Algebraic Aspects of Solving Ring-LWE, Including Ring-Based Improvements in the Blum--Kalai--Wasserman Algorithm

We provide a reduction of the Ring-LWE problem to problems in subrings, presence samples restricted form (i.e., $(a,b)$ such that $a$ is multiplicative coset subring). To create and exploit samples, we propose Ring-BKW, version Blum--Kalai--Wasserman (BKW) algorithm which respects ring structure. Off-the-shelf BKW dimension (including coded-BKW sieving) can be used for phase. Its primary advantage there no need back-substitution, solving/hypothesis-testing phase parallelized. also present method symmetry reduce table sizes, needed, runtime during The results apply 2-power cyclotomic with parameters proposed practical use all splitting types).