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EUROCRYPT
2011
Springer

Faster Explicit Formulas for Computing Pairings over Ordinary Curves

8 years 1 months ago
Faster Explicit Formulas for Computing Pairings over Ordinary Curves
Abstract. We describe efficient formulas for computing pairings on ordinary elliptic curves over prime fields. First, we generalize lazy reduction techniques, previously considered only for arithmetic in quadratic extensions, to the whole pairing computation, including towering and curve arithmetic. Second, we introduce a new compressed squaring formula for cyclotomic subgroups and a new technique to avoid performing an inversion in the final exponentiation when the curve is parameterized by a negative integer. The techniques are illustrated in the context of pairing computation over Barreto-Naehrig curves, where they have a particularly efficient realization, and are also combined with other important developments in the recent literature. The resulting formulas reduce the number of required operations and, consequently, execution time, improving on the state-of-the-art performance of cryptographic pairings by 28%-34% on several popular 64-bit computing platforms. In particular, our...
Diego F. Aranha, Koray Karabina, Patrick Longa, Ca
Added 28 Aug 2011
Updated 28 Aug 2011
Type Journal
Year 2011
Where EUROCRYPT
Authors Diego F. Aranha, Koray Karabina, Patrick Longa, Catherine H. Gebotys, Julio López
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