International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 21 August 2015

Gérald Gavin
ePrint Report ePrint Report
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.

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