Paper 2017/091

Software Implementation of 2-Depth Pairing-based Homomorphic Encryption Scheme

Vincent Herbert and Caroline Fontaine

Abstract

We propose a software implementation of a variant of Boneh-Goh-Nissim scheme \cite{BGN05} with multiplicative depth $2$, {whereas the original one only tackled multiplicative depth $1$}. We employ together two improvements of the original scheme, based on \cite{Freeman10,Catalano15}. We give a full description of the resulting scheme, denoted $\operatorname{BGN2}$, where encryption is performed bitwise. In this scheme, the homomorphic multiplication asks to compute pairings. We chose to compute an optimal Ate pairing over an elliptic curve in the Barreto-Naehrig curve family \cite{Barreto05} using a library called $\operatorname{DCLXVI}$ \cite{Naehrig10}. We provide simulation results, showing the interest of this solution for applications requiring a low multiplicative depth.