A Lattice Attack on Homomorphic NTRU with Non-invertible Public Keys

초록

In 2011, Stehle and Steinfeld modified the original NTRU to get a provably IND-CPA secure NTRU under the hardness assumption of standard worst-case problems over ideal lattices. In 2012, Lopez-Alt et al. proposed the first multikey fully homomorphic encryption scheme based on the IND-CPA secure NTRU. Interestingly, this homomorphic NTRU and subsequent homomorphic variants of NTRU removed the condition 'invertible public key' of the underlying IND-CPA secure NTRU. In this paper, we investigate the security influence of using non-invertible public key in the homomorphic NTRU. As a result, we present how to mount a lattice attack to message recovery for the homomorphic NTRU when the public key is non-invertible. Our result suggests that using invertible public keys in the homomorphic NTRU is necessary for its security.

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