Most of the slides of this talk will be either pretty pictures or colourful arrays of numbers. I'll start by explaining what an elliptic curve is: how it is also a group and also a lattice. Then I'll talk about integer recurrence sequences, and explain how these two topics are related. Then I'll tell you about my thesis (which is basically just some integers and a few plus signs -- yes, you too can have a thesis some day!) and how it can be used for the cryptography of elliptic curves.

I'll use words like "prime," "divides," and "denominator." I will not use words like "scheme," "L-function," or "Hodge-Sato-Birch-Poincare-Riemann-Frobenius motivic cohomological representations of topoi." But it'll be cool anyway.