In lattice cryptography, we always face the probem of discrete gaussian sampling. To the beginners, it is a bit complex. However, gaussian sampling from a continous space is much easier to understand, and a lot of tools are available. Say, we can use MATLAB to do gaussian sampling very efficiently. So, I want to know what is the difference between the following to process:
(1) discrete-then-gaussian: Just as required is many lattice cryptography papers.
(2) gaussian-then-discrete: At first, get continous gaussian samples, say by using MATLAB, and then perform nearest rounding operations, i.e., discrete to the nearest integers.