Solving the search-LWE problem over projected lattices

The learning with errors (LWE) problem is one of the hard problems assuring the security of modern lattice-based cryptography. Kannan's embedding can reduce Search-LWE, the search version of LWE, to a specific case of the shortest vector problem (SVP). Lattice basis reduction is a powerful instrument for solving lattice problems including SVP. We propose a new way for efficiently solving Search-LWE. While a whole basis is reduced in a standard way, ours reduces only a projected basis. To realize our strategy, we also provide an algorithm for reducing projected bases, based on DeepBKZ that is an enhancement of the block Korkine-Zolotarev (BKZ) algorithm. Moreover, we show implementation results for solving some instances within the Darmstadt LWE challenge. (C) 2022 Elsevier B.V. All rights reserved.