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We provide a reduction of the Ring-LWE problem to Ring-LWE problems insubrings, in the presence of samples of a restricted form (i.e. $(a,b)$ suchthat $a$ is restricted to a multiplicative coset of the subring). To create andexploit such restricted samples, we propose Ring-BKW, a version of theBlum-Kalai-Wasserman algorithm which respects the ring structure. Off-the-shelfBKW dimension reduction (including coded-BKW and sieving) can be used for thereduction phase. Its primary advantage is that there is no need forback-substitution, and the solving/hypothesis-testing phase can beparallelized. We also present a method to exploit symmetry to reduce tablesizes, samples needed, and runtime during the reduction phase. The resultsapply to two-power cyclotomic Ring-LWE with parameters proposed for practicaluse (including all splitting types).

Algebraic aspects of solving Ring-LWE, including ring-based improvements in the Blum-Kalai-Wasserman algorithm