Ajtai and Dwork have introduced a probabilistic public-key encryption scheme which is secure under the assumption that a certain computational problem on lattices is hard on the worst-case. In this paper, the author demonstrates how Ajtai-Dwork cryptosystem can be abused. Using this kind of abuses, users can communicate secrets in a key escrowed Ajtai-Dwork cryptosystem without fearing that their secrets will be revealed later by reconstructing their escrowed private-keys. However, it is also shown that users have to trust their implementers because unscrupulous implementers of Ajtai-Dwork cryptosystem may leak their private-keys without their awareness. The author shows how one can make Ajtai-Dwork cryptosystem abuse-free.