An Efficient and Secure Public Key Authenticated Encryption With Keyword Search in the Logarithmic Time

Searchable encryption is an important cryptographic technique that achieves data security and keyword retrieval over encrypted data in cloud. In 2004, Boneh et.al proposed the first searchable encryption scheme based on asymmetric cryptography. Since then, many variants of public key searchable encryption schemes were proposed. However, most previous works are vulnerable to multi-ciphertext attack, and they cannot provide trapdoor indistinguishability. Another problem is how to improve the searching efficiency. To deal with two issues, we construct a fast and secure public key authenticated searchable encryption scheme with designed server. Our scheme can resist keyword guessing attacks, chosen multi-keyword attacks and multi-trapdoor attacks. The search function in our scheme achieves the logarithmic search time in number of keywords while most existing schemes required the linear time. By comparison with previous schemes in computational complexity, our scheme is very fast in keyword search.