International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Co-Z Addition Formulae and Binary Ladders on Elliptic Curves

Raveen R. Goundar
Marc Joye
Atsuko Miyaji
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Abstract: 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 Weierstrass 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.
  title={Co-Z Addition Formulae and Binary Ladders on Elliptic Curves},
  booktitle={IACR Eprint archive},
  keywords={implementation / Elliptic curves, Meloni’s technique, Jacobian coordinates, regular binary ladders, implementation attacks, embedded systems.},
  note={Extended abstract appears in CHES 2010.  This is the full version. 14756 received 24 May 2010, last revised 27 May 2010},
  author={Raveen R. Goundar and Marc Joye and Atsuko Miyaji},