Lattice-Based Cryptography Explained

Lattice-based cryptography is the branch of modern encryption that hides its secrets inside a grid of points in high-dimensional space. It is the mathematics underneath the two headline standards the United States published in 2024, and it is the reason most of the internet’s future key exchanges will look nothing like the ones running today. This page is about the machinery rather than the policy. If you want the wider picture of the migration, our guide to post-quantum cryptography covers it, and the vendor landscape is mapped separately. What follows is the geometry that lattice-based cryptography is built from, the hard problems, the protocols standing on them, and an honest account of why anyone believes a quantum computer cannot break them. A lattice is a repeating grid of points, and the hard part is finding the nearest one. In two dimensions a child can do it by eye, and in the several hundred dimensions lattice-based cryptography uses, nobody knows how. The same lattice can be described by an easy basis or an impossible one. That asymmetry between a short near-orthogonal description and a long skewed one is the trapdoor the whole field is built on. Learning With Errors is linear…