Huff’s Model for Elliptic Curves

  • Marc Joye
  • Mehdi Tibouchi
  • Damien Vergnaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


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 formulæ for point addition and doubling on Huff curves. It also addresses the problem of the efficient evaluation of pairings over Huff curves. Remarkably, the so-obtained formulæ feature some useful properties, including completeness and independence of the curve parameters.


Elliptic curves Huff’s model unified addition law complete addition law explicit formulæ scalar multiplication Tate pairing Miller’s algorithm 


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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marc Joye
    • 1
  • Mehdi Tibouchi
    • 2
  • Damien Vergnaud
    • 2
  1. 1.Technicolor, Security & Content Protection LabsCesson-Sévigné CedexFrance
  2. 2.École Normale Supérieure – C.N.R.S. – I.N.R.I.A.Paris CEDEX 05France

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