Cryptology ePrint Archive: Report 2017/091

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

Vincent Herbert and 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.

Category / Keywords: Homomorphic encryption, pairing-based cryptography, elliptic curves, low depth circuits.

Date: received 6 Feb 2017, last revised 3 Aug 2017

Contact author: vincent herbert at cea fr

Available format(s): PDF | BibTeX Citation

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

Version: 20170803:140722 (All versions of this report)

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