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Encapsulated Search Index: Public-Key, Sub-linear, Distributed, and Delegatable

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Public-Key Cryptography – PKC 2022 (PKC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13178))

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Abstract

We build the first sub-linear (in fact, potentially constant-time) public-key searchable encryption system:

  • server can publish a public key PK.

  • anybody can build an encrypted index for document D under PK.

  • client holding the index can obtain a token \(z_w\) from the server to check if a keyword w belongs to D.

  • search using \(z_w\) is almost as fast (e.g., sub-linear) as the non-private search.

  • server granting the token does not learn anything about the document D, beyond the keyword w.

  • yet, the token \(z_w\) is specific to the pair (D, w): the client does not learn if other keywords \(w'\ne w\) belong to D, or if w belongs to other, freshly indexed documents \(D'\).

  • server cannot fool the client by giving a wrong token \(z_w\).

We call such a primitive Encapsulated Search Index (ESI). Our ESI scheme can be made (t, n)-distributed among n servers in the best possible way: non-interactive, verifiable, and resilient to any coalition of up to \((t-1)\) malicious servers. We also introduce the notion of delegatable ESI and show how to extend our construction to this setting.

   Our solution — including public indexing, sub-linear search, delegation, and distributed token generation — is deployed as a commercial application by a real-world company.

Y. Dodis–Partially supported by gifts from VMware Labs and Google, and NSF grants 1619158, 1319051, 1314568.

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Notes

  1. 1.

    In fact, our solution will allow for generating secure indices even outside the Desktop, possibly by different parties. But for simplicity, we discuss the already interesting setting where Alice herself generates indices on the Desktop.

  2. 2.

    ESI is the first searchable encryption primitive to do so; see Sect. 1.3.

  3. 3.

    As other prior distributed VRFs were either interactive [23, 33], or had no verifiability [2, 36] or offered no formal model/analysis [16, 17, 21, 32, 41].

  4. 4.

    E.g., we cannot use the interactive threshold Cramer-Shoup [19] construction of [13].

  5. 5.

    From an application perspective, universal and document-specific setting are incomparable, as some application might want to restrict which keywords are allowed for different databases. On a technical level, however, a universal scheme can always be converted to a document-specific one, by prefixing the keyword with the name of the document D. Thus, universal searching is more powerful.

  6. 6.

    Unfortunately, as surveyed by Cash et al. [14] and further studied by [20, 31] (and others), all SSE schemes in the literature do not achieve the strongest possible keyword privacy and suffer from various forms of information leakage.

  7. 7.

    It is easy to see that our syntax guarantees that any ESI construction is unconditionally Privacy-Preserving (even with knowledge of SK), for the simple reason that \( \textsc {Prep}\) that produces c does not depend on the input document D. Thus, we will never explicitly address this property, but list it for completeness, as it is important for our motivating application.

  8. 8.

    The algorithm \( \textsc {Split}\) is not technically needed, as one can always set \(R=C\). In fact, this will be the case for our EVRF in Sect. 5.1. However, one could envision EVRF constructions where the \( \textsc {Split}\) procedure can do a non-trivial (input-independent) part of the overall \( {\textsc {Prove}}= \textsc {Core}( \textsc {Split})\) procedure, and without the need to know the secret key SK. This will be the case for some of the delegatable EVRFs we consider in Sect. 7.1.

  9. 9.

    Without loss of generality, we will always assume that all the t partial evaluations \(z_i'\) satisfy \( \textsc {Shr}\hbox {-}\textsc {Vfy}(PK,vk_i,z_i')= 1\) (else, we output \(\bot \) before calling \( \textsc {Combine}\)). See also the definition of \( {\textsc {Eval}}\) below to explicitly model this assumption.

  10. 10.

    Of course, the indexing step is proportional to the size of the file.

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Authors and Affiliations

  1. Atakama, Atakama, Chile

    Erik Aronesty, Daniel H. Gallancy, Christopher Higley & Oren Tysor

  2. University of Chicago, Chicago, USA

    David Cash

  3. New York University, New York City, USA

    Yevgeniy Dodis & Harish Karthikeyan

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  1. Erik Aronesty
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Correspondence to Harish Karthikeyan .

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  1. National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan

    Goichiro Hanaoka

  2. Yokohama National University, Yokohama, Japan

    Junji Shikata

  3. The University of Electro-Communications, Tokyo, Japan

    Yohei Watanabe

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Aronesty, E. et al. (2022). Encapsulated Search Index: Public-Key, Sub-linear, Distributed, and Delegatable. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds) Public-Key Cryptography – PKC 2022. PKC 2022. Lecture Notes in Computer Science(), vol 13178. Springer, Cham. https://doi.org/10.1007/978-3-030-97131-1_9

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