# Registered Keyword Searchable Encryption Based on SM9
## 2 Preliminaries
### Baver Triple
Thus, compared with the scheme of [8], our scheme improves the efficiency of the PEKS Ciphertext by 84%. Figure 5 shows the running time of the Trapdoor in each scheme, where the x-axis is the number of keywords and the y-axis is the time required by the Trapdoor. From the figure, we can see that when generating 1000 keyword trapdoors, the time of our scheme as well as [30] is 3.6 s, while the time of the scheme of [8] is 2.3 s. It can be seen from Table 3 that our Trapdoor time is slower than that of [8] in theoretical analysis, as it is in the experiment. Figure 6 displays the amount of time that Testing takes to execute in each scheme, with the time needed for Testing shown on the y-axis and the number of keywords on the x-axis. It can be seen that the efficiency of our scheme is slightly lower than the scheme of [30], but is much better than the scheme of [8]. Specifically, when running Testing 1000 times, the time of our scheme is 67 s, the time of [8] is 114.2 s, and the time of [30] is 66 s. Compared with the scheme of [8], our scheme does not require the time-consuming operations of \(H_{G_{T}}\); our scheme improves the efficiency of the Testing by 41.3%. Figure 4: Computation cost of PEKS Ciphertext generation. Figure 5: Computation cost of trapdoor generation. Figure 7 displays the average runtime of each algorithm under different schemes, with time shown on the y-axis. In our scheme, the total time required to execute the whole process of PEKS ciphertext, Trapdoor, and Testing is 88 milliseconds, the [30] is 87 milliseconds, and the [8] is 236 milliseconds. It can be seen that the overall efficiency of our scheme is 63% higher than the scheme of [8]. Although the efficiency is reduced by 1% compared with the scheme of [30], our scheme guarantees stronger security against KGA using a few additional computing operations. Figure 8 compares the registration keyword algorithm's efficiency between the basic scheme and the improved scheme put forward in this work. The x-axis represents the number of keywords, while the y-axis represents time. This improved scheme includes the time the two registration servers operated together. It can be clearly seen from Figure 8 that the improved scheme is two times slower than the original scheme, but its security can satisfy the indistinguishability of the registered keywords. Figure 6: Computation cost of testing. Figure 7: Comparing the average time of each algorithm. To sum up, under the theoretical analysis and practical implementation, our SM9-based searchable encryption scheme considers the factors of computation overhead and communication overhead. Compared with the server-aided registration keyword searchable encryption scheme of [8], its efficiency has a significant advantage. Compared with the SM9-based searchable encryption scheme of [30], its efficiency is only reduced by 1% to ensure stronger security against keyword-guessing attacks. ## 6 Conclusions

Aiming at the existing SM9 public key searchable encryption scheme, it cannot resist internal KGA. A searchable encryption scheme based on SM9 with registration keywords is proposed. The identity key generation algorithm in SM9 is used to construct a registered keyword generation algorithm, and a registered keyword server is used against insider KGA. The scheme has been proven correct and secure in different security models. However, the basic scheme can only ensure that a part of the keyword information is covered and still needs to satisfy registered keywords' privacy. To solve this issue, we add two servers, use Beaver triples to run the registration keyword algorithm interactively, and propose an improved searchable encryption scheme for registered keywords. It can cover up keyword information reasonably and efficiently, improve security, realize the privacy-preserving user data, and satisfy the indistinguishability of registered keywords.