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Large Scale, Actively Secure Computation from LPN and Free-XOR Garbled Circuits

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Advances in Cryptology – EUROCRYPT 2021 (EUROCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12698))

Abstract

We (MPC) protocol based on garbled circuits which is both actively secure and supports the free-XOR technique, and which has communication complexity O(n) per party. This improves on a protocol of Ben-Efraim, Lindell and Omri which only achieved passive security, without support for free-XOR. Our construction is based on a new variant of LPN-based encryption, but has the drawback of requiring a rather expensive garbling phase. To address this issue we present a second protocol that assumes at least n/c of the parties are honest (for an arbitrary fixed value c). This second protocol allows for a significantly lighter preprocessing, at the cost of a small sacrifice in online efficiency. We demonstrate the practicality of our evaluation phase with an implementation.

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Notes

  1. 1.

    The complexity can be reduced to O(1) for all but one of the parties in SPDZ-like protocols by ‘opening’ being performed in a king-followers fashion: Followers send their shares to the king, who then replies to all followers with the reconstructed value (hence O(n) complexity for the king). For more details, see e.g. [15].

  2. 2.

    This increase in complexity is due to parties still needing to reconstruct the circuit and send their masked inputs around.

  3. 3.

    If the requirement does not hold, then this operation needs to be done using Tiny-OT directly as in [22]. Hence, this optimization is mainly for large-scale MPC.

  4. 4.

    For simplicity, we assume the message space is at least \(|\hat{{\mathcal P}}| \cdot s\) bits long. If the message space was only of \(|\hat{{\mathcal P}}| \cdot s/ r\) bits, one would compute r ciphertext, each of them with the \(\xi ^i\) values of \(|\hat{{\mathcal P}}| / r\) parties.

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Acknowledgements

This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contract No. N66001-15-C-4070, FA8750-19-C-0502 and HR001120C0085, by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA) via Contract No. 2019-1902070006, by the FWO under an Odysseus project GOH9718N, and by CyberSecurity Research Flanders with reference number VR20192203. Eduardo Soria-Vazquez was supported by the Carlsberg Foundation under the Semper Ardens Research Project CF18-112 (BCM). Aner Ben-Efraim and Eran Omri were supported by ISF grant 152/17, and by the Ariel Cyber Innovation Center in conjunction with the Israel National Cyber directorate in the Prime Minister’s Office.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of any of the funders. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.

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Authors and Affiliations

  1. imec-COSIC, KU Leuven, Leuven, Belgium

    Kelong Cong, Emmanuela Orsini & Nigel P. Smart

  2. Department of Computer Science, Ariel Univeristy, Ariel, Israel

    Aner Ben-Efraim & Eran Omri

  3. Department of Computer Science, University of Bristol, Bristol, UK

    Nigel P. Smart

  4. Department of Computer Science, Aarhus University, Aarhus, Denmark

    Eduardo Soria-Vazquez

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  1. Aner Ben-Efraim
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  2. Kelong Cong
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  3. Eran Omri
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  4. Emmanuela Orsini
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  6. Eduardo Soria-Vazquez
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Correspondence to Aner Ben-Efraim .

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  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Ben-Efraim, A., Cong, K., Omri, E., Orsini, E., Smart, N.P., Soria-Vazquez, E. (2021). Large Scale, Actively Secure Computation from LPN and Free-XOR Garbled Circuits. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12698. Springer, Cham. https://doi.org/10.1007/978-3-030-77883-5_2

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