Problem
Research questions and friction points this paper is trying to address.
LWE
Search-LWE
cryptography
post-quantum security
A New Algebraic Algorithm for LWE
🤖 AI Summary
本文提出了一种新的代数算法来解决Search-LWE问题，结合了线性代数技术和基于S-多项式的Groebner基计算方法，复杂度分析直接且优于先前结果。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Algebraic Algorithm
S-polynomial
Groebner Basis
Complexity Analysis
Search-LWE
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