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An Analysis of FV Parameters Impact Towards Its Hardware Acceleration

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Financial Cryptography and Data Security (FC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10323))

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Abstract

The development of cloud computing services is restrained by privacy concerns. Centralized medical services for instance, require a guarantee of confidentiality when using outsourced computation platforms. Fully Homomorphic Encryption is an intuitive solution to address such issue, but until 2009, existing schemes were only able to evaluate a reduced number of operations (Partially Homomorphic Encryption). In 2009, C. Gentry proposed a blueprint to construct FHE schemes from SHE schemes. However, it was not practical due to the huge data size overhead and the exponential noise growth of the initial SHE. Since then, major improvements have been made over SHE schemes and their noise management, and resulting schemes, like BGV and FV, allow to foresee small applications.

Besides scheme improvements, new practical approaches were proposed to bring homomorphic encryption closer to practice. The IV-based stream cipher trans-ciphering approach brought by Canteaut et al. in 2015 reduces the on-line latency of the trans-ciphering process to a simple homomorphic addition. The homomorphic evaluation of stream ciphers, that produces the trans-ciphering keystream, could be computed in an off-line phase, resulting in an almost transparent trans-ciphering process from the user point of view. This approach combined with hardware accelerations could bring homomorphic encryption closer to practice.

This paper deals the choice of FV parameters for efficient implementation of this scheme in the light of related works’ common approaches. At first sight, using large polynomial degree to reduce the coefficients size seemed to be advantageous, but further observations contradict it. Large polynomial degrees imply larger ciphertexts and more complex implementations, but smaller ones imply more primes to find for CRT polynomial representation. The result of this preliminary work for the choice of an adequate hardware target motivates the choice of small degree polynomials rather than small coefficients for the FV scheme.

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Authors and Affiliations

  1. CEA, LIST, 91191, Gif-sur-Yvette, France

    Joël Cathébras, Alexandre Carbon, Renaud Sirdey & Nicolas Ventroux

Authors
  1. Joël Cathébras
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  2. Alexandre Carbon
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  3. Renaud Sirdey
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  4. Nicolas Ventroux
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Correspondence to Joël Cathébras .

Editor information

Editors and Affiliations

  1. Leibniz Universität Hannover, Hannover, Germany

    Michael Brenner

  2. New Jersey Institute of Technology, Newark, New Jersey, USA

    Kurt Rohloff

  3. New York University, New York, New York, USA

    Joseph Bonneau

  4. University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

    Andrew Miller

  5. University of Luxembourg, Luxembourg, Luxembourg

    Peter Y.A. Ryan

  6. University of Melbourne, Parkville, Victoria, Australia

    Vanessa Teague

  7. University of Stirling, Stirling, United Kingdom

    Andrea Bracciali

  8. University of Trento, Trento, Italy

    Massimiliano Sala

  9. University of Trento, Trento, Italy

    Federico Pintore

  10. Agari Inc., San Mateo, California, USA

    Markus Jakobsson

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Cathébras, J., Carbon, A., Sirdey, R., Ventroux, N. (2017). An Analysis of FV Parameters Impact Towards Its Hardware Acceleration. In: Brenner, M., et al. Financial Cryptography and Data Security. FC 2017. Lecture Notes in Computer Science(), vol 10323. Springer, Cham. https://doi.org/10.1007/978-3-319-70278-0_6

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  • DOI: https://doi.org/10.1007/978-3-319-70278-0_6

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