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

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, as those required for OK-ECDH or OK-ECDSA. Keywords. Elliptic curve cryptosystems, unified addition formula, sidechannel analysis, SPA-like attacks, smart cards.

• Type: Conference
• Year: 2003
• Where: AAECC
• Authors: Olivier Billet, Marc Joye
• Keywords: AAECC 2003, Algorithms, Elliptic Curve, SPA-like Attacks, Unified Addition Formula