On the secrecy gain of $\ell$-modular lattices

Counterexample to the $l$-modular Belfiore-Solé Conjecture

We show that the secrecy function conjecture that states that the maximum of the secrecy function of an $l$-modular lattice occurs at $1/\sqrt{l}$ is false, by proving that the 4-modular lattice $C^(4) = \mathbb{Z} \oplus \sqrt{2}\mathbb{Z} \oplus 2\mathbb{Z}$ fails to satisfy this conjecture. We also indicate how the secrecy function must be modified in the $l$-modular case to have a more reasonable chance for it to have a maximum at $1/\sqrt{l}$, and show that the conjecture, modified with this new secrecy function, is true for various odd 2-modular lattices.

Modular Lattices from a Variation of Construction A over Number Fields

We consider a variation of Construction A of lattices from linear codes based on two classes of number fields, totally real and CM Galois number fields. We propose a generic construction with explicit generator and Gram matrices, then focus on modular and unimodular lattices, obtained in the particular cases of totally real, respectively, imaginary, quadratic fields. Our motivation comes from coding theory, thus some relevant properties of modular lattices, such as minimal norm, theta series, kissing number and secrecy gain are analyzed. Interesting lattices are exhibited.

RIS辅助太赫兹无线系统在存在指向误差的$α-μ$衰落下的保密性研究

On the Secrecy of RIS-aided THz Wireless System subject to $α-μ$ fading with Pointing Errors

针对RIS辅助太赫兹系统在指向误差和$α-μ$衰落下的保密性能，推导了SOP和IP的近似与渐近表达式，并通过蒙特卡洛仿真验证。

Unimodular Lattices for the Gaussian Wiretap Channel

In a recent paper, the authors introduced a lattice invariant called "Secrecy Gain" which measures the confusion experienced by a passive eavesdropper on the Gaussian Wiretap Channel. We study, here, the behavior of this invariant for unimodular lattices by using tools from Modular Forms and show that, for some families of unimodular lattices, indexed by the dimension, the secrecy gain exponentially goes to infinity with the dimension.