Kannan最短格向量算法的改进分析
Improved Analysis of Kannan's Shortest Lattice Vector Algorithm
摘要：
基于格的密码系统（如NTRU、GGH和Ajtai-Dwork）的安全性本质上依赖于在高维中计算最短非零格向量和最接近给定目标向量的格向量的困难性。这些任务的最佳算法是由Kannan提出的，虽然非常简单，但其复杂性估计自20多年来一直没有改进。Kannan的解决最短向量问题的算法在Schnorr的著名的块缩减算法中尤其重要，该算法是基于对上述基于格的加密方案的最知名攻击。准确理解Kannan算法对于提供有意义的密钥大小至关重要。本文改进了Kannan算法的复杂性分析，并讨论了改进基本枚举策略的可能性。
英文摘要：
The security of lattice-based cryptosystems such as NTRU, GGH and Ajtai-Dwork essentially relies upon the intractability of computing a shortest non-zero lattice vector and a closest lattice vector to a given target vector in high dimensions. The best algorithms for these tasks are due to Kannan, and, though remarkably simple, their complexity estimates have not been improved since more than twenty years. Kannan's algorithm for solving the shortest vector problem is in particular crucial in Schnorr's celebrated block reduction algorithm, on which are based the best known attacks against the lattice-based encryption schemes mentioned above. Understanding precisely Kannan's algorithm is of prime importance for providing meaningful key-sizes. In this paper we improve the complexity analyses of Kannan's algorithms and discuss the possibility of improving the underlying enumeration strategy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
