Original sentence: The setting of parameters used in proofs of correctness and security is
Edited sentence: Although the above works for any , the disadvantage of this construction is that for creating a cryptosystem, the  have to be polynomial in.Regev shows that there is a reduction from  to.Regev then shows that there exists a efficient quantum algorithm for  given access to an oracle for  for integer  and  such that.The goal is to output a sample from.The setting ofn parameters used in proofs of correctness and security is.Then the discrete Gaussian sampling problem(DGS) is defined as follows: An instance of  is given by an -dimensional lattice  and a number.This implies the hardness for