Paper 2013/740 Original: eprint.iacr.org/2013/740 ↗
An efficient FHE proposal based on the hardness of solving systems of nonlinear multivariate equations (II)
Abstract
We propose a general framework to develop fully homomorphic encryption schemes (FHE) without using Gentry's technique. Initially, a private-key cryptosystem is built over $\mathbb{Z}_n$ ($n$ being an RSA modulus). An encryption of $x\in \mathbb{Z}_n$ is a randomly chosen vector $e$ such that $\Phi(e)=x$ where $\Phi$ is a secret multivariate polynomial. This private-key cryptosystem is not homomorphic in the sense that the vector sum is not a homomorphic operator. Non-linear homomorphic operators are then developed. The security relies on the difficulty of solving systems of nonlinear equations (which is a $\mathcal{NP}$-complete problem). While the security of our scheme has not been reduced to a provably hard instance of this problem, its security is globally investigated.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2013-11-17: last updated
- 2013-11-17: published
- Short URL
- https://ia.cr/2013/740
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2013/740,
author = {Gérald Gavin},
title = {An efficient FHE proposal based on the hardness of solving systems of nonlinear multivariate equations (II)},
howpublished = {Cryptology {ePrint} Archive, Paper 2013/740},
year = {2013},
url = {https://eprint.iacr.org/2013/740}
}