Abstract

The landscape of Fully Homomorphic Encryption (FHE) has known great changes these past six years. As computational costs drop, libraries are developed and new applications become possible. Prototypes demonstrating private health diagnosis, signal processing, genome statistics and database queries spur hope on the practical deployment of FHE in the near future. However, in most of these applications, increasing the privacy, security or enabling new functionalities comes in pair with some significant computation and/or communication burden.

In this work, we depart from the latter paradigm and demonstrate that FHE might be useful to increase the practical performance of elliptic-curve cryptography. More precisely, we show how to reduce the computational burden of computing elliptic-curve points from a generator through delegation. We show that using homomorphic encryption it is possible to reduce in practice computational costs even with respect to traditional, not based on homomorphic-encryption, delegation protocols. We demonstrate the feasibility of our protocols with proof-of-concept implementations using HElib (adapted to handle multiprecision plaintext space moduli).

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Bibtex

@inproceedings{SPC:ADGLR18,
  title={Delegating Elliptic-Curve Operations with Homomorphic Encryption},
  author={Aguilar-Melchor, Carlos and Deneuville, {Jean-Christophe} and Gaborit, Philippe and Lepoint, Tancrede and Ricosset, Thomas},
  booktitle={2018 IEEE Conference on Communications and Network Security (CNS)},
  pages={1--9},
  year={2018},
  organization={IEEE}
}