Date: 2010/12/16 (Thu)Place: Collaboration Room #7 (Information Science Building, 5th floor)
Name: Marc JoyeTechnicolor, Security & Content Protection Labs, France
Title: The arithmetic of Huff curves and its cryptographic applications
Abstract:
In this talk, we revisit a model for elliptic curves over Q introduced
by Huff in 1948 to study a diophantine problem. Huff's model readily
extends over fields of odd characteristic. Every elliptic curve over
such a field and containing a copy of Z/4Z x Z/2Z is birationally
equivalent to a Huff curve over the original field. We extend and generalize
Huff's model to cover more isomorphism classes of elliptic curves.
We also address the case of binary fields. Applications to cryptographic
implementations are discussed. We present fast explicit formulae for point
addition and doubling on (generalized) Huff curves. Remarkably,
the so-obtained formulae feature some useful properties, including
completeness and independence of the curve parameters.
(Joint work with Julien Devigne, Mehdi Tibouchi, and Damien Vergnaud)
