In a lecture, by Chris Peikert (link 40:20), he showed more efficient cryptosystems that have the secret be drawn from the Gaussian error distribution $\chi$. In the lecture he said "some applications which really really need secrets to come from the error distribution and they don't really work so well if they come from uniform distribution" and he adds "for some strange reason this is the form is what gets you further in terms of building applications like Full Homomorphic Encryption (FHE)".
- Do we know today why this is the case?
- What efficiency does error distribution bring over a uniform one?
Edit: update the information