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In the cloud, users prefer to store their sensitive data in encrypted form. Searching keywords over encrypted data without loss of data confidentiality is an important issue. In 2004, Boneh et al. proposed the first public-key searchable encryption scheme which allows users to search by the private key. However, most existing public-key searchable encryption schemes are vulnerable to keyword guessing attack and can not satisfy multi-ciphertext indistinguishability. In this paper, we construct a secure designated server public-key searchable encryption based on Diffie-Hellman problem. Our security analysis shows that our proposed scheme can resist against keyword guessing attack and provide multi-ciphertext indistinguishability for any adversity. Furthermore, the proposed scheme can achieve multi-trapdoor privacy for external attackers. Moreover, the simulation results between our scheme and previous schemes demonstrate our new scheme is suitable for practical application.

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