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Public-key encryption with keyword search (PEKS) is a versatile tool. It allows a third party knowing the search trapdoor of a keyword to search encrypted documents containing that keyword without decrypting the documents or knowing the keyword. However, it is shown that the keyword will be compromised by a malicious third party under a keyword guess attack (KGA) if the keyword space is in a polynomial size. We address this problem with a keyword privacy enhanced variant of PEKS referred to as public-key encryption with fuzzy keyword search (PEFKS). In PEFKS, each keyword corresponds to an exact keyword search trapdoor and a fuzzy keyword search trapdoor. Two or more keywords share the same fuzzy keyword trapdoor. To search encrypted documents containing a specific keyword, only the fuzzy keyword search trapdoor is provided to the third party, i.e., the searcher. Thus, in PEFKS, a malicious searcher can no longer learn the exact keyword to be searched even if the keyword space is small. We propose a universal transformation which converts any anonymous identity-based encryption (IBE) scheme into a secure PEFKS scheme. Following the generic construction, we instantiate the first PEFKS scheme proven to be secure under KGA in the case that the keyword space is in a polynomial size.