Getting Started

Lattice cryptography is one of the main foundations of post-quantum cryptography.

If you want to understand schemes like ML-KEM, ML-DSA, or Falcon, you need to understand lattices. Not every proof or every parameter choice, but the basic ideas: grids, vectors, matrices, short values, modular arithmetic, and noise. This course covers those ideas from the ground up. Each chapter builds on the last.

First, we cover the maths needed:

vectors
matrices
modular arithmetic
sampling
noise

Then we cover lattices:

basis vectors
integer combinations
different bases for the same lattice
short vectors
distance
closest points

Then we move to the two core problems:

SIS: find a short solution to a modular equation
LWE: recover or distinguish noisy modular equations

Then we explain the structure used in real schemes:

polynomials
rings
modules
compression
rounding

After that, we look at ML-KEM, ML-DSA, and Falcon.

The goal here is not to avoid the maths but to make the maths readable and intuitive. Virtually all of the notaation used will be explained clearly.

By the end, you should understand how lattice schemes work: what the public data is, what the secret data is, where the noise appears, why rounding works, what and how it can fail, and how this connects to post-quantum security.