A complete classification of well-rounded real quadratic ideal lattices (Q2329278)

A lattice of full rank in \(\mathbb{R}^n\) is called well-rounded if its set of minimal vectors spans the entire space. These lattices have important applications in cryptography. The author gives a complete classification of well-rounded ideal lattices coming from real quadratic fields \(\mathbb{Q}(\sqrt{d})\) where \(d\) is a field discriminant. Further, it shown that the ideals that give such lattices are those that correspond to divisors \(a\) of \(d\) that satisfy \(\sqrt{\frac{d}{3}}<a<\sqrt{3d}.\)