Well-Rounded Lattices via Polynomials

TL;DR

This paper investigates conditions under which lattices derived from polynomials with integer coefficients are well-rounded, a property important in cryptography and communication security.

Contribution

It provides new insights into when polynomial-derived lattices are well-rounded, expanding understanding of lattice structures in mathematical and cryptographic contexts.

Findings

Characterization of polynomial-derived lattices that are well-rounded

Conditions for minimal vectors to span the entire space

Applications to cryptography and wiretap channels

Abstract

Well-rounded lattices have been a topic of recent studies with applications in wiretap channels and in cryptography. A lattice of full rank in Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. In this paper, we investigate when lattices coming from polynomials with integer coefficients are well-rounded.