Algorithms for the Shortest Lattice Vector Problem

In this paper, we solve the problem of an integer lattice vector. Currently, there are a large number of algorithms that can solve this problem. The task is relevant due to the fact that it is directly related to cryptography. A lattice is the set of all integer linear combinations of a given system of vectors. In the case when the vectors have integer coordinates, the lattice struck by them is called integer. the task is to find the shortest non-zero lattice vector defined by columns A. There are a large number of algorithms for solving this problem. There are deterministic, randomized, accurate, matched algorithms. The most famous are Cannon's algorithms, LLL - an algorithm, as well as an algorithm based on the properties of Voronov diagrams. In most algorithms, the main parameter on which complexity depends is the dimension. Since the problem is NP-hard, the dependence of complexity on dimension is exponential. Studying the performance of the algorithm of work [] and the final work is devoted. These studies will help to better understand which algorithms for solving the SVP problem can be applied in various situations. This question is relevant since there is a wide range of applied problems, for example, from the cryptography industry, which use SVP solutions as an important subtask.