A Note on Ring-LWE Security in the Case of Fully Homomorphic Encryption

Evaluating the practical security of Ring-LWE based cryptography has attracted lots of efforts recently. Indeed, some differences from the standard LWE problem enable new attacks. In this paper we discuss the security of Ring-LWE as found in Fully Homomorphic Encryption (FHE) schemes. These schemes require parameters of very special shapes, that an attacker might use to its advantage. First we present the specificities of this case and recall state-of-the-art attacks, then we derive a new specialpurpose attack. Our experiments show that this attack has unexpected performance and confirm that we need to study the security of special parameters sets carefully.