how lattices work.
Closest-vector problems, from first principles.
A lattice is a grid of points in high-dimensional space. The hard problem: given an arbitrary point, find the nearest lattice point. Easy to describe, believed hard to solve — even for quantum computers.
problemclosest vector
dimension512+
classicalhard
quantumno speedup
why it's hard
In 2D you can eyeball the nearest lattice point. In 512 dimensions, the search space is astronomically large, and there's no known shortcut — quantum included. That's the entire security argument.