Paper 2017/333

Faster Homomorphic Function Evaluation using Non-Integral Base Encoding

Charlotte Bonte, Carl Bootland, Joppe W. Bos, Wouter Castryck, Ilia Iliashenko, and Frederik Vercauteren


In this paper we present an encoding method for fixed-point numbers tailored for homomorphic function evaluation. The choice of the degree of the polynomial modulus used in all popular somewhat homomorphic encryption schemes is dominated by security considerations, while with the current encoding techniques the correctness requirement allows for much smaller values. We introduce a generic encoding method using expansions with respect to a non-integral base, which exploits this large degree at the benefit of reducing the growth of the coefficients when performing homomorphic operations. In practice this allows one to choose a smaller plaintext coefficient modulus which results in a significant reduction of the running time. We illustrate our approach by applying this encoding in the setting of homomorphic electricity load forecasting for the smart grid which results in a speed-up by a factor 13 compared to previous work, where encoding was done using balanced ternary expansions.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
Contact author(s)
wouter castryck @ gmail com
2017-04-18: received
Short URL
Creative Commons Attribution


      author = {Charlotte Bonte and Carl Bootland and Joppe W.  Bos and Wouter Castryck and Ilia Iliashenko and Frederik Vercauteren},
      title = {Faster Homomorphic Function Evaluation using Non-Integral Base Encoding},
      howpublished = {Cryptology ePrint Archive, Paper 2017/333},
      year = {2017},
      note = {\url{}},
      url = {}
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