The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction Factors

Abstract

The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques, was proposed. In this paper, we improve that algorithm by using different reduction factors in different steps of the sieving part of the algorithm. In the Regev setting, where q = n2 and $\sigma = {n^{1.5}}/\left( {\sqrt {2\pi } \log _2^2n} \right)$, the asymptotic complexity is 20.8917n, improving the previously best complexity of 20.8927n. When a quantum computer is assumed or the number of samples is limited, we get a similar level of improvement.