Key Recovery Attacks Against NTRU-Based Somewhat Homomorphic Encryption Schemes

摘要

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 due to Lopez-Alt et al. (2012) and Bos et al. (2013), which have not gained much attention in the literature. Parallel to our work, Dahab, Galbraith and Morais (2015) have also proposed similar attacks but only for specific parameter settings. In comparison, our attacks apply to all parameter settings and are more efficient.