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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)
PDF
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
Creative Commons Attribution
CC BY
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