Following Ajtai's lead, Ajtai and Dwork have recently introduced a
public-key encryption scheme which is secure under the assumption
that a certain computational problem on lattices is hard on the
worst-case. Their encryption method may cause decryption errors,
though with small probability (i.e., inversely proportional to the
security parameter).
In this note we modify the encryption method of Ajtai and Dwork
so that the legitimate receiver always recovers the message sent.
That is, we make the Ajtai-Dwork Cryptosystem error-free.