Efficient implementation of elliptic curve cryptosystems

Abstract

Efficient implementation of elliptic curve cryptography can be targeted at 2 levels, specifically on the elliptic curve group operations and the underlying finite field arithmetic. The focus of this thesis is to investigate and devise better algorithms for performing scalar multiplication on a point P of an elliptic curve, as well as to improve the computation of the underlying finite field arithmetic. In particular, the optimizations introduced are tailored for implementation on low cost 8 bit microcontrollers. Such microcontrollers are commonly used in embedded system and smart cards.