Faster pairing computations on curves with high-degree twists
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Conference Paper
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Accepted Version. c34177.pdf. |
Description
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.
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ID Code: | 34177 |
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Item Type: | Contribution to Journal (Journal Article) |
Refereed: | Yes |
Measurements or Duration: | 19 pages |
Keywords: | Weierstrass curves, ate pairing, miller functions, pairings, tate pairing |
DOI: | 10.1007/978-3-642-13013-7_14 |
ISSN: | 0302-9743 |
Pure ID: | 32203165 |
Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > Institutes > Information Security Institute Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Research Centres > Australian Research Centre for Aerospace Automation |
Copyright Owner: | Consult author(s) regarding copyright matters |
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au |
Deposited On: | 20 Aug 2010 02:05 |
Last Modified: | 07 May 2024 09:15 |
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