A New Lattice Sieving Algorithm Base on Angular Locality-Sensitive Hashing

Abstract

Currently, the space requirement of sieving algorithms to solve the shortest vector problem (SVP) grows as \(2^{0.2075n+o(n)}\), where n is the lattice dimension. In high dimensions, the memory requirement makes them uncompetitive with enumeration algorithms. Shi Bai et al. presents a filtered triple sieving algorithm that breaks the bottleneck with memory \( 2^{0.1887n+o(n)}\) and time \( 2^{0.481n+o(n)}\).