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security, although these schemes are still not semantically secure. So far, deterministic PEKS schemes can guarantee semantic security only if the keyword space has a high min-entropy. Otherwise, an adversary can extract the encrypted keyword by a simple encrypt-and-test attack. Hence, deterministic PEKS schemes are applicable to applications where the keyword space is of a high min-entropy. III. PROBLEM DEFINITION One of the prominent works to accelerate the search over encrypted keywords in the public-key setting is deterministic encryption introduced by Bellare et al. An encryption scheme is deterministic if the encryption algorithm is deterministic. Bellare et al. focus on enabling search over encrypted keywords to be as efficient as the search for unencrypted keywords, such that a ciphertext containing a given keyword can be retrieved in time complexity logarithmic in the total number of all ciphertexts. This is reasonable because the encrypted keywords can form a tree-like structure when stored according to their binary values. Search on encrypted data has been extensively investigated in recent years. From a cryptographic perspective, the existing works fall into two categories, i.e., symmetric searchable encryption and public-key searchable encryption. The disadvantages of the system is, Existing semantically secure PEKS schemes take search time linear with the total number of all cipher texts. This makes retrieval from large-scale databases prohibitive. Therefore,

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