# A Searchable Encryption with Forward/Backward Security and Constant Storage
## 1 Introduction  
With the development of network communication technologies such as 5G [1], Internet users choose to store local data in the cloud for use anywhere and anytime, while it is often believed that cloud servers are semi-trusted and sensitive data uploaded by users may create new security risks. Therefore, data users choose to encrypt their data locally before handing it over to cloud servers for hosting, and the ability to manipulate encrypted data stored on remote and untrustworthy servers is gradually becoming a basic need for users [2; 3]. [PERSON] et al. [4] first proposed the concept of searchable encryption (SE) by using a symmetric cryptosystem, which was used to solve the problem of ciphertext retrieval of data stored on the cloud server [5]. In a general searchable encryption algorithm, the data owner is responsible for encrypting and uploading the data, and the cloud server stores and retrieves the data ciphertext. The data user can perform an exact search by generating and submitting a search trapdoor. Symmetric searchable encryption is widely used due to its low computational overhead, among other reasons, but its key distribution is complicated, and its use is limited in some areas. To expand the application scope of searchable encryption techniques, [PERSON] et al. [6] proposed a searchable encryption scheme based on the public key cryptosystem. Early research on SE focused on static storage systems, in which users transfer encrypted documents to a cloud server and then generate trapdoors to send search requests to the server. Based on this model, numerous static searchable encryption schemes have been proposed [7; 8]. Due to the high overhead of public key searchable encryption in the algorithm construction process, many scholars havefocused on improving the efficiency of the algorithm [9; 10; 11; 12]. The computational overhead can be significantly reduced by reducing the operations of bilinear pairs in the trapdoor matching process, and the optimization in the storage structure can likewise lessen the system operation load. At present, the static SE scheme has been increasingly improved, but has also gradually revealed its shortcomings: the data in the cloud cannot be updated in a timely manner, and the system can only be reinitialized when there is an updated demand, which is problematic in practical use. To achieve real-time database updates in the cloud, more scholars have focused on dynamic searchable encryption (DSE), which is used to achieve real-time data updates in the cloud without reinitializing the algorithm. For better performance, usually, some data information is allowed to be leaked to the cloud server in DSE schemes [13; 14], and the leakage may occur during the algorithm initialization phase, as well as during the query algorithm, etc. Since updating the database may leak some information to the cloud server, DSE will bring a whole new challenge regarding data leakage. The possible leakage for dynamic, searchable encryption was first proposed by [PERSON] et al. [15] at the 2014 NDSS conference and formally defined by [PERSON] et al. [16]. Forward security [17; 18] means that no information about keywords will be leaked when performing update operations or that old search trapdoors cannot be used to search updated files; backward security [19] means that the search algorithm should not leak file identifiers that have been deleted, i.e., subsequent searches will not leak the index information corresponding to deleted files. [PERSON] et al. [20] propose a symmetric cryptography-based and efficiently searchable encryption scheme based on symmetric cryptography, with high I/O efficiency, which only satisfies the forward security, and still exhibits the risk of leakage for the keyword search algorithm that has been deleted. To solve the above problem, based on the work of [PERSON] et al. [16], [PERSON] et al. [17] and [PERSON] et al. [19] proposed schemes that also provide forward and backward security, with improvements in both operational efficiency and algorithm construction.