This article is basically an exercise in understanding ECDSA (Elliptic Curve Digital Signature Algorithm) from scratch. All I assume is some basic math and a willingness to pick up a bit of abstract math along the way. I try to explain everything as intuitively as possible, but, despite that, the article still demands some serious effort from the reader.

When I analyzed the Extended Euclidean Algorithm, one thing led to another, and I ended up writing a little intro to generating functions. You can even jump to that part and ignore the rest, if you want! Other readers may instead choose to skip that section altogether, as it's self-contained.