International Association
for Cryptologic Research

In this paper we present adaptive key recovery attacks on NTRU-based somewhat homomorphic encryption schemes. Among such schemes, we study the proposal by Bos et al [BLLN13] in 2013. Given access to a decryption oracle, the attack allows us to compute the private key for all parameter choices. Such attacks show that one must be very careful about the use of homomorphic encryption in practice. The existence of a key recovery attack means that the scheme is not CCA1-secure. Indeed, almost every somewhat homomorphic construction proposed till now in the literature is vulnerable to an attack of this type. Hence our result adds to a body of literature that shows that building CCA1-secure homomorphic schemes is not trivial.