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arXiv · 2608.29977

A New Algebraic Algorithm for LWE

Luca Campa·Massimo Fumiani·Arnab Roy
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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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Luca Campa, Massimo Fumiani, Arnab Roy. 2026-08-30. A New Algebraic Algorithm for LWE. https://arxiv.org/abs/2608.29977

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