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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Co-Z Addition Formulæ and Binary Ladders on Elliptic Curves
(Extended Abstract)
verfasst von : Raveen R. Goundar, Marc Joye, Atsuko Miyaji
Erschienen in: Cryptographic Hardware and Embedded Systems, CHES 2010
Verlag: Springer Berlin Heidelberg
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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 formulæ 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.