# Efficient Conjunctive Keywords Search over Encrypted E-Mail Data in Public Key Setting
## 1 Introduction  
Nowadays, with the rapid development of cloud computing technology, enterprises and individuals can obtain good e-mail services at lower costs. However, the events of leakage of sensitive e-mail data from the cloud server have occurred occasionally since e-mail data stored in the server is in plaintext. How to safely and effectively retrieve e-mail data from the cloud server is one of the concerns in the e-mail system. A straightforward solution is encrypting e-mails before outsourcing it to the cloud server. But the traditional encryption schemes disrupt the structure of the original data and then hinder users querying e-mails stored in the cloud server. To solve this problem, searchable encryption (SE) [1,2]--which can realize information retrieval over the encrypted data--is regarded as one of suitable techniques. SE supporting keyword search can be built in symmetric key setting or public key setting. In symmetric key setting, authorized users sends encrypted documents and encrypted indexes to a server and retrieve documents containing certain keywords which they query by using a trapdoor without loss of data confidentiality. In this setting, the index and the trapdoor are constructed by using the same secret key. However, if one of the authorized users leaks the secret key, all authorized users' data will be revealed. Thus, it is impractical in some applications, such as encrypted e-mail system (EES) [2] and wireless sensor networks (WSNs) [3]. For the EES system, there are three roles in an EES system, that is, data senders, data receiver and service provider. Under this scenario, any data senders use the searchable public key encryption (SPE) scheme to encrypt e-mails and send these encrypted e-mails to service provider. After that, data receiver performs a secure query to the e-mail service provider and the service provider executes query operations over the encrypted e-mails and returns e-mails associated to this query. The interactive process among these three roles is described in Figure 1. In this application scenario, the security requirements is summarized as follows: (1) any data senders can generate the encrypted e-mails; (2) only data receiver can perform data query and decrypt theencrypted e-mails; (3) anyone except the data receiver cannot obtain the contents of encrypted e-mails. According to these security requirements, we can find that SPE is very suitable for constructing a secure EES than searchable symmetric key encryption (SSE). The first SPE scheme supporting keyword search was introduced by [PERSON] et al. [2]. But, this scheme only supports single keyword search. For supporting multi-keywords search, [PERSON] et al. first proposed a SPE supporting conjunctive keywords search scheme [4], which is called the public key encryption with conjunctive keywords search (PECK). After that, an efficient PECK scheme [5] was proposed to reduce the time and space cost. Note that these schemes all need keyword fields as compulsory information, which is not practical for many applications. For example, if documents which send to the server are scientific papers, each paper has its keyword list and the keywords in the list are arranged in the alphabetical order. So, the same keyword might occur in different positions of the keyword list for different papers. In this situation, schemes with fixed-position keyword fields are not suitable for a keywords search. To overcome this problem, [PERSON] and [PERSON] introduced a public key encryption scheme called hidden vector encryption (HVE) which can support conjunctive keyword search without keyword field [6]. To achieve a better efficiency, a PECK scheme without keyword field was proposed in Reference [7]. In order to achieve advanced keywords search function, many SPE schemes which can support conjunctive or disjunctive keywords search have been proposed in recent years [8; 9; 10].