We all rely on asymmetric encryption every day, both as developers and consumers. It's what keeps our web traffic safe, what lets us sign our git commits, and what powers almost every single authentication flow.

Most of us will know the names of the most commonly used asymmetric encryption algorithms, RSA and ECDSA. But how many of us know how they actually work? What are their drawbacks and limitations, and where are they vulnerable?

Join me for a mathematical deep dive into one of the most fundamental underpinnings of our security infrastructure, journeying from the inception of these algorithms and their algebraic foundations to their modern day usage. We'll talk about why ECDSA has superseded RSA, why it's still not good enough in a post-quantum world, and what's next for asymmetric encryption.

This talk assumes knowledge of how asymmetric encryption functions in a development context (what private and public keys are and ho they should be handled) but no more than that. Some mathematical literacy (raising numbers to powers like squaring or cubing, what a remainder is) is required, but no more than that.