On the method of manufacturing lattice packings of equal spheres corresponding to the packing density of the “Lambda” series

Recieved: 11/28/2024

Accepted: 12/23/2024

Published: 06/20/2025

Keywords: post-quantum cryptography, geometry of numbers, lattice theory, arithmetic minima of positive quadratic forms, lattice packings of equal spheres, Hermite constant

To cite this article

Lyalin M.A., Fomin S.A. On the method of manufacturing lattice packings of equal spheres corresponding to the packing density of the “Lambda” series. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2025. N 2, p.38-47 https://doi.org/10.55959/MSU/0137–0782–15–2025–49–2–38–47.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Lyalin M.A. (Immanuel Kant Baltic Federal University)
Fomin S.A. (Ivannikov Institute for System Programming of the Russian Academy of Sciences)

Abstract

The creation of cryptographic systems based on lattice theory is a promising direction in the field of post-quantum cryptography. The aim of this work is to obtain new properties of lattices through related objects — dense packings of equal spheres. The article proposes a method for constructing lattice packings of equal spheres corresponding to the packing density of the “Lambda” series in dimensions 1–24, using a series of coefficients to the height of a fundamental parallelepiped of dimension (n−1): 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2, √−1, 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2, √−1, 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2. The construction of lattice packings of equal spheres using this method was carried out up to dimension 11 inclusive.