# A Security-Enhanced Query Result Verification Scheme for Outsourced Data in Location-Based Services
## 6 Evaluation
### Performance of Verification Objects  
As a key technique in our query solution, the time to construct the verification objects greatly affects how well the solution works. Therefore, we first conducted experiments on the construction time of two types of verification objects. To evaluate the performances of verification objects, we chose five representative types of POIs for this experiment: _Hotels_, _Restaurants_, _Supermarkets_, _Gas stations_, and _Attractions_. Table 4 shows the amounts of these POIs in the regions. Moreover, we set the total inserted times \(S\) to 500, which is much more than any number of POIs in our experiments. The time required to construct the verification objects are shown in Figure 6. The graph should have consisted of the constructing time of the fog node verification object and the constructing time of the description file verification object. However, due to the difference in the construction method of the verification objects (i.e., the difference in the number of numbers inserted into the verification objects), the construction time of the fog node verification object was much less than that of the description file verification object and was negligible in the construction process for both types of verification objects. The highest bar in the graph represents the construction time corresponding to the _Restaurants_, which is positively correlated with the number of POIs in the area; that is, the more POIs of the same type in the area, the more time it took to construct, which is in line with the common perception. However, the differences between the different categories were not very large, especially during the whole process of location-based services. Thus, it is not a concern for an attacker to infer from the construction time of a verification object on what it represents. For the description file verification objects, although the POI numbers were distinguished different, the _Restaurant_ numbers were five times more the _Gas station_ numbers, and the time cost of _Restaurants_ was only 6.3% (138.17 and 137.30 ms) more than the _Gas stations_; hence, not very different. The reason for this result is that the verification object construction time is mainly determined by the selected pseudo-random function. Moreover, as shown in Figure 7, we compare our verification object construction scheme with [9]. It is clear that our construction time is slightly higher, also because the pseudo-random function chosen is different. Compared to the HMAC-MD5 used in [9], our pseudo-random function key grew from 128 to 256 bits, addressing the potential security concerns associated with the use of an insecure cryptographic algorithm in the former, and the increase in construction time is within acceptable limits. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fog Node** & **Hotel** & **Restaurant** & **Supermarket** & **Gas Station** & **Attraction** & **Total** \\ \hline \(g_{1}\) & 29 & 41 & 18 & 7 & 5 & 100 \\ \hline \(g_{2}\) & 33 & 32 & 22 & 2 & 11 & 100 \\ \hline \(g_{3}\) & 30 & 38 & 16 & 4 & 12 & 100 \\ \hline \(g_{4}\) & 24 & 38 & 10 & 10 & 18 & 100 \\ \hline \(g_{5}\) & 29 & 36 & 18 & 6 & 11 & 100 \\ \hline \(g_{6}\) & 29 & 31 & 24 & 11 & 5 & 100 \\ \hline \(g_{7}\) & 22 & 43 & 11 & 8 & 16 & 100 \\ \hline \(g_{8}\) & 23 & 42 & 12 & 5 & 18 & 100 \\ \hline \(g_{9}\) & 24 & 41 & 13 & 10 & 12 & 100 \\ \hline total & 243 & 342 & 144 & 63 & 108 & 900 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The numbers and distribution of the POIs. Figure 6: Time costs of constructing the verification objects. The construction time of the verification object affects the efficiency of the outsourced storage of description files; it is the verification time of the verification object that is critical for the user. Low latency is an important indicator to verify the feasibility of our solution. We made experiments on the verification time of the verification object. Figure 8 shows the time cost increased with the number of data queried in our scheme.