## Cryptology ePrint Archive: Report 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.

**Category / Keywords: **public-key cryptography /

**Date: **received 11 Nov 2013

**Contact author: **gavin at univ-lyon1 fr

**Available format(s): **PDF | BibTeX Citation

**Version: **20131117:010726 (All versions of this report)

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