Paper 2008/490
On the final exponentiation for calculating pairings on ordinary elliptic curves
Michael Scott and Naomi Benger and Manuel Charlemagne and Luis J. Dominguez Perez and Ezekiel J. Kachisa
Abstract
When using pairing-friendly ordinary elliptic curves to compute the Tate and related pairings, the computation consists of two main components, the Miller loop and the so-called final exponentiation. As a result of good progress being made to reduce the Miller loop component of the algorithm (particularly with the discovery of ``truncated loop'' pairings like the R-ate pairing), the final exponentiation has become a more significant component of the overall calculation. Here we exploit the structure of pairing friendly elliptic curves to reduce the computation required for the final exponentiation to a minimum.
Note: Thanks to Yu Chen and Fre Vercauteren for pointing out an error in the sign of x for the BN curves.
Metadata
- Available format(s)
- Category
- Implementation
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Tate Pairing
- Contact author(s)
- mike @ computing dcu ie
- History
- 2010-08-24: last of 4 revisions
- 2008-11-24: received
- See all versions
- Short URL
- https://ia.cr/2008/490
- License
-
CC BY