Cryptology ePrint Archive: Report 2010/383

Huff's Model for Elliptic Curves

Marc Joye and Mehdi Tibouchi and Damien Vergnaud

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.

Category / Keywords: public-key cryptography / Elliptic curves, Huff's model, unified addition law, complete addition law, explicit formulas, scalar multiplication, Tate pairing, Miller algorithm

Date: received 6 Jul 2010

Contact author: mehdi tibouchi at normalesup org

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Version: 20100707:013131 (All versions of this report)

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