A general framework for building noise-free homomorphic cryptosystems

Abstract

We present a general framework for developing and analyzing homomorphic cryptosystems whose security relies on the difficulty of solving systems of nonlinear equations over Z/nZ, n being an RSA modulus. In this framework, many homomorphic cryptosystems can be conceptualized. Based on symmetry considerations, we propose a general assumption that ensures the security of these schemes. To highlight this, we present an additive homomorphic private-key cryptosystem and we prove its security. Finally, we propose two motivating perspectives of this work. We first propose an FHE based on the previous scheme by defining a simple multiplicative operator. Secondly, we propose ways to remove the factoring assumption in order to get pure multivariate schemes