Group Theory, Finite Fields and Elliptic Curves

09 Nov

Practical information

  • Date: 9. November 2018
  • Time: 14.15 - 16.00
  • Location: Campus Kongsberg, Jakob Cinema Hall, Campus Kongsberg, Hasbergsvei 36, 3616 Kongsberg.

The talk is scheduled in two parts. While the first part is for all the general audience, the second part is targeted for audience interested in cryptography.

About Daniel Larsson

Professor Daniel Larsson currently works as a professor at USN and teaches mathematics at various levels. When his teaching duties permit, he thinks about- Moduli and deformation theory of algebraic and arithmetic structures, Arithmetic geometry, e.g., Galois representations/modules, L-functions, arithmetic schemes, higher-dimensional class field theory and Arithmetic Hom-Lie algebras and their applications. In his lecture on 09th Nov, 2018, Prof. Larsson will introduce the audience to abstract algebra, more precisely, group theory and finite fields. These topics are essential for the understanding of elliptic curve cryptography which is emerging as a candidate for Post-Quantum cryptography.

 

Abstract

Part 1: Group theory and finite fields

This lecture will be a very short introduction to abstract algebra. More precisely, group theory and finite fields. These topics are essential for the understanding of elliptic curve cryptography.

Part 2: Elliptic curves

In this second part, Larsson will present the basics of elliptic curves. These are curves defined by cubic equations that enjoy extremely deep properties and connections to such (seemingly) diverse fields as algebra, geometry, number theory and even physics. For instance, elliptic curves is one of two key ingredients in Andrew Wiles’ proof of Fermat’s last theorem. The amazing thing that is essential for cryptography is that the points on these curves form a group: one can add points and the resulting point is also on the curve. How one uses elliptic curves in cryptography will not be explained. Rather, the necessary tools for further self-study will be provided.