4 papers
A Note on Banaszczyk's Inequality
Hongyuan Qu, Chengliang Tian, Guangwu Xu
Banaszczyk's inequality establishes a tail estimate for the discrete Gaussian measure on a lattice in . This classic result has been influential and plays an importan…
Algorithms for the Shortest Vector Problem in -dimensional Lattices, Revisited
Lihao Zhao, Chengliang Tian, Jingguo Bi +2
Efficiently solving the Shortest Vector Problem (SVP) in two-dimensional lattices holds practical significance in cryptography and computational geometry. While simpler than its hi…
Chinese Remainder Theorem Approach to Montgomery-Type Algorithms
Guangwu Xu, Yiran Jia, Yanze Yang
This paper explores the ability of the Chinese Remainder Theorem formalism to model Montgomery-type algorithms. A derivation of CRT based on Qin's Identity gives Montgomery reducti…
Qin's Algorithm, Continued Fractions and 2-dimensional Lattices
Han Wu, Guangwu Xu
In his celebrated book "Mathematical Treatise in Nine Sections" of 1247, Qin, Jiushao described the Chinese remainder theorem with great detail and generality. He also gave a metho…