Quasi-polynomially hard LWE ⇒ LWE with polynomial ratio

Fully-black-box reduction · standard model · folklore · security loss: none

Statement

Quasi-polynomially hard LWE implies LWE with polynomial modulus-to-noise ratio with the same parameters: an adversary of size $n^k$ has size at most $2^{(\log n{)}^2}$ for all large $n$, so its advantage is at most $2^{-(\log n{)}^2}$, which is negligible — folklore.