Fully Homomorphic Encryption for Point Numbers

Seiko Arita; Shota Nakasato

Paper 2016/402

Fully Homomorphic Encryption for Point Numbers

Seiko Arita and Shota Nakasato

Abstract

In this paper, based on the FV scheme, we construct a first fully homomorphic encryption scheme FHE4FX that can homomorphically compute addition and/or multiplication of encrypted fixed point numbers without knowing the secret key. Then, we show that in the FHE4FX scheme one can efficiently and homomorphically compare magnitude of two encrypted numbers. That is, one can compute an encryption of the greater-than bit that represents whether or not $x > x'$ given two ciphertexts $c$ and $c'$ (of $x$ and $x'$, respectively) without knowing the secret key. Finally we show that these properties of the FHE4FX scheme enables us to construct a fully homomorphic encryption scheme FHE4FL that can homomorphically compute addition and/or multiplication of encrypted floating point numbers.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: Fully homomorphic encryption FV scheme Fixed point number Floating point number Greater-than bit.
Contact author(s): arita @ iisec ac jp
History: 2016-04-25: received
Short URL: https://ia.cr/2016/402
License: CC BY

BibTeX

@misc{cryptoeprint:2016/402,
      author = {Seiko Arita and Shota Nakasato},
      title = {Fully Homomorphic Encryption for Point Numbers},
      howpublished = {Cryptology {ePrint} Archive, Paper 2016/402},
      year = {2016},
      url = {https://eprint.iacr.org/2016/402}
}