Method for constructing elliptic curves using complex multiplication and its optimizations
Number Theory
2012-07-31 v1
Abstract
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer coefficients. We will prove theoretical results and give a detailed account of the method itself and how one can use a divisor of the mentioned polynomial with coefficients in some extension of the field of rational numbers.
Cite
@article{arxiv.1207.6983,
title = {Method for constructing elliptic curves using complex multiplication and its optimizations},
author = {E. A. Grechnikov},
journal= {arXiv preprint arXiv:1207.6983},
year = {2012}
}
Comments
29 pages. Translation of the main part of my thesis, originally published in Russian; http://mi.mathnet.ru/eng/pdm335