Thanks, great question!
In short: I got obsessed by making it as fast as possible and read a ton of elliptic curve cryptography papers.
It was a journey that started from reading WireGuard kernel sources,
then I was thinking about deriving IPv6 address from peer key,
left a random comment on a dated gist https://gist.github.com/artizirk/c91e4f8c237dec07e3ad1b286f1...
from which I learned about vanity key concept.
I naturally enjoy doing performance optimization work so when I discovered incremental approach idea here
https://github.com/warner/wireguard-vanity-address/pull/15 I decided to create my own tool.
I've implemented first version of https://github.com/AlexanderYastrebov/wireguard-vanity-key and then continuously profiled it to improve performance.
From profiling I saw that field inversion and multiplication are the main operations.
I realized I need to reduce unnecessary computation to make it faster and for that I need to understand the underlying math which is actually quite simple.
I read RFCs for Curve25519 and papers from D. J. Bernstein who invented it.
You can see how my understanding evolved from the commit history https://github.com/AlexanderYastrebov/wireguard-vanity-key/c...
Once I have the fastest algorithm to generate vanity Curve25519 keypairs I can apply it to other things that use Curve25519 (https://ianix.com/pub/curve25519-deployment.html) or Ed25519 (https://ianix.com/pub/ed25519-deployment.html) which is an equivalent curve.
See also my other related projects:
* [age-vanity-keygen](https://github.com/AlexanderYastrebov/age-vanity-keygen) — Fast vanity age X25519 identity generator.
* [vanity25519](https://github.com/AlexanderYastrebov/vanity25519) — Efficient Curve25519 vanity key generator.
