Paper 2014/813
Boosting Linearly-Homomorphic Encryption to Evaluate Degree-2 Functions on Encrypted Data
Dario Catalano and Dario Fiore
Abstract
We show a technique to transform a linearly-homomorphic encryption into a homomorphic encryption scheme capable of evaluating degree-2 computations on ciphertexts. Our transformation is surprisingly simple and requires only one very mild property on the underlying linearly-homomorphic scheme: the message space must be a public ring in which it is possible to sample elements uniformly at random. This essentially allows us to instantiate our transformation with virtually all existing number-theoretic linearly-homomorphic schemes, such as Goldwasser-Micali, Paillier, or ElGamal. Our resulting schemes achieve circuit privacy and are compact when considering a subclass of degree-2 polynomials in which the number of additions of degree-2 terms is bounded by a constant. As an additional contribution we extend our technique to build a protocol for outsourcing computation on encrypted data using two (non-communicating) servers. Somewhat interestingly, in this case we can boost a linearly-homomorphic scheme to support the evaluation of any degree-2 polynomial while achieving full compactness.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- homomorphic encryption
- Contact author(s)
- dario fiore @ imdea org
- History
- 2014-10-11: received
- Short URL
- https://ia.cr/2014/813
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2014/813,
author = {Dario Catalano and Dario Fiore},
title = {Boosting Linearly-Homomorphic Encryption to Evaluate Degree-2 Functions on Encrypted Data},
howpublished = {Cryptology {ePrint} Archive, Paper 2014/813},
year = {2014},
url = {https://eprint.iacr.org/2014/813}
}
