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 $2$ on ciphertexts. In our scheme, we use constructions coming from \cite{F10,CF15}, to propose a variant of $\operatorname{BGN}$ scheme that can handle the homomorphic evaluation of polynomials of degree at most $4$. 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 encryptionpairing-based cryptographyelliptic curveslow 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}
}