On the Asymptotics of Solving the LWE Problem Using Coded-BKW with Sieving

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Abstract

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 $\sigma = n^{1.5}/(\sqrt{2\pi}\log_{2}^{2}n)$, 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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Subject classification (UKÄ) – MANDATORY

  • Other Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • LWE, BKW, Coded-BKW, Lattice codes, Lattice sieving
Original languageEnglish
Number of pages16
JournalIEEE Transactions on Information Theory
StateSubmitted - 2018 Mar
Publication categoryResearch
Peer-reviewedYes