Elliptic curves are relatively obscure mathematical objects: you can get a PhD in maths without ever having come across them. Yet these objects play an important role in modern cryptography and as such are found in most HTTPS connections, in Bitcoin, and in a large number of other places.
To really understand elliptic curve cryptography (ECC) to the point that you can implement algorithms, you'd have to study the maths behind it. This talk assumes that you haven't studied the maths, but just want to understand what ECC is about, how is works and how it is implemented.
It will discuss how 'point addition' works and how the Elliptic Curve Diffie-Hellman algorithm is used, for example in HTTPS - and how you can find it using Wireshark. It will explain how to use elliptic curve for digital signatures and why you don't want to be like Sony when it comes to implementing them. It will discuss how ECC was used in an infamous random number generator and, finally, will take a brief look at the use of elliptic curves in post-quantum algorithms.
The goal of this talk is to keep things simple and understandable and no knowledge of maths is assumed. The talk won't make you an expert on ECC -- that would take years of studying. But it might help you understand the context a bit better when you come across them in your research. And hopefully it will also be a little bit fun.