# Registered Keyword Searchable Encryption Based on SM9
###### Abstract  
The SM9 algorithm is an Identity-Based Encryption (IBE) algorithm independently made by China. The existing SM9 searchable encryption scheme cannot be effective against insider keyword guessing attacks and violates users' data privacy. This article utilizes the SM9 encryption method to propose a Registered Public Keyword Searchable Encryption based on SM9 (RKSE-SM9), which uses the SM9 user keys in the registration keyword algorithm. For RKSE-SM9 to generate the keyword ciphertext or trapdoor, a secure server must first register the keyword, which effectively and reasonably protects users' data and resists honest and curious cloud servers. From there, we also utilize Beaver's triple to construct an improved registered keyword generation algorithm, defining and proving that the improved algorithm satisfies the concept of indistinguishability against registration keywords, achieving a higher level of privacy. In addition, compared with existing SM9 searchable encryption, our scheme proved  
In 2016, China State Cryptography Administration released a cryptographic standard for identity-based cryptography (IBC), which includes three primitives: identity-based signature, identity-based encryption, and identity-based encapsulation. The SM9 algorithm [6] is also an ISO standard since 2021. In the commercial cryptography system, besides SM2 elliptic curve cryptosystem, the SM9 IBC algorithm has become China's other commercial standard for public key cryptography. The research on the SM9 algorithm is conducive to promoting the retail cryptography industry's development, improving its technology's innovation, and ensuring network and information security. This research combined the SM9 algorithm with searchable encryption technology to create an effective and safe public key searchable encryption algorithm, therefore extending the application of the SM9 algorithm. These are the contributions we produced:  
* In the anonymous IBE, the identity information in its algorithm is replaced by keywords, and the IBE can be converted into a PEKS. We first involve a third-party server for keyword registration using SM9's deterministic key generation algorithm and then construct a public key encryption scheme with a registered keyword search. By employing [PERSON]'s protocol [7] to ensure secure keyword generation, we ensured the privacy of registered keywords;
* We describe the framework of our suggested system and examine its security model in this paper. We simplify the proposed method to the \(q\)-BCAA problem and prove its security in the presence of random oracles. Our searchable encryption method is more resistant to insider keyword guessing attacks than the existing SM9 searchable encryption scheme;
* Compared with existing Registered Keyword Searchable Encryption Schemes [8], our scheme has significant advantages in both computational overhead and communication overhead, especially in terms of the PEKS Ciphertext and Testing. According to experimental data, the PEKS Ciphertext's efficiency has grown by 84 percent, Testing's efficiency has increased by 41.3 percent, and the overall efficiency has increased by 63 percent.