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

Olivier Billet; Marc Joye

Paper 2002/125

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

Olivier Billet and Marc Joye

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 different 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.

Metadata

Available format(s): PDF PS
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Keywords: Elliptic curve cryptosystems side-channel analysis
Contact author(s): marc joye @ gemplus com
History: 2002-08-22: received
Short URL: https://ia.cr/2002/125
License: CC BY

BibTeX

@misc{cryptoeprint:2002/125,
      author = {Olivier Billet and Marc Joye},
      title = {The Jacobi Model of an Elliptic Curve and Side-Channel Analysis},
      howpublished = {Cryptology {ePrint} Archive, Paper 2002/125},
      year = {2002},
      url = {https://eprint.iacr.org/2002/125}
}