Paper 2010/383

Huff's Model for Elliptic Curves

Marc Joye, Mehdi Tibouchi, and Damien Vergnaud


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.

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Elliptic curvesHuff's modelunified addition lawcomplete addition lawexplicit formulasscalar multiplicationTate pairingMiller algorithm
Contact author(s)
mehdi tibouchi @ normalesup org
2010-07-07: received
Short URL
Creative Commons Attribution


      author = {Marc Joye and Mehdi Tibouchi and Damien Vergnaud},
      title = {Huff's Model for Elliptic Curves},
      howpublished = {Cryptology ePrint Archive, Paper 2010/383},
      year = {2010},
      note = {\url{}},
      url = {}
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