Gentry's breakthrough of Fully Homomorphic Encryption (FHE) in 2009 revolutionized the field of secure computation. Since then, most applications of homomorphic encryption have been oriented towards offloading computations to the cloud in a secure fashion. Indeed, the user usually does not have full confidence in the cloud provider and wants to keep its data secrecy. A similar situation appears in most embedded systems, where information leakages through hardware or software side-channel attacks might compromise data confidentiality. In this work, we attempt to leverage Homomorphic Encryption in a different threat model, adapted to CPS (Cyber-Physical Systems) use cases. The main challenge is that, even today's most promising FHE schemes remain orders of magnitude too big to fit in a constrained system. To address this issue, we show how a trade-off can be achieved by securing a noise reduction module against side-channel leakages. This approach is described and evaluated on FPGA using the BGV scheme, a very efficient homomorphic scheme based on Ring-LWE encryption. We conclude that such homomorphic encryption can fit in an embedded system, while offering reasonable performances with respect to the security provided.