Key Recovery Attacks Against NTRU-Based Somewhat Homomorphic Encryption Schemes

A key recovery attack allows an attacker to recover the private key of an underlying encryption scheme when given a number of decryption oracle accesses. Previous research has shown that most existing Somewhat Homomorphic Encryption (SHE) schemes suffer from this attack. In this paper, we propose efficient key recovery attacks against two NTRU-based SHE schemes, which have not gained much attention in the literature. One is published by Lopez-Alt et al. at STOC conference 2012 and the other is published by Bos et al. at the IMACC conference 2013. Parallel to our work, Dahab, Galbraith and Morais have also proposed similar attacks but only for specific parameter settings at ICITS conference 2015. In comparison, our attacks apply to all parameter settings and are more efficient than theirs.