International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Huff's Model for Elliptic Curves

Marc Joye
Mehdi Tibouchi
Damien Vergnaud
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Abstract: This paper revisits 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×Z/2Z is birationally equivalent to a Huff curve over the original field. This paper extends and generalizes Huff's model. It presents fast explicit formulas for point addition and doubling on Huff curves. It also addresses the problem of the efficient evaluation of pairings over Huff curves. Remarkably, the formulas we obtain feature some useful properties, including completeness and independence of the curve parameters.
  title={Huff's Model for Elliptic Curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Elliptic curves, Huff's model, unified addition law, complete addition law, explicit formulas, scalar multiplication, Tate pairing, Miller algorithm},
  note={ 14796 received 6 Jul 2010},
  author={Marc Joye and Mehdi Tibouchi and Damien Vergnaud},