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Polynomial Approximation of Inverse sqrt Function for FHE

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Cyber Security, Cryptology, and Machine Learning (CSCML 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13301))

Abstract

Inverse sqrt and sqrt function have numerous applications in linear algebra and machine learning such as vector normalisation, eigenvalue computation, dimensionality reduction, clustering, etc. This paper presents a method to approximate and securely perform the inverse sqrt function using CKKS homomorphic encryption scheme. Since the CKKS homomorphic scheme allows only computation of polynomial functions, we propose a method to approximate the inverse sqrt function polynomially. In the end, we provide an implementation of our method for the inverse sqrt function.

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Notes

  1. 1.

    We consider non-scalar multiplicative depth i.e. ciphertext-ciphertext multiplication.

  2. 2.

    By convergence we mean that the difference between the actual and predicted value is bounded by some predefined error.

References

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Author information

Authors and Affiliations

  1. International Institute of Information Technology, Hyderabad, Hyderabad, India

    Samanvaya Panda

Authors
  1. Samanvaya Panda
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Corresponding author

Correspondence to Samanvaya Panda .

Editor information

Editors and Affiliations

  1. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Shlomi Dolev

  2. University of Maryland, College Park, MD, USA

    Jonathan Katz

  3. Ben-Gurion University of the Negev, Be’er Sheva, Israel

    Amnon Meisels

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Panda, S. (2022). Polynomial Approximation of Inverse sqrt Function for FHE. In: Dolev, S., Katz, J., Meisels, A. (eds) Cyber Security, Cryptology, and Machine Learning. CSCML 2022. Lecture Notes in Computer Science, vol 13301. Springer, Cham. https://doi.org/10.1007/978-3-031-07689-3_27

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  • DOI: https://doi.org/10.1007/978-3-031-07689-3_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-07688-6

  • Online ISBN: 978-3-031-07689-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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