Paper 2024/1112

HERatio: Homomorphic Encryption of Rationals using Laurent Polynomials

Luke Harmon, Algemetric
Gaetan Delavignette, Algemetric
Hanes Oliveira, Algemetric

In this work we present $\mathsf{HERatio}$, a homomorphic encryption scheme that builds on the scheme of Brakerski, and Fan and Vercauteren. Our scheme naturally accepts Laurent polynomials as inputs, allowing it to work with rationals via their bounded base-$b$ expansions. This eliminates the need for a specialized encoder and streamlines encryption, while maintaining comparable efficiency to BFV. To achieve this, we introduce a new variant of the Polynomial Learning With Errors (PLWE) problem which employs Laurent polynomials instead of the usual ``classic'' polynomials, and provide a reduction to the PLWE problem.

Note: Excluding correction of minor typos, this is the version which was initially submitted to ACISP 2024.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. 29th Australasian Conference on Information Security and Privacy (ACISP 2024)
homomorphic encryptionLaurent polynomialsrational numberspolynomial learning with errors
Contact author(s)
lharmon @ algemetric com
gdelavignette @ algemetric com
holiveira @ algemetric com
2024-07-10: approved
2024-07-08: received
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Creative Commons Attribution


      author = {Luke Harmon and Gaetan Delavignette and Hanes Oliveira},
      title = {{HERatio}: Homomorphic Encryption of Rationals using Laurent Polynomials},
      howpublished = {Cryptology ePrint Archive, Paper 2024/1112},
      year = {2024},
      note = {\url{}},
      url = {}
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