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Efficient Laconic Cryptography from Learning with Errors

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Advances in Cryptology – EUROCRYPT 2023 (EUROCRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14006))

Abstract

Laconic cryptography is an emerging paradigm that enables cryptographic primitives with sublinear communication complexity in just two messages. In particular, a two-message protocol between Alice and Bob is called laconic if its communication and computation complexity are essentially independent of the size of Alice’s input. This can be thought of as a dual notion of fully-homomorphic encryption, as it enables “Bob-optimized” protocols. This paradigm has led to tremendous progress in recent years. However, all existing constructions of laconic primitives are considered only of theoretical interest: They all rely on non-black-box cryptographic techniques, which are highly impractical.

This work shows that non-black-box techniques are not necessary for basic laconic cryptography primitives. We propose a completely algebraic construction of laconic encryption, a notion that we introduce in this work, which serves as the cornerstone of our framework. We prove that the scheme is secure under the standard Learning With Errors assumption (with polynomial modulus-to-noise ratio). We provide proof-of-concept implementations for the first time for laconic primitives, demonstrating the construction is indeed practical: For a database size of \(2^{50}\), encryption and decryption are in the order of single digit milliseconds.

Laconic encryption can be used as a black box to construct other laconic primitives. Specifically, we show how to construct:

  • Laconic oblivious transfer

  • Registration-based encryption scheme

  • Laconic private-set intersection protocol

All of the above have essentially optimal parameters and similar practical efficiency. Furthermore, our laconic encryption can be preprocessed such that the online encryption step is entirely combinatorial and therefore much more efficient. Using similar techniques, we also obtain identity-based encryption with an unbounded identity space and tight security proof (in the standard model).

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Notes

  1. 1.

    That is, independent or at least sublinear in n.

  2. 2.

    We denote the continuous Gaussian distribution with parameter \(\sigma \) by \(D_{\sigma }\), i.e. the probability density function of \(D_\sigma \) is proportional to \(e^{-\pi \frac{x^2}{\sigma ^2}}\).

  3. 3.

    [12] defined a similar notion of randomized \(\textbf{G} ^{-1}\), which however samples a discrete gaussian preimage.

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Acknowledgments

Nico Döttling and Chuanwei Lin: Funded by the European Union (ERC, LACONIC, 101041207). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. Giulio Malavolta and Ahmadreza Rahimi: This work was partially funded by the German Federal Ministry of Education and Research (BMBF) in the course of the 6GEM research hub under grant number 16KISK038 and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2092 CASA - 390781972. Dimitris Kolonelos: Received funding from projects from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under project PICOCRYPT (grant agreement No. 101001283), from the Spanish Government under project PRODIGY (TED2021-132464B-I00), and from the Madrid Regional Government under project BLOQUES (S2018/TCS-4339). The last two projects are co-funded by European Union EIE, and NextGenerationEU/PRTR funds.

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Authors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Nico Döttling & Chuanwei Lin

  2. IMDEA Software Institute, Madrid, Spain

    Dimitris Kolonelos

  3. Universidad Politecnica de Madrid, Madrid, Spain

    Dimitris Kolonelos

  4. Aalto University, Espoo, Finland

    Russell W. F. Lai

  5. Max Planck Institute for Security and Privacy, Bochum, Germany

    Giulio Malavolta & Ahmadreza Rahimi

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  1. Nico Döttling
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Correspondence to Russell W. F. Lai .

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  1. Bar-Ilan University, Ramat Gan, Israel

    Carmit Hazay

  2. Simula UiB, Bergen, Norway

    Martijn Stam

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Döttling, N., Kolonelos, D., Lai, R.W.F., Lin, C., Malavolta, G., Rahimi, A. (2023). Efficient Laconic Cryptography from Learning with Errors. In: Hazay, C., Stam, M. (eds) Advances in Cryptology – EUROCRYPT 2023. EUROCRYPT 2023. Lecture Notes in Computer Science, vol 14006. Springer, Cham. https://doi.org/10.1007/978-3-031-30620-4_14

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