You are looking at a specific version 20100614:081650 of this paper. See the latest version.

Paper 2009/615

Faster Pairing Computations on Curves with High-Degree Twists

Craig Costello and Tanja Lange and Michael Naehrig

Abstract

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 high-degree 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 formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Unknown where it was published
Keywords
PairingsMiller functionsexplicit formulasTate pairingate pairingtwistsWeierstrass curves.
Contact author(s)
michael @ cryptojedi org
History
2010-06-14: last of 3 revisions
2009-12-14: received
See all versions
Short URL
https://ia.cr/2009/615
License
Creative Commons Attribution
CC BY
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.