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Springer Verlag, Lecture Notes in Computer Science, p. 34-42

DOI: 10.1007/3-540-44828-4_5

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The Jacobi Model of an Elliptic Curve and Side-Channel Analysis

Journal article published in 2003 by Published In M. Fossorier, A. Poli, Olivier Billet, T. Hholdt, Marc Joye
This paper is available in a repository.
This paper is available in a repository.

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Abstract

A way for preventing SPA-like attacks on elliptic curve systems is to use the same formula for the doubling and the general addition of points on the curve. Various proposals have been made in this direction with di#erent results. This paper re-investigates the Jacobi form suggested by Liardet and Smart (CHES 2001). Rather than considering the Jacobi form as the intersection of two quadrics, the addition law is directly derived from the underlying quartic. As a result, this leads to substantial memory savings and produces the fastest unified addition formula for curves of order a multiple of 2, as those required for OK-ECDH or OK-ECDSA.