# Efficient Conjunctive Keywords Search over Encrypted E-Mail Data in Public Key Setting
## 2 Related Work  
Searchable encryption supporting keyword search has been researched widely in recent years, which are grouped into two categories. One is searchable symmetric key encryption (SSE); the other is searchable public key encryption (SPE). In symmetric key setting, [PERSON] et al. introduced the concept of search over encrypt data and gave an approach about it [1]. [PERSON] defined the notion of security for searchable encryption and presented an effective scheme by using Bloom filter [12]. However, these works only provide a single keyword search. The concept of conjunctive keyword search on encrypted data in symmetric key setting was first proposed by [PERSON] et al. [13]. In their paper, they also gave two constructions which are based on this concept. In comparing with [PERSON]'s work, subsequent works [14; 15] were trying to construct schemes which had much better performance in computational and communication cost. Considering that the practical scheme requires supporting multi-keyword search and returning the top-k search results, [PERSON] et al. [16] constructed a multi-keyword rank search scheme over encrypted cloud data. After that, many SSE schemes supporting rank search were given in References [17; 18], which achieve a better search performance. In public key setting, [PERSON] et al. defined the concept of public key encryption with keyword search and gave one construction of importance which were related to the Identity-Based Encryption scheme proposed by [PERSON] and [PERSON] [19]. [PERSON] et al. defined the computational and statistical notion of PEKS and presented a new scheme that is statistically consistent [20]. However, their works only support a single keyword search in public key setting. The concept and security model of conjunctive keyword search over encrypted data in public key system were proposed in Reference [4] in which they also gave two PECK schemes. The first scheme needs lots of bilinear pairing computations and the second scheme needs private keys in proportion to the number of keywords. Then, [PERSON] and [PERSON] designed a more efficient scheme on time and space complexities than the previous works and introduced a new concept called a multi-user PECK scheme which can effectively manage the encrypted documents in a server for a group of users [5]. The above PECK schemes all use keyword fields as an addition of information. In order to eliminate the keyword field, [PERSON] and [PERSON] proposed a public key system that supports comparison queries(such as \(x\geq a\)) and conjunctive keywords queries [6]. To achieve a better performance on time and space complexities, [PERSON] and [PERSON] addressed this issue and proposed a more efficient PECK scheme without using keyword field [7]. For supporting disjunctions and polynomial equations, [PERSON] et al. proposed a predicate encryption supporting inner product scheme (IPE) [21]. In their work, they also give a method for applying IPE scheme to realize conjunctive or disjunctive keywords search. To achieve a fully secure level, fully secure IPE scheme was proposed by [PERSON] et al. in Reference [22]. After this, an IPE scheme with less time and space cost was introduced in Reference [8]. In the past of few years, numerous efforts have been devoted to constructing a SPE scheme with advanced keywords search. [PERSON] et al. described a new SPE scheme to support range search [23]. [PERSON] et al. achieved disjunctive and conjunctive keywords search over encrypted data [9; 10]. [PERSON] et al. proposed a SPE scheme supporting fuzzy keyword search [24]. [PERSON] et al. [15] firstly defined offline keyword guessing attack and showed that SPE schemes are insecure against keyword guessing attack. [PERSON] et al. [25] pointed that the consistency implies insecurity of a PEKS scheme against keyword guessing attack. Addressing this problem, two works [26; 27] were constructed to defeat the offline keyword guessing attack. The first work using the method of registered keyword was given by [PERSON] and [PERSON] [27].