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Faster pairing computations on curves with high-degree twists

Costello, Craig, Lange, Tanja, & Naehrig, Michael (2010) Faster pairing computations on curves with high-degree twists. In Public Key Cryptography – PKC 2010 : 13th International Conference on Practice and Theory in Public Key Cryptography, Proceedings, Springer Verlag, Paris, pp. 224-242.

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    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.

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    25 citations in Scopus
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    13 citations in Web of Science®

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    ID Code: 34177
    Item Type: Conference Paper
    Keywords: pairings, Miller functions, explicit formulas, Tate pairing, ate pairing, twists, Weierstrass curves
    DOI: 10.1007/978-3-642-13013-7_14
    ISBN: 9783642130137
    Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Computation Theory and Mathematics not elsewhere classified (080299)
    Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
    Past > Institutes > Information Security Institute
    Copyright Owner: Copyright 2010 International Association for Cryptologic Research
    Deposited On: 20 Aug 2010 12:05
    Last Modified: 11 Aug 2011 02:25

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