The double-base number system and its application to elliptic curve cryptography
Vassil S. Dimitrov, Laurent Imbert, Pradeep Kumar Mishra · Mathematics of Computation · 2007
We describe an algorithm for point multiplication on generic elliptic curves, based on a representation of the scalar as a sum of mixed powers of 2 2 and 3 3 . The sparseness of this so-called double-base number system, combined with some efficient point tripling formulae, lead to efficient point multiplication algorithms for curves defined over both prime and binary fields. Side-channel resistance is provided thanks to side-channel atomicity.