—In a searchable public-key encryption scheme with a designated tester (dPEKS), only the designated server can test which dPEKS ciphertext is related with a given trapdoor generated by a user with a keyword w by using the server’s private key, but learn nothing else. In this paper, we study the keyword guessing attack of dPEKS and shows that two dPEKS schemes are insecure against this type of attack. Then an enhanced scheme is proposed and proved secure against chosen keyword attack and keyword guessing attack. To resolve the problem that dPEKS scheme does not allow the user to decrypt the encrypted keyword which limits its applicability, we give the definition of decryptable searchable public key encryption with a designated tester which enables keyword decryption from keyword ciphertext and get a concrete construction based on our dPEKS scheme. At last, we extend the dPEKS scheme to a bidirectional searchable proxy re-encryption with a designated tester scheme(RedPEKS).
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