Recently there has been much interest in performing search queries over encrypted data to enable functionality while protecting sensitive data. One particularly efficient mechanism for executing such queries is order-preserving encryption encoding (OPE) which results in ciphertexts that preserve the relative order of the underlying plaintexts thus allowing range and comparison queries to be performed directly on ciphertexts. Recently, (SP 2013) gave the first construction of an ideally-secure OPE scheme and Kerschbaum (CCS 2015) showed how to achieve the even stronger notion of frequency-hiding OPE. However, as (CCS 2015) have recently demonstrated, these constructions remain vulnerable to several attacks. Additionally, all previous ideal OPE schemes (with or without frequency-hiding) either require a large round complexity of O(log n) rounds for each insertion, or a large persistent client storage of size O(n), where n is the number of items in the database. It is thus desirable to achieve a range query scheme addressing both issues gracefully. In this paper, we propose an alternative approach to range queries over encrypted data that is optimized to support insert-heavy workloads as are common in "big data" applications while still maintaining search functionality and achieving stronger security. Specifically, we propose a new primitive called partial order preserving encoding (POPE) that achieves ideal OPE security with frequency hiding and also leaves a sizable fraction of the data pairwise incomparable. Using only O(1) persistent and O(ne) non-persistent client storage for 0
A related primitive to OPE is order-revealing encryption (ORE) @cite_48 , which provides a public mechanism for comparing two encrypted values and thus also enables range searches over encrypted data. (Note, OPE is the special case where this mechanism is lexicographic comparison,) The first construction of ORE satisfying security @cite_2 was based on multi-linear maps @cite_34 and is thus unlikely to be practical in the near future. An alternative scheme based only on pseudorandom functions @cite_35 , however, has additional leakage that weakens the achieved security.
@cite_48 @cite_34 @cite_35 @cite_2
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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. 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. 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.