Paper 2010/309

Co-Z Addition Formulae and Binary Ladders on Elliptic Curves

Raveen R. Goundar, Marc Joye, and Atsuko Miyaji

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.

Metadata
Available format(s)
PDF
Category
Implementation
Publication info
Published elsewhere. Extended abstract appears in CHES 2010. This is the full version.
Keywords
Elliptic curvesMeloni’s techniqueJacobian coordinatesregular binary laddersimplementation attacksembedded systems.
Contact author(s)
raveen rg @ gmail com
History
2010-05-27: revised
2010-05-25: received
See all versions
Short URL
https://ia.cr/2010/309
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2010/309,
      author = {Raveen R.  Goundar and Marc Joye and Atsuko Miyaji},
      title = {Co-Z Addition Formulae and Binary Ladders on Elliptic Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2010/309},
      year = {2010},
      note = {\url{https://eprint.iacr.org/2010/309}},
      url = {https://eprint.iacr.org/2010/309}
}
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