# A Secure Key Aggregate Searchable Encryption with Multi Delegation in Cloud Data Sharing Service
## 6 Security and Efficiency Features Comparison
### Comparison of Computation Costs  
This section performs a testbed experiment on cryptographic computation of the data retrieve phase using the popular \"Multiprecision Integer and Rational Arithmetic Cryptographic Library (MIRACL)\" [13] on two platforms:  
* **Platform 1**: The platform 1 is general personal computer environment, and the detailed performance of the personal computer is as follows: \"Ubuntu 18.04.4 LTS with memory 8 GiB, processor: Intel Core i7-4790 @ 3.60 GHz \(\times\) 4, CPU Architecture: 64-bit.\" The experiments are executed for \"one-way-hash-function (\(T_{h}\))\", \"Bilinear pairing operation (\(T_{b}\))\", \"Scalar point multiplication (\(T_{spm}\))\", and \"Exponentiation operation (\(T_{e}\))\" for 100 runs. After that the average run-time in milliseconds are recorded for \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Security Properties** & **[PERSON] et al. [10]** & **[PERSON] et al. [20]** & **Ours** \\ \hline Man-in-the-middle attack & o & o & o \\ Replay attack & o & o & o \\ Impersonation attack & x & x & o \\ User anonymity & o & o & o \\ Privileged-insider attack & x & o & o \\ Session key disclosure attack & x & o & o \\ Mutual authentication & x & x & o \\ Multi-access & - & - & o \\ Multi-delegation & - & - & o \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Security Properties. Figure 7: (left) Results of data retrieve phase. (right) Results of authentication for delegation phase. these operations or functions from 100 runs, which are 0.003 ms, 6.575 ms, 2.373 ms, and 0.819 ms, respectively. * **Platform 2**: The platform 2 is Raspberry PI environment for considering mobile device, and the detailed performance of the Raspberry PI is as follows: \"Model: Raspberry PI 3 B, with CPU 64-bit, Processor: 1.2 GHz Quad-core, Memory: 1 GiB, and OS: Ubuntu 20.04.2 LTS 64-bit.\" Figure 8 shows the setting of Raspberry PI environment. The experiments are executed for \"one-way-hash-function \((T_{h})\)\", \"Bilinear pairing operation \((T_{b})\)\", \"Scalar point multiplication \((T_{spm})\)\", and \"Exponentiation operation \((T_{e})\)\" for 100 runs. After that the average run-time in milliseconds are recorded for these operations or functions from 100 runs, which are 0.020 ms, 21.348 ms, 5.686 ms, and 2.973 ms, respectively. Table 4 reveals the message computation costs of data user and cloud server entities in the data retrieval phase. As a result of comparing [PERSON] et al., [PERSON] et al., and ours, respectively, it can be seen that our scheme has a higher total cost compared to the existing schemes. However, the proposed scheme has the strength of showing that it is safe against various attacks. ### Comparison of Computation Costs  
The number of keywords in the ciphertext and the number of keywords in the search query set affect computation and communication costs. In our scheme, the pairing operation between the user and the cloud server is additionally calculated compared to other schemes, but authentication is performed only once regardless of the number of keyword value. Therefore, according to \((O)\) asymptotic notation, our scheme has the same computational and communication costs as other existing KASE schemes. A comparative analysis in Table 5 shows that the complexity of computational and communication costs for the different features of the proposed scheme are comparable to those of the other schemes.