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Optimisations and Tradeoffs for HElib

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Topics in Cryptology – CT-RSA 2023 (CT-RSA 2023)

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Abstract

In this work, we investigate the BGV scheme as implemented in HElib. We begin by performing an implementation-specific noise analysis of BGV. This allows us to derive much tighter bounds than what was previously done. To confirm this, we compare our bounds against the state of the art. We find that, while our bounds are at most 1.8 bits off the experimentally observed values, they are as much as 29 bits tighter than previous work. Finally, to illustrate the importance of our results, we propose new and optimised parameters for HElib. In HElib, the special modulus is chosen to be k times larger than the current ciphertext modulus \(Q_i\). For a ratio of subsequent ciphertext moduli \(\log (\frac{Q_i}{Q_{i-1}}) = 54\) (a very common choice in HElib), we can optimise k by up to 26 bits. This means that we can either enable more multiplications without having to switch to larger parameters, or reduce the size of the evaluation keys, thus reducing on communication costs in relevant applications. We argue that our results are near-optimal.

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Acknowledgements

We would like to thank Leroy Odunlami for insightful discussions on statistics and probability theory.

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Authors and Affiliations

  1. Norwegian University of Science and Technology (NTNU), Trondheim, Norway

    Anamaria Costache & Lea Nürnberger

  2. Royal Holloway, University of London, London, UK

    Rachel Player

Authors
  1. Anamaria Costache
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  2. Lea Nürnberger
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  3. Rachel Player
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Corresponding author

Correspondence to Lea Nürnberger .

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Editors and Affiliations

  1. Oregon State University, Corvallis, OR, USA

    Mike Rosulek

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Costache, A., Nürnberger, L., Player, R. (2023). Optimisations and Tradeoffs for HElib. In: Rosulek, M. (eds) Topics in Cryptology – CT-RSA 2023. CT-RSA 2023. Lecture Notes in Computer Science, vol 13871. Springer, Cham. https://doi.org/10.1007/978-3-031-30872-7_2

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  • DOI: https://doi.org/10.1007/978-3-031-30872-7_2

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