A reduction from LWE problem to dihedral coset problem

TL;DR

This paper establishes a quantum reduction from the LWE problem, fundamental in cryptography, to the dihedral coset problem, suggesting that solving DCP efficiently could break LWE-based cryptography.

Contribution

It introduces a novel quantum reduction from LWE to DCP, linking their complexities and implications for cryptographic security.

Findings

Quantum algorithm generates LWE input for two point problem

Reduction from two point problem to DCP on large dihedral groups

Subexponential DCP algorithms could compromise LWE security

Abstract

Learning with Errors (LWE) problems are the foundations for numerous applications in lattice-based cryptography and are provably as hard as approximate lattice problems in the worst case. Here we present a reduction from LWE problem to dihedral coset problem(DCP). We present a quantum algorithm to 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 problem on D_{{{({n^{13}})}^{n\log n}}}. Our reduction implicate that any algorithm solves DCP in subexponential time would lead a quantum algorithm for LWE.