Co-Z Addition Formulae and Binary Ladders on Elliptic Curves.
Raveen R. Goundar, Marc Jóye, Atsuko Miyaji · IACR Cryptology ePrint Archive · 2010
Meloni recently introduced a new type of arithmetic on elliptic curves when adding projective points sharing the same Z-coordinate. This paper presents further co-Z addition formulae (and register allocations) for various point additions on Weierstras elliptic curves. It explains how the use of conjugate point addition and other implementation tricks allow one to develop efficient scalar multiplication algorithms making use of co-Z arithmetic. Specifically, this paper describes efficient co-Z based versions of Montgomery ladder and Joye’s double-add algorithm. Further, the resulting implementations are protected against a large variety of implementation attacks.