Extended DBNS and applications to elliptic curve cryptography
Dr Christophe Doche
Macquarie University
We investigate the impact of larger digit sets on the length of Double-Base Number system (DBNS) expansions.
We present a new representation system called extended DBNS whose expansions can be extremely sparse.
We also discuss a new approach to approximate an integer $n$ by $d2^a3^b$ where $d$ belongs to a given digit set.
This method, which requires some precomputations as well, leads to realistic DBNS implementations.
Finally, a left-to-right scalar multiplication relying on extended DBNS is given.
In the context of scalar multiplications in Jacobian coordinates, we show that this
method outperforms NAF-based methods using the same number of precomputations.