Closest point search in lattices

In this semitutorial paper, a comprehensive survey of closest point search methods for lattices without a regular structure is presented. The existing search strategies are described in a unified framework, and differences between them are elucidated. An efficient closest point search algorithm, based on the Schnorr–Euchner variation of the Pohst method, is implemented. Given an arbitrary point and a generator matrix for a lattice , the algorithm computes the point of that is closest to . The algorithm is shown to be substantially faster than other known methods, by means of a theoretical comparison with the Kannan algorithm and an experimental comparison with the Pohst algorithm and its variants, such as the recent Viterbo–Boutros decoder. Modifications of the algorithm are developed to solve a number of related search problems for lattices, such as finding a shortest vector, determining the kissing number, computing the Voronoi-relevant vectors, and finding a Korkine–Zolotareff reduced basis.