Encodings for Range Majority Queries

Navarro, Gonzalo; Thankachan, Sharma V.

doi:10.1007/978-3-319-07566-2_27

Cited by 3 publications

(2 citation statements)

References 16 publications

(41 reference statements)

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“…Several solutions have been proposed that solve the approximate range mode problem with varying degrees of efficiency. Many of these schemes use bit-packing techniques that, as explained previously, we can not directly translate to STE structures (e.g., [33,52]) or rely on theoretical data structures with no practical implementation (e.g., [23]). Additionally, while some recent schemes achieve lower storage requirements than our chosen approach, their query algorithms require non-constant query time (e.g., [23]).…”

Section: Range Mode Querymentioning

confidence: 99%

Time- and Space-Efficient Aggregate Range Queries over Encrypted Databases

Espiritu

Markatou

Tamassia

2022

PoPETs

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We present ARQ, a systematic framework for creating cryptographic schemes that handle range aggregate queries (sum, minimum, median, and mode) over encrypted datasets. Our framework does not rely on trusted hardware or specialized cryptographic primitives such as property-preserving or homomorphic encryption. Instead, ARQ unifies structures from the plaintext data management community with existing structured encryption primitives. We prove how such combinations yield efficient (and secure) constructions in the encrypted setting. We also propose a series of domain reduction techniques that can improve the space efficiency of our schemes against sparse datasets at the cost of small leakage. As part of this work, we designed and implemented a new, open-source, encrypted search library called Arca and implemented the ARQ framework using this library in order to evaluate ARQ’s practicality. Our experiments on real-world datasets demonstrate the efficiency of the schemes derived from ARQ in comparison to prior work.

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Section: Range Mode Querymentioning

confidence: 99%

Time- and Space-Efficient Aggregate Range Queries over Encrypted Databases

Espiritu

Markatou

Tamassia

2022

PoPETs

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“…In our previous work [20], we had obtained O((1/τ ) log n) time, but using O((n/τ ) log * n) bits of space. It is not hard to obtain that time, using O(n/τ ) bits, by simply representing the coalesced bitmaps M ′ using plain rank/select structures [8,18], or even using O(n log(1/τ ) + (n/τ )/ polylog n) bits, for any polylog n, using compressed representations [24].…”

Section: Reducing the Space To O(n Log(1/τ )) Bitsmentioning

confidence: 99%

Optimal Encodings for Range Majority Queries

Navarro

Thankachan

2015

Algorithmica

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We revisit the range τ-majority problem, which asks us to preprocess an array A[1..n] for a fixed value of τ ∈ (0, 1/2], such that for any query range [i, j] we can return a position in A of each distinct τ-majority element. A τ-majority element is one that has relative frequency at least τ in the range [i, j]: i.e., frequency at least τ (j − i + 1). Belaz-zougui et al. [WADS 2013] presented a data structure that can answer such queries in O(1/τ) time, which is optimal, but the space can be as much as Θ(n lg n) bits. Recently, Navarro and Thankachan [Algorithmica 2016] showed that this problem could be solved using an O(n lg(1/τ)) bit encoding, which is optimal in terms of space, but has suboptimal query time. In this paper, we close this gap and present a data structure that occupies O(n lg(1/τ)) bits of space, and has O(1/τ) query time. We also show that this space bound is optimal, even for the much weaker query in which we must decide whether the query range contains at least one τ-majority element.

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