# Registered Keyword Searchable Encryption Based on SM9
### Related Works  
The concept of Symmetric Searchable Encryption (SSE) was proposed by [PERSON] et al. [9] in 2000. This is the first scheme to search for encrypted data, but it uses symmetric encryption. In 2004, [PERSON] et al. [10] took the mail system as the background, proposed the concept of PEKS, and gave the first PEKS scheme. The security of this scheme was reduced to the difficult problem of the Bilinear Diffie-Hellman (BDH). In 2005, [PERSON] et al. [11] demonstrated the PEKS game's consistency issue and provided a general approach for converting an anonymous IBE scheme to a PEKS scheme. In 2006, [PERSON] et al. [12] said that in our daily life, we usually use high-frequency keywords to search, which shows that there is little room for keywords, which may lead to keyword guessing attacks (KGA). In order to combat KGA, [PERSON] et al. [13] added two pairs of keys to their scheme and defined a new type of PEKS named Designated Public-key Encryption with Keyword Search (dPEKS). It suggested the idea of trapdoor indistinguishability, a notion that can defy offline KGA. In 2010, [PERSON] and [PERSON] [14] proposed a new model, namely Public Key Encryption with Registered Keyword Search (PERKS). PERKS requires the receiver to run the registered keyword algorithm to generate pre-labels. When testing the algorithm, it needs to input the generated pre-label, keyword ciphertext, and keyword trapdoor. In 2016, [PERSON] et al. [8] added an aided server against offline keyword guessing attacks. It applied deterministic blind signatures, e.g., FDH-RSA, to generate a signature as the registered keyword. In 2017, another form of PEKS was given by [PERSON] et al. [15]. With this approach, the sender's private key should be included for generating the ciphertext. The sender's authenticity may be verified by the receiver. As a result, the server is resistant to insider KGA and cannot encrypt keywords. In 2018, [PERSON] et al. [16] combined PEKS with SSE, they adopted a signcryption algorithm when generating the searchable ciphertext, and the scheme is secured against insider KGA. In 2019, [PERSON] et al. [17] added identity authentication on the basis of dPEKS and proved it can resist insider offline KGA. In 2020, [PERSON] et al. [18] showed that the security of [PERSON] and [PERSON]'s [15] scheme was not ideal, and they proposed an improved PAEKS scheme that satisfies keyword privacy and trapdoors to resist chosen multi-ciphertext attacks and insider offline KGA [19]. In recent years, there have been more and more scenarios for searchable encryption, such as [20; 21; 22; 23].  
The SM9 algorithm is the only IBE standard in China, and it has also become a research hotspot in recent years. In 2020, [PERSON] et al. [24] proposed a fully distributed SM9 \((t,n)\) threshold private key generation mechanism to completely eliminate the single-point failure problem. In 2021, [PERSON] et al. [25] proposed an identity-based broadcast encryption based on SM9. To alleviate SM9 key exposure issues, [PERSON] et al. [26] and [PERSON] et al. [27] introduced a dependable third party to take after a part of the user's private key so that it could conduct key updates and revocations. Most recently, with the popularization of applications such as big data and cloud computing, several new cryptographic algorithms have been derived based on the national secret SM9, such as [28; 29]. In 2022, [PERSON] et al. [30] built a public-key searchable encryption method on the SM9 identity-based encryption algorithm for the first time, but it cannot resist the problem of KGA. SM9 public key searchable encryption continues to be researched, and at this point, no method that can resist KGA has been discovered. As a result, this work, for the first time, suggests a searchable encryption system with registered keywords based on SM9. Higher safety and appropriate efficiency can be achieved.