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.
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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|Item Type:||Conference Paper|
|Keywords:||pairings, Miller functions, explicit formulas, Tate pairing, ate pairing, twists, Weierstrass curves|
|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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