Efficient and Provable Security Searchable Asymmetric Encryption in the Cloud.

Cloud and remote storage, which has become the preferred method for reducing the security risk and safeguarding our data, is widely used for backups or outsourcing. Thus, for effective utilization of data, it is desirable to perform keyword queries directly over the encrypted data. In the single-data owner architecture, it is common to use symmetric encryption cryptography and allows only the holder who has the secret key to create searchable ciphertexts and trapdoors. In the multi-data owner (MDO) architecture, the scheme uses asymmetric encryption cryptography and allows anyone to create searchable ciphertexts under the public key, while the corresponding private key creates the trapdoors. In the real world, the data come from different providers. Thus, the MDO architecture may meet more applications. However, the existing solutions, in the MDO architecture, do not guarantee security for the trapdoors and provide only linear time search. In this paper, we present a comprehensive study of searching over encrypted data in the MDO architecture, and we propose a novel scheme that supports the inverted index structure, complex search, and dynamic update. After extensive analysis and several experiments, the results indicate that our proposed method is both efficient and secure. We believe that this is the first work that achieves trapdoor security and logarithmic time pairing free search over encrypted data in the MDO architecture.