Efficient Arithmetic in Finite Fields of Small Odd Characteristic

In this thesis we present and analyse a generic representation for finite fields of small, odd, characteristic. The technique was originally developed at Ericsson Research, but was improved upon as a part of the thesis work. As the primary practical interest for this class of fields lies in elliptic curve cryptography, we also give an introduction to this subject along with considerations of particular interest for the context of this thesis. Finally, a software library for finite field arithmetic was implemented, and benchmarks of this implementation seem promising. We also give descriptions of some cryptographically suitable elliptic curves found using this library. Effektiv aritmetik i ändliga kroppar av liten, udda karaktäristik med tillämpningar inom kryptografi med elliptiska kurvor