Dynamic searchable symmetric encryption (DSSE) is a useful cryptographic tool in encrypted cloud storage. However, it has been reported that DSSE usually suffers from file-injection attacks and content leak of deleted documents. To mitigate these attacks, forward privacy and backward privacy have been proposed. Nevertheless, the existing forward backward-private DSSE schemes can only support single keyword queries. To address this problem, in this paper, we propose two DSSE schemes supporting range queries. One is forward-private and supports a large number of documents. The other can achieve backward privacy, while it can only support a limited number of documents. Finally, we also give the security proofs of the proposed DSSE schemes in the random oracle model.
Apart from the binary tree technique, order preserving encryption (OPE) can also be used to support range queries. The concept of OPE was proposed by @cite_17 , and it allows the order of the plaintexts to be preserved in the ciphertexts. It is easy to see that this kind of encryption would lead to the leakage in @cite_23 @cite_12 . To reduce this leakage, @cite_18 proposed another concept named order revealing encryption (ORE), where the order of the ciphertexts are revealed by using an algorithm rather than comparing the ciphertexts (in OPE) directly. More efficient ORE schemes were proposed later @cite_9 . However, ORE-based SSE still leaks much information about the underlying plaintexts. To avoid this, in this paper, we focus on how to use the binary tree structure to achieve range queries.
@cite_18 @cite_9 @cite_23 @cite_12 @cite_17
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We further the study of order-preserving symmetric encryption (OPE), a primitive for allowing efficient range queries on encrypted data, recently initiated (from a cryptographic perspective) by (Eurocrypt'09). First, we address the open problem of characterizing what encryption via a random order-preserving function (ROPF) leaks about underlying data (ROPF being the "ideal object" in the security definition, POPF, satisfied by their scheme.) In particular, we show that, for a database of randomly distributed plaintexts and appropriate choice of parameters, ROPF encryption leaks neither the precise value of any plaintext nor the precise distance between any two of them. The analysis here is quite technically non-trivial and introduces useful new techniques. On the other hand, we also show that ROPF encryption does leak both the value of any plaintext as well as the distance between any two plaintexts to within a range of possibilities roughly the square root of the domain size. We then study schemes that are not order-preserving, but which nevertheless allow efficient range queries and achieve security notions stronger than POPF. In a setting where the entire database is known in advance of key-generation (considered in several prior works), we show that recent constructions of "monotone minimal perfect hash functions" allow to efficiently achieve (an adaptation of) the notion of IND-O(rdered) CPA also considered by , which asks that only the order relations among the plaintexts is leaked. Finally, we introduce modular order-preserving encryption (MOPE), in which the scheme of is prepended with a shift cipher. MOPE improves the security of OPE in a sense, as it does not leak any information about plaintext location. We clarify that our work should not be interpreted as saying the original scheme of , or the variants that we introduce, are "secure" or "insecure." Rather, the goal of this line of research is to help practitioners decide whether the options provide a suitable security-functionality tradeoff for a given application. We initiate the cryptographic study of order-preserving symmetric encryption (OPE), a primitive suggested in the database community by (SIGMOD '04) for allowing efficient range queries on encrypted data. Interestingly, we first show that a straightforward relaxation of standard security notions for encryption such as indistinguishability against chosen-plaintext attack (IND-CPA) is unachievable by a practical OPE scheme. Instead, we propose a security notion in the spirit of pseudorandom functions (PRFs) and related primitives asking that an OPE scheme look "as-random-as-possible" subject to the order-preserving constraint. We then design an efficient OPE scheme and prove its security under our notion based on pseudorandomness of an underlying blockcipher. Our construction is based on a natural relation we uncover between a random order-preserving function and the hypergeometric probability distribution. In particular, it makes black-box use of an efficient sampling algorithm for the latter. We propose a multi-user Symmetric Searchable Encryption (SSE) scheme based on the single-user Oblivious Cross Tags (OXT) protocol (, CRYPTO 2013). The scheme allows any user to perform a search query by interacting with the server and any ( -1 ) ‘helping’ users, and preserves the privacy of database content against the server even assuming leakage of up to ( -1 ) users’ keys to the server (for a threshold parameter ( )), while hiding the query from the ( -1 ) ‘helping users’. To achieve the latter query privacy property, we design a new distributed key-homomorphic pseudorandom function (PRF) that hides the PRF input (search keyword) from the ‘helping’ key share holders. By distributing the utilized keys among the users, the need of constant online presence of the data owner to provide services to the users is eliminated, while providing resilience against user key exposure. As Cloud Computing becomes prevalent, sensitive information are being increasingly centralized into the cloud. For the protection of data privacy, sensitive data has to be encrypted before outsourcing, which makes effective data utilization a very challenging task. Although traditional searchable encryption schemes allow users to securely search over encrypted data through keywords, these techniques support only boolean search, without capturing any relevance of data files. This approach suffers from two main drawbacks when directly applied in the context of Cloud Computing. On the one hand, users, who do not necessarily have pre-knowledge of the encrypted cloud data, have to post process every retrieved file in order to find ones most matching their interest, On the other hand, invariably retrieving all files containing the queried keyword further incurs unnecessary network traffic, which is absolutely undesirable in today's pay-as-you-use cloud paradigm. In this paper, for the first time we define and solve the problem of effective yet secure ranked keyword search over encrypted cloud data. Ranked search greatly enhances system usability by returning the matching files in a ranked order regarding to certain relevance criteria (e.g., keyword frequency), thus making one step closer towards practical deployment of privacy-preserving data hosting services in Cloud Computing. We first give a straightforward yet ideal construction of ranked keyword search under the state-of-the-art searchable symmetric encryption (SSE) security definition, and demonstrate its inefficiency. To achieve more practical performance, we then propose a definition for ranked searchable symmetric encryption, and give an efficient design by properly utilizing the existing cryptographic primitive, order-preserving symmetric encryption (OPSE). Thorough analysis shows that our proposed solution enjoys as-strong-as-possible" security guarantee compared to previous SSE schemes, while correctly realizing the goal of ranked keyword search. Extensive experimental results demonstrate the efficiency of the proposed solution.