In this talk, I explain that under quantum polynomial time reductions, LWE is equivalent to a relaxed version of the dihedral coset problem (DCP), called extrapolated DCP (eDCP). The extent of extrapolation varies with the LWE noise rate. By considering different extents of extrapolation, the result generalizes Regev’s famous proof that if DCP is in BQP (quantum poly-time) then so is LWE (FOCS 02). We'll also discuss a connection between eDCP and Childs and Van Dam’s algorithm for generalized hidden shift problems (SODA 07). The result implies that a BQP solution for LWE might not require the full power of solving DCP, but rather only a solution for its relaxed version, eDCP, which could be easier.