Cryptology ePrint Archive: Report 2010/309

Co-Z Addition Formulae and Binary Ladders on Elliptic Curves

Raveen R. Goundar and 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.

Category / Keywords: implementation / Elliptic curves, Meloni’s technique, Jacobian coordinates, regular binary ladders, implementation attacks, embedded systems.

Publication Info: Extended abstract appears in CHES 2010. This is the full version.

Date: received 24 May 2010, last revised 27 May 2010

Contact author: raveen rg at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20100527:061259 (All versions of this report)

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