The FHE (fully homomorphic encryption) schemes [7, 13] based on the modified AGCD problem (noise-free AGCD problem) are vulnerable to quantum attacks, because its security relies partly on the hardness of factoring, and some FHE schemes based on the decisional AGCD without the noise-free assumption, for example [1], has a drawback that its ciphertexts are very large.
In this paper, we construct a new batch FHE scheme based on the decisional AGCD problem to overcome these weaknesses and prove its security