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

Katherine E. Stange
2020 arXiv   pre-print
We provide a reduction of the Ring-LWE problem to Ring-LWE problems in subrings, in the presence of samples of a restricted form (i.e. (a,b) such that a is restricted to a multiplicative coset of the subring). To create and exploit such restricted samples, we propose Ring-BKW, a version of the Blum-Kalai-Wasserman algorithm which respects the ring structure. Off-the-shelf BKW dimension reduction (including coded-BKW and sieving) can be used for the reduction phase. Its primary advantage is that
more » ... there is no need for back-substitution, and the solving/hypothesis-testing phase can be parallelized. We also present a method to exploit symmetry to reduce table sizes, samples needed, and runtime during the reduction phase. The results apply to two-power cyclotomic Ring-LWE with parameters proposed for practical use (including all splitting types).
arXiv:1902.07140v3 fatcat:mnzwyrit7zenpbjl2lgpmy5y2u