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PKC
2010
Springer

Faster Pairing Computations on Curves with High-Degree Twists

14 years 1 months ago
Faster Pairing Computations on Curves with High-Degree Twists
Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the highdegree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formula...
Craig Costello, Tanja Lange, Michael Naehrig
Added 14 Aug 2010
Updated 14 Aug 2010
Type Conference
Year 2010
Where PKC
Authors Craig Costello, Tanja Lange, Michael Naehrig
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