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Approximate Distance-Comparison-Preserving Symmetric Encryption

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Security and Cryptography for Networks (SCN 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13409))

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Abstract

We introduce distance-comparison-preserving symmetric encryption (DCPE), a new type of property-preserving encryption that preserves relative distance between plaintext vectors. DCPE is naturally suited for nearest-neighbor search on encrypted data. To boost security, we divert from prior work on Property Preserving Encryption (PPE) and ask for approximate comparison, which is natural given the prevalence of approximate nearest neighbor (ANN) search. We study what security approximate DCPE can provide and how to construct it.

Based on a relation we prove between approximate DCP and approximate distance-preserving functions, we design our core approximate DCPE scheme for Euclidean distance we call Scale-And-Perturb (\(\mathsf {SAP}\)). The encryption algorithm of our core scheme processes plaintexts on-the-fly. To further enhance security, we also introduce two preprocessing techniques: (1) normalizing the plaintext distribution, and (2) shuffling, wherein the component-wise encrypted dataset is randomly permuted. We prove that \(\mathsf {SAP}\) achieves a suitable indistinguishability-based security notion we call real-or-replaced indistinguishability (\(\mathsf {RoR}\)). In particular, our \(\mathsf {RoR}\) result implies that our scheme prevents a form of membership inference attack. Moreover, we show for i.i.d. multivariate normal plaintexts, we get security against approximate frequency-finding attacks, the main line of attacks against property-preserving encryption. This follows from a one-wayness \((\mathsf {OW})\) analysis. Finally, carefully combining our \(\mathsf {OW}\) and \(\mathsf {RoR}\) results, we are able characterize bit-security of \(\mathsf {SAP}\).

Overall, we find that our DCPE scheme not only has superior bit-security to Order Preserving Encryption (OPE) but resists relevant attacks that even ideal order-revealing encryption (Boneh et al., EUROCRYPT 2015) does not.

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Notes

  1. 1.

    Property-preserving encryption (PPE) is a special case that our construction actually falls into, but we stick with FRE terminology for generality.

  2. 2.

    In our terminology, it could also be called equality-preserving encryption.

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Authors and Affiliations

  1. TU Wien, Vienna, Austria

    Georg Fuchsbauer

  2. UCLA, Los Angeles, USA

    Riddhi Ghosal

  3. Georgetown University, Washington D.C., USA

    Nathan Hauke

  4. Manning College of Information and Computer Sciences, University of Massachusetts, Amherst, USA

    Adam O’Neill

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  1. Georg Fuchsbauer
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  2. Riddhi Ghosal
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  3. Nathan Hauke
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  4. Adam O’Neill
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Correspondence to Riddhi Ghosal .

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Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Clemente Galdi

  2. University of California at Irvine, Irvine, CA, USA

    Stanislaw Jarecki

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Fuchsbauer, G., Ghosal, R., Hauke, N., O’Neill, A. (2022). Approximate Distance-Comparison-Preserving Symmetric Encryption. In: Galdi, C., Jarecki, S. (eds) Security and Cryptography for Networks. SCN 2022. Lecture Notes in Computer Science, vol 13409. Springer, Cham. https://doi.org/10.1007/978-3-031-14791-3_6

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