Date: 2010/12/16 (Thu)

      Place: Collaboration Room #7 (Information Science Building, 5th floor)

      Name: Marc Joye
          Technicolor, 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)