# How Can We Achieve Query Keyword Frequency Analysis in Privacy-Preserving Situations?
## 2 Related Work  
Since the concept of SE was first introduced in [8], SE has been divided into two categories: symmetric searchable encryption (SSE) [9; 10; 11] and PEKS [4; 12; 13; 14; 15]. The two have different application scenarios and construction methods. SSE generally considers the use of a single user, which is equivalent to establishing a personal encrypted cloud disk, and relies on symmetric encryption algorithms for scheme construction; PEKS, which mainly relies on public key cryptography algorithms, usually considers multi-user scenarios, such as mail systems or multi-person file-sharing systems.  
The first PEKS scheme was proposed by [PERSON] et al. [4], wherein the data owner could use the public key of a specified data user, so that the user could use their key to generate a trapdoor for query keywords to search encrypted data. Since then, many PEKS schemes have been proposed. Among these schemes, examples in the literature, such as [16; 17], support multi-keyword search; however, these schemes cannot support multiple data owners and data users at the same time. [PERSON] et al. propose a PEKS scheme [18] supporting multiple keyword queries and multiple users, which combines a data structure representing a keyword/identity representation (T-set) in [11], and ciphertext-policy attribute-based encryption (CP-ABE) in [19]. In their proposed scheme, the data owners grant keys to the data users, requiring each data user to maintain a set of keys in order to access data that are outsourced by different data owners. In addition, because this scheme does not deal with the relationship between the ciphertext and keywords, it brings a huge storage overhead to each entity in the scheme. In 2019, [PERSON] et al. [20] proposed a lattice-based PEKS scheme that was derived from a blind identity-based encryption (blind IBE) [21] scheme, by substituting identities with keywords. Their construction involves an identity-based PEKS that maps the identity of the data owner to a matrix, allowing the data owner to encrypt data with the identity of the data user. In 2021, [PERSON] [22] et al. combined a subset decision mechanism on a distributed two-trapdoor public key cryptosystem [23] to construct a PEKS scheme to be applied in distributed systems. In this scheme, both the data owner and data user have their public and private key pairs, and can generate corresponding searchable ciphertexts and trapdoors with their respective public keys. However, this scheme, similarly to all previously proposed PEKS schemes, loses the availability of data; in addition, it cannot expand the potential application scenarios of public key searchable encryption, because it does not consider keyword frequency analysis of query keywords.  
In 2019, [PERSON] et al. [24] proposed the first PEKS scheme based on blind IBE [21], which can accomplish keyword frequency analysis under the premise of protecting user privacy. Unfortunately, due to its single-server setup, this solution is not immune to KGA [25; 26]. In addition, it is difficult to extend the query method from a single keyword to multiple keywords. KGA is a common type of attack facing PEKS schemes. Within KGA, an attacker can generate searchable ciphertexts for any desired keyword using the public key of the data user, and can then test these ciphertexts against the search trapdoor. To mitigate KGA, various cryptographic primitives have been proposed, including public key authenticated encryption with keyword search (PAEKS) [27; 28; 29] and public key encryption with fuzzy keyword search (PEKS) [30]. Based on [22], we propose a PEKS that can achieve keyword frequency analysis while protecting data privacy and user privacy. In addition, this PEKS is suitable for multi-user distributed scenarios and is resistant to KGA.