[Resource Topic] 2013/740: An efficient FHE proposal based on the hardness of solving systems of nonlinear multivariate equations (II)

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

Authors: 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.

ePrint: https://eprint.iacr.org/2013/740

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