Abstract : 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 and 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.
Vassil Dimitrov, Laurent Imbert, Pradeep Mishra. The Double-Base Number System and its Application to Elliptic Curve Cryptography. Mathematics of Computation, American Mathematical Society, 2008, 77 (262), pp.1075-1104. ⟨lirmm-00341742⟩
