Module Lattice Security (Part III): Structured CVP Distance on the Log-Unit Lattice

Ming-Xing Luo

We prove that the $L^2$ CVP distance from a random short ring element to the log-unit lattice of $\Q(ζ_{2^k})$ converges to $\frac{\pi }{2\sqrt{6}}\sqrt{n}$ as $n=2^{k-1}\to \infty$. We…