Eliminating decryption errors in the ajtai-dwork cryptosystem

Abstract

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 paper 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.