Level\) and \(Activation\)\(Mechanism\). The \(Insertion\)\(Phase\) attribute can be replaced by the attributes of \(Abstraction\)\(Level\) and \(Activation\)\(Mechanism\). In reality, for HTs inserted in the fabrication phase, their \(Abstraction\)\(Level\) and \(Activation\)\(Mechanism\) are rather limited. According to the results of the attribute weight analysis, the \(Abstraction\)\(Level\), \(Activation\)\(Mechanism\), \(Effect\), and \(Location\)\(\;\) are the core attributes, and are the most important indices for assessing HT threat. Numerically, the weight of \(Effect\) is the largest and that of \(Abstraction\)\(Level\) is the lowest. In fact, HT threats are mainly determined by their attack effects. In comparison, the description language used has relatively low impact on the HT threat. Our overall threat analysis of the 94 HTs is shown in Figure 1. Among them, the threat of multpyrmid-T200 is the greatest, with a CC of 1. This is because the multpyrmid-T200 HT is inserted during the Fabrication phase, is included in the layout design, is always active, causes denial of service, and resides in the processor. It has the highest value on all five attributes, serving as the positive ideal reference point in TOPSIS. On the contrary, the threat of RS232-T200 is the lowest; with a CC of 0. It is inserted at the Design phase, is included in the Register Transfer level, is activated by a Physical Condition, results in Degraded Performance, and resides at a location, Other, that is not one of the five specifically named in Table 1. It has the lowest value on all five attributes, serving as the negative ideal reference point in TOPSIS.