Existing semantically secure public-key searchable encryption schemes take search time linear with the total number of the ciphertexts. This makes retrieval from large-scale databases prohibitive. To alleviate this problem, this paper proposes searchable public-key ciphertexts with hidden structures (SPCHS) for keyword search as fast as possible without sacrificing semantic security of the encrypted keywords. In SPCHS, all keyword-searchable ciphertexts are structured by hidden relations, and with the search trapdoor corresponding to a keyword, the minimum information of the relations is disclosed to a search algorithm as the guidance to find all matching ciphertexts efficiently. We construct an SPCHS scheme from scratch in which the ciphertexts have a hidden star-like structure. We prove our scheme to be semantically secure in the random oracle (RO) model. The search complexity of our scheme is dependent on the actual number of the ciphertexts containing the queried keyword, rather than the number of all ciphertexts. Finally, we present a generic SPCHS construction from anonymous identity-based encryption and collision-free full-identity malleable identity-based key encapsulation mechanism (IBKEM) with anonymity. We illustrate two collision-free full-identity malleable IBKEM instances, which are semantically secure and anonymous, respectively, in the RO and standard models. The latter instance enables us to construct an SPCHS scheme with semantic security in the standard model.
Following the seminal work on PEKS, Abdalla. @cite_24 fills some gaps w.r.t. consistency for PEKS and deals with the transformations among primitives related to PEKS. Some efforts have also been devoted to make PEKS versatile. The work of this kind includes conjunctive search @cite_17 @cite_18 @cite_27 @cite_26 @cite_20 @cite_39 , range search @cite_41 @cite_28 @cite_8 , subset search @cite_8 , time-scope search @cite_24 @cite_40 , similarity search @cite_31 , authorized search @cite_47 @cite_30 , equality test between heterogeneous ciphertexts @cite_4 , and fuzzy keyword search @cite_9 . In addition, @cite_37 proposed a PEKS scheme to keep the privacy of keyword search trapdoors.
@cite_30 @cite_18 @cite_26 @cite_47 @cite_4 @cite_37 @cite_8 @cite_41 @cite_28 @cite_9 @cite_39 @cite_24 @cite_27 @cite_40 @cite_31 @cite_20 @cite_17
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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. We identify and fill some gaps with regard to consistency (the extent to which false positives are produced) for public-key encryption with keyword search (PEKS). We define computational and statistical relaxations of the existing notion of perfect consistency, show that the scheme of [7] is computationally consistent, and provide a new scheme that is statistically consistent. We also provide a transform of an anonymous IBE scheme to a secure PEKS scheme that, unlike the previous one, guarantees consistency. Finally we suggest three extensions of the basic notions considered here, namely anonymous HIBE, public-key encryption with temporary keyword search, and identity-based encryption with keyword search. Asymmetric searchable encryption allows searches to be carried over ciphertexts, through delegation, and by means of trapdoors issued by the owner of the data. Public Key Encryption with Keyword Search (PEKS) is a primitive with such functionality that provides delegation of exact-match searches. As it is important that ciphertexts preserve data privacy, it is also important that trapdoors do not expose the user’s search criteria. The difficulty of formalizing a security model for trapdoor privacy lies in the verification functionality, which gives the adversary the power of verifying if a trapdoor encodes a particular keyword. In this paper, we provide a broader view on what can be achieved regarding trapdoor privacy in asymmetric searchable encryption schemes, and bridge the gap between previous definitions, which give limited privacy guarantees in practice against search patterns. Since it is well-known that PEKS schemes can be trivially constructed from any Anonymous IBE scheme, we propose the security notion of Key Unlinkability for IBE, which leads to strong guarantees of trapdoor privacy in PEKS, and we construct a scheme that achieves this security notion. We present two provably secure and efficient schemes for performing conjunctive keyword searches over symmetrically encrypted data. Our first scheme is based on Shamir Secret Sharing and provides the most efficient search technique in this context to date. Although the size of its trapdoors is linear in the number of documents being searched, we empirically show that this overhead remains reasonable in practice. Nonetheless, to address this limitation we provide an alternative based on bilinear pairings that yields constant size trapdoors. This latter construction is not only asymptotically more efficient than previous secure conjunctive keyword search schemes in the symmetric setting, but incurs significantly less storage overhead. Additionally, unlike most previous work, our constructions are proven secure in the standard model.