|Abstract: Meloni introduced a new type of arithmetic on elliptic
curves when adding projective points sharing the same
Z-coordinate in 2007. This work presents further co-Z addition
formulae for various point additions on Weierstrass elliptic curves.
It also 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 Left-to-Right and Right-to-Left
elliptic curve scalar multiplications.