In this talk we present the most important work related to OEFs which was done since they were introduced by us in 1998. In particular, we will describe fast multiplication algorithms and fast finite field inversion. We used OEFs to construct efficient elliptic curve cryptosystems on both DEC Alpha workstations and Pentium-class PCs. These results show that OEFs, when used with our new inversion algorithm, provide a substantial performance increase over other reported methods. We will also present recent results in which OEFs were used successfully for realizing elliptic curve cryptosystem on smart cards without coprocessors.
Classical approaches using stochastic arguments depend highly on the choice of mutation model.
Unfortunately, it is hard to justify which mutation model is suitable for a particular sample. We propose a method to model allele frequencies without assuming a mutation model. The estimation procedure is divided into two steps. Simulation studies have shown that both steps are robust to different mutation models. The advantages of our approach include robustness to mutation model and ability to be easily extended to allelic, genotypic and protein structure data.