An efficient FHE proposal based on the hardness of solving systems of nonlinear multivariate equations (II)

Gérald Gavin

Paper 2013/740

An efficient FHE proposal based on the hardness of solving systems of nonlinear multivariate equations (II)

Gérald Gavin

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. MINOR revision.
Contact author(s): gavin @ univ-lyon1 fr
History: 2013-11-17: received
Short URL: https://ia.cr/2013/740
License: CC BY

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}
}