Mathematics – Number Theory
Scientific paper
2009-04-06
Mathematics
Number Theory
15 pages, 2 figures. Final version accepted for publication in Journal of Number Theory
Scientific paper
This paper proposes new explicit formulas for the doubling and addition step in Miller's algorithm to compute the Tate pairing. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on Edwards curves by presenting the functions which arise in the addition and doubling. Computing the coefficients of the functions and the sum or double of the points is faster than with all previously proposed formulas for pairings on Edwards curves. They are even competitive with all published formulas for pairing computation on Weierstrass curves. We also speed up pairing computation on Weierstrass curves in Jacobian coordinates. Finally, we present several examples of pairing-friendly Edwards curves.
Arene Christophe
Lange Tanja
Naehrig Michael
Ritzenthaler Christophe
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