4 research outputs found
The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction Factors
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 and , the asymptotic complexity is ,
improving the previously best complexity of . When a quantum
computer is assumed or the number of samples is limited, we get a similar level
of improvement.Comment: Longer version of a paper to be presented at ISIT 2019. Updated after
comments from the peer-review process. Includes an appendix with a proof of
Theorem
On the Asymptotics of Solving the LWE Problem Using Coded-BKW with Sieving
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 and noise level , the asymptotic complexity is in the standard setting, improving on the previously best known complexity of roughly . The newly proposed algorithm also provides asymptotic improvements when a quantum computer is assumed or when the number of samples is limited