Helpful topic to teach yourself lattice-based crypto: abstract algebra

I'll be honest: when talking about lattice-based crypto, I don't know who my audience is. But I do have aspirations that someone with just a high school background can pick up this topic, even if it only means that they'll be able to implement in a rote fashion, rather than having a more nuanced discussion about it. But for people who are actually interested in pursuing certain topics in mathematics, or theoretical cryptography, I'm hoping these articles act as a gateway for them.

There are so many topics to dive into in order to actually have a finer understanding of how things work, but for my first article to my blog about this topic to teach absolute beginners, I'm going to point to a brilliant series that introduces abstract algebra.

At the highest level, lattice-based cryptography builds on the idea of a grid of points (a lattice). We choose a secret point, and then hide it by adding a small, controlled amount of “noise.” But unlike the lattices you might picture from geometry class, these aren’t built from real numbers on graph paper. Instead, the points live in a polynomial ring space, where arithmetic is done with addition, subtraction, and multiplication (but not ordinary division). The rules look familiar, but they play out in a different, more abstract setting.

Unlike university lecture recordings, these series of videos feel a lot more approachable. The tone almost feels like it is welcoming to those who don't even have any experience beyond basic algebra.

Definitely check them out: https://www.youtube.com/playlist?list=PLi01XoE8jYoi3SgnnGorR_XOW3IcK-TP6