# Centrality of Gaussian distribution for LWE error

Consider the LWE problem.

Let $$A$$ be an $$m \times n$$ matrix, $$x$$ is an $$n \times 1$$ vector, $$u$$ is a $$m \times 1$$ vector, and $$e$$ is sampled from a Gaussian distribution.

We are given either $$Ax + e ~~(mod~q)$$ or $$u ~(mod~q)$$ the conjecture being that it is difficult to distinguish between these samples in polynomial time, with high probability over the choice of $$A$$, $$x$$, $$u$$ and $$e$$ (for appropriate choices of $$m$$ and $$q$$.)

I wanted to ask about the centrality of the Gaussian distribution while considering the security of LWE.

Is LWE hard if $$e$$ is sampled from other distributions — like the uniform distribution or the exponential distribution?

• eprint.iacr.org/2015/939.pdf look at the page 40 "Note that this original error e can come from any distribution, as long as it is relatively short." Jan 14 at 22:29
• That quote is about the correctness of a procedure for generating fresh LWE samples from some given ones. It’s not about the security of LWE with alternative error distributions. Jan 15 at 12:35
• @ChrisPeikert Are there references on the correctness of LWE with alternative other distributions? Jan 15 at 15:29