Fast Implementation of Elliptic Curve Cryptosystems over a Finite Field F_2ⁿ

The center to the implementation of elliptic curve cryptosystems efficiently lies in the arithmetic of scalar multiplication and addition. In order to improve their speed of implementation a new method using a database to avoid field inversion is given. The method accelerates scalar multiplication and addition. Compared with the best projective algorithm presently in use this method not only gives higher efficiency but also reduces data expansion.