Co-Z Addition Formulæ and Binary Ladders on
Raveen R. Goundar, Marc Jóye, Atsuko Miyaji · 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 for various point additions on Weierstras elliptic curves. It explains how the use of conjugate point addition and other implementa- tion 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 re- sulting implementations are protected against a large variety of implementation attacks.