User data security and privacy preserving has been becoming one of the most crucial issues in cloud computing environment, where cryptographic technologies are taken as a useful solution to achieve these goals. Nowadays, secure data searching and sharing and differential privacy preserving have attracted much more attention. This paper reviews the state-of-the-art in the field of ciphertext search, ciphertext sharing and differential privacy, and identifies their inappropriateness. Then, a series of recent research results in ciphertext search and ciphertext sharing are presented. In the respect of ciphertext search，this paper introduces the encrypted spatial keyword searth method, which achieves lightweight access control and efficient keyword search. In the respect of ciphertext sharing, this paper proposes the cross-cryptosystem fine-grained data sharing scheme, in which a data owner can formulate an access policy such that the part of encrypted data satisfying the access policy can be shared with the users in a different cryptosystem. Finally, this paper provides several open research issues and the trend in the future.