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Computationally Volume-Hiding Structured Encryption

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Advances in Cryptology – EUROCRYPT 2019 (EUROCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11477))

Abstract

We initiate the study of structured encryption schemes with computationally-secure leakage. Specifically, we focus on the design of volume-hiding encrypted multi-maps; that is, of encrypted multi-maps that hide the response length to computationally-bounded adversaries. We describe the first volume-hiding STE schemes that do not rely on naïve padding; that is, padding all tuples to the same length. Our first construction has efficient query complexity and storage but can be lossy. We show, however, that the information loss can be bounded with overwhelming probability for a large class of multi-maps (i.e., with lengths distributed according to a Zipf distribution). Our second construction is not lossy and can achieve storage overhead that is asymptotically better than naïve padding for Zipf-distributed multi-maps. We also show how to further improve the storage when the multi-map is highly concentrated in the sense that it has a large number of tuples with a large intersection. We achieve these results by leveraging computational assumptions; not just for encryption but, more interestingly, to hide the volumes themselves. Our first construction achieves this using a pseudo-random function whereas our second construction achieves this by relying on the conjectured hardness of the planted densest subgraph problem which is a planted variant of the well-studied densest subgraph problem. This assumption was previously used to design public-key encryptions schemes (Applebaum et al., STOC ’10) and to study the computational complexity of financial products (Arora et al., ICS ’10).

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Notes

  1. 1.

    Our constructions also reveal the query equality—even to a bounded adversary—but the latter can be suppressed using the cache-based transform from [27].

  2. 2.

    The PBS construction has two variants. One can hide the response length on non-repeating sub-patterns but has a probability of failure in the sense that the client might not receive all its query responses. The second variant is always correct but reveals the sequence response length on non-repeating sub-patterns.

  3. 3.

    Kellaris, Kollios, Nissim and O’Neil show in [31] how to use differential privacy to perturb the response length in ORAM. This is different from this naïve approach which completely hides the response length.

  4. 4.

    The ranking function can be any ordering defined by the user; including standard ranking algorithms from information retrieval.

  5. 5.

    Note that the computation of the \(\mathsf {slide}_i\)’s is \(O(\nu )\). These evaluations can be performed once and stored at the client which reduces the total PRF evaluations at query time to 2t.

  6. 6.

    Note that one cannot use tree-based ORAM schemes such as Path ORAM [41] as the security is function of the size of the RAM. In our case, under realistic parameters, the bin’s load is very small to consider any of these schemes.

  7. 7.

    Note that the same multi-map encryption scheme \(\mathsf{STE}^\mathsf {RH}_\mathsf {EMM}= (\mathsf{Setup}, \mathsf{Get}, {\mathsf{Put}}, \mathsf {Remove})\) has to be used as the underlying multi-map encryption scheme for \(\mathsf {VLH} \).

  8. 8.

    Note that the same dictionary encryption scheme \(\mathsf{STE}^\mathsf {RH}_\mathsf {EDX}= (\mathsf{Setup}, \mathsf{Get}, {\mathsf{Put}}, \mathsf {Remove})\) has to be used as the underlying dictionary encryption scheme for \(\mathsf {AVLH} \).

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Authors and Affiliations

  1. Brown University, Providence, USA

    Seny Kamara & Tarik Moataz

Authors
  1. Seny Kamara
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  2. Tarik Moataz
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Correspondence to Seny Kamara .

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Editors and Affiliations

  1. Technion, Haifa, Israel

    Yuval Ishai

  2. COSIC Group, KU Leuven, Heverlee, Belgium

    Vincent Rijmen

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Kamara, S., Moataz, T. (2019). Computationally Volume-Hiding Structured Encryption. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11477. Springer, Cham. https://doi.org/10.1007/978-3-030-17656-3_7

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  • DOI: https://doi.org/10.1007/978-3-030-17656-3_7

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