## Cryptology ePrint Archive: Report 2013/262

An efficient FHE based on the hardness of solving systems of non-linear multivariate equations

Gérald Gavin

Abstract: We propose a general framework to develop fully homomorphic encryption schemes (FHE) without using the Gentry's technique. The security relies on the difficulty of solving systems of non-linear 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, security is globally investigated.

Category / Keywords: FHE, homomorphic cryptosystem

Date: received 8 May 2013, last revised 19 May 2013

Contact author: gavin at univ-lyon1 fr

Available format(s): PDF | BibTeX Citation

Note: In this second version, Problem 1 and Problem 2 are slightly modified (see Section 2). The symmetric functions s_j should be constrained to be polynomials : this is needed In the proof of Proposition 1 to ensure that s_j(y_1,y_2,....)=s_j(y_2',y_1',...).

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