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Learning with Errors (LWE) problems are the foundations for numerousapplications in lattice-based cryptography and are provably as hard asapproximate lattice problems in the worst case. Here we present a reductionfrom LWE problem to dihedral coset problem(DCP). We present a quantum algorithmto generate the input of the two point problem which hides the solution of LWE.We then give a new reduction from two point problem to dihedral coset problemon D_{{{({n^{13}})}^{n\log n}}}. Our reduction implicate that any algorithmsolves DCP in subexponential time would lead a quantum algorithm for LWE.

A reduction from LWE problem to dihedral coset problem