Design and Implementation of Low Depth Pairing-based Homomorphic Encryption Scheme

Vincent Herbert; Bhaskar Biswas; Caroline Fontaine

Paper 2017/091

Design and Implementation of Low Depth Pairing-based Homomorphic Encryption Scheme

Vincent Herbert, Bhaskar Biswas, and Caroline Fontaine

Abstract

Homomorphic Encryption is a recent promising tool in modern cryptography, that allows to carry out operations on encrypted data. In this paper we focus on the design of a scheme based on pairings and elliptic curves, that is able to handle applications where the number of multiplication is not too high, with interesting practical efficiency when compared to lattice based solutions. The starting point is the Boneh-Goh-Nissim (BGN for short) encryption scheme \cite{BGN05}, which enables the homomorphic evaluation of polynomials of degree at most on ciphertexts. In our scheme, we use constructions coming from \cite{F10,CF15}, to propose a variant of scheme that can handle the homomorphic evaluation of polynomials of degree at most . We discuss both the mathematical structure of the scheme, and its implementation. We provide simulation results, showing the relevance of this solution for applications requiring a low multiplicative depth, and give relative comparison with respect to lattice based homomorphic encryption schemes.

Note: A new author, Bhaskar Biswas, joined us to compare our scheme with existing lattice-based schemes implementations.

Metadata

Available format(s): PDF
Publication info: Preprint. MAJOR revision.
Keywords: Homomorphic encryption pairing-based cryptography elliptic curves low depth circuits.
Contact author(s): vincent herbert @ cea fr
History: 2017-08-03: last of 4 revisions; 2017-02-10: received; See all versions
Short URL: https://ia.cr/2017/091
License: CC BY

BibTeX

@misc{cryptoeprint:2017/091,
      author = {Vincent Herbert and Bhaskar Biswas and Caroline Fontaine},
      title = {Design and Implementation of Low Depth Pairing-based Homomorphic Encryption Scheme},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/091},
      year = {2017},
      url = {https://eprint.iacr.org/2017/091}
}