发表机构
University of Innsbruck（因斯布鲁克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对后量子密码核心的Search-LWE问题，提出一种结合线性代数与格罗比纳基S-多项式方法的新型代数算法，通过直接复杂度分析避免半正则性假设，复杂度较同类方法实现多项式级改进。
AI 中文摘要
带误差学习（Learning With Errors，LWE）问题由Regev于2005年提出，是现代密码学与后量子安全的核心。求解该问题搜索版本（Search-LWE）的算法可大致分为代数类、组合类与格基类。本研究针对Search-LWE问题提出一种新型代数算法，该算法将线性代数技术与格罗比纳基（Groebner基）计算中基于S-多项式的方法相结合；我们对该算法进行直接复杂度分析，避免了半正则性假设及由正则度导出的复杂度界，其复杂度较此前用格罗比纳基方法求解Search-LWE的结果实现了多项式级改进。
英文摘要
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.
CommentsUnder peer review
