Scalar Multiplication on Elliptic Curves Defined over Fields of Small Odd Characteristic

@inproceedings{Ngre2005ScalarMO,
title={Scalar Multiplication on Elliptic Curves Defined over Fields of Small Odd Characteristic},
author={Christophe N{\`e}gre},
booktitle={INDOCRYPT},
year={2005}
}

This paper explores elliptic curve cryptosystems over fields of small odd characteristic p = 3 or 5. We establish formulas multiplying by p a random point on an ordinary curve defined over Fpn , thereby improving scalar multiplication on random and special curves for p = 3 or 5 using a p-Multiply-and-Add method. We study the complexity of our method and compare it to other schemes.