A New Algebraic Algorithm for LWE
cs.CR, math.AG
Submitted: 2026-08-30
Updated: 2026-08-30
Comments: Under peer review
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
The gist: The Learning With Errors (LWE) problem, introduced by Regev in 2005, is central to modern cryptography and post-quantum security.
Terminology
Abstract
The Learning With Errors (LWE) problem, introduced by Regev in 2005, is central to modern cryptography and post-quantum security. The algorithms to solve the search version of the problem, Search-LWE, can be broadly categorised into algebraic, combinatorial and lattice-based. In this work we propose a new algebraic algorithm for the Search-LWE problem. At a high level, the algorithm combines linear-algebraic techniques with S-polynomial-based methods from Groebner basis computation. We provide a direct complexity analysis of our algorithm, avoiding semi-regularity assumptions and complexity bounds derived from the degree of regularity. Our algorithm achieves a polynomial improvement in complexity over prior results that use Groebner basis methods to solve Search-LWE.
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