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

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 [1], which enables the homomorphic evaluation of polynomials of degree at most 2 on ciphertexts. In our scheme, we use constructions coming from [2,3], to propose a variant of 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.