The Learning with Errors problem (LWE) has become a central topic in recent cryptographic research. In this paper, we present a new solving algorithm combining important ideas from previous work on improving the Blum-Kalai-Wasserman (BKW) algorithm and ideas from sieving in lattices. The new algorithm is analyzed and demonstrates an improved asymptotic performance. For the Regev parameters q = n 2 and noise level σ = n 1.5 /( √ 2π log 2 2 n), the asymptotic complexity is 2 0.893n in the standard setting, improving on the previously best known complexity of roughly 2 0.930n . The newly proposed algorithm also provides asymptotic improvements when a quantum computer is assumed or when the number of samples is limited.

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