Well-rounded lattices for reliability and security in Rayleigh fading SISO channels
For many wiretap channel models asymptotically optimal coding schemes are known, but
less effort has been put into actual realizations of wiretap codes for practical parameters …
less effort has been put into actual realizations of wiretap codes for practical parameters …
Well-Rounded ideal lattices of cyclic cubic and quartic fields
In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-
rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded …
rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded …
On the geometry of nearly orthogonal lattices
L Fukshansky, D Kogan - Linear Algebra and its Applications, 2021 - Elsevier
Nearly orthogonal lattices were formally defined in [4], where their applications to image
compression were also discussed. The idea of “near orthogonality” in 2-dimensions goes …
compression were also discussed. The idea of “near orthogonality” in 2-dimensions goes …
[HTML][HTML] Well-rounded twists of ideal lattices from real quadratic fields
MT Damir, D Karpuk - Journal of Number Theory, 2019 - Elsevier
We study ideal lattices in R 2 coming from real quadratic fields, and give an explicit method
for computing all well-rounded twists of any such ideal lattice. We apply this to ideal lattices …
for computing all well-rounded twists of any such ideal lattice. We apply this to ideal lattices …
Constructions of well-rounded algebraic lattices over odd prime degree cyclic number fields
Algebraic lattices are those obtained from modules in the ring of integers of algebraic
number fields through the canonical or twisted embeddings. In turn, well-rounded lattices …
number fields through the canonical or twisted embeddings. In turn, well-rounded lattices …
On well-rounded lattices and lower bounds for the minimum norm of ideal lattices
In this paper, we study properties of well-rounded ideal lattices focusing on the lower
bounds for their minimum norm. We present counterexamples showing that the stated …
bounds for their minimum norm. We present counterexamples showing that the stated …
Stability of ideal lattices from quadratic number fields
L Fukshansky - The Ramanujan Journal, 2015 - Springer
We study semi-stable ideal lattices coming from quadratic number fields. We prove that all
ideal lattices of trace type from rings of integers of imaginary quadratic number fields are …
ideal lattices of trace type from rings of integers of imaginary quadratic number fields are …
[BUCH][B] On the relationship between two embeddings of ideals into geometric space and the shortest vector problem in principal ideal lattices
SC Batson - 2015 - search.proquest.com
An ideal lattice is the geometric embedding of an ideal in the algebraic integer ring of some
number field. Many recent developments in lattice-based cryptography are centered around …
number field. Many recent developments in lattice-based cryptography are centered around …
Well-rounded twists of ideal lattices from imaginary quadratic fields
In this paper, we investigate the properties of well-rounded twists of a given ideal lattice of
an imaginary quadratic field K. We show that every ideal lattice I of K has at least one well …
an imaginary quadratic field K. We show that every ideal lattice I of K has at least one well …
The linear transformation that relates the canonical and coefficient embeddings of ideals in cyclotomic integer rings
SC Batson - International Journal of Number Theory, 2017 - World Scientific
The geometric embedding of an ideal in the algebraic integer ring of some number field is
called an ideal lattice. Ideal lattices and the shortest vector problem (SVP) are at the core of …
called an ideal lattice. Ideal lattices and the shortest vector problem (SVP) are at the core of …