# A Searchable Encryption with Forward/Backward Security and Constant Storage
## 4 Our Proposed Algorithm
### Decryption
### Evaluation of Computation Cost

This section focuses on the comparison from the encryption and update, as well as the search phase, and compares our scheme with others regarding the computational overhead generated for the processing of the same amount of data, so as to analyze the differences between the algorithms of different schemes. Table 3 shows the comparison of different DSE schemes. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbols** & **Meaning** \\ \hline \(T_{sm}\) & scalar multiplication \\ \(T_{p}\) & bilinear pair operations \\ \(T_{h}\) & hash operations \\ \(T_{mutch}\) & \(Match()\) function operation \\ \(T_{F}\) & pseudo-random function operations \\ \(T_{Div_{C}}\) & division operation in group \(G\) \\ \(T_{map}\) & mapping calculation \\ \(T/T^{-1}\) & \(T/T^{-1}\) operation \\ \(T_{mul_{C}}\) & multiplication in group \(G\) \\ \(T_{e}\) & exponential arithmetic \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computation time. Figure 4 describes the performance of different schemes in the encryption and update. Figure 4 shows that among the above four comparison schemes, the running time of [PERSON] et al. [16] and [PERSON] et al. [21] exceeds 5 s when the number of keywords is 1000, and the increase is large. It can be expected that in the environment of more keywords, the scheme will bring great pressure to the server. The scheme of [PERSON] et al. [18] shows a certain advantage in running time when compared to our scheme. Furthermore, when our scheme processes up to 2000 keywords, the time required by our scheme is only 55% of that of [PERSON] et al. [18]. This will bring great advantages to our scheme in the overall operation phase. From the analysis in Figure 5, it is clear that the overhead of [PERSON] et al. [21] is larger, which is due to the fact that a large number of exponential operations are used in the search process, and each cryptographic operation needs to be re-invoked, resulting in a negative impact, requiring more power operations, on its overall scheme. The scheme of [PERSON] et al. [16] requires long-term maintenance of the inverted index, which puts great computational pressure on the server, and it also uses more bilinear pairings operations, which further reduces the performance of the scheme algorithm. [PERSON] et al. [18] use bilinear pairings operations, which have some impact on the algorithm efficiency. These only need to be calculated once when the system is established, guaranteeing the efficient operation of the subsequent algorithms, to some extent. Our scheme boasts a lightweight construction and adopts a bilinear pair-free design in the search phase. This is a huge improvement to the scheme, and the advantage becomes more obvious as the number of keywords increases. It can be observed from Figures 4 and 5 that the overhead of the above scheme is much higher in the encryption and update phase than in the search phase. Therefore, the impact of the encryption phase performance on the overall performance of the scheme is



and the number of keyword/document pairs in Dataset 1, Dataset 2, and Dataset 3 increase in descending order. In Table 5, the storage space of [PERSON] et al. (2016), [PERSON] et al. (2018) and [PERSON] et al. (2011), without the optimization of the storage structure, increases significantly with the increase in keywords. Some of the above schemes use inverted indexing to maintain the keyword state, while our scheme uses a global counter generated by a key and a hash function to maintain the keyword state. Although the iterative use of hashing incurs additional overhead, the feasibility of the scheme is demonstrated in the next phase of performance evaluation. ### Discussion of Comparison

The above two parts of the performance evaluation are evaluated in terms of computational efficiency and storage overhead, respectively.