Efficient Pairing Computation with Theta Functions

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Efficient Pairing Computation with Theta Functions
In this paper, we present a new approach based on theta functions to compute Weil and Tate pairings. A benefit of our method, which does not rely on the classical Miller's algorithm, is its generality since it extends to all abelian varieties the classical Weil and Tate pairing formulas. In the case of dimension 1 and 2 abelian varieties our algorithms lead to implementations which are efficient and naturally deterministic. We also introduce symmetric Weil and Tate pairings on Kummer varieties and explain how to compute them efficiently. We exhibit a nice algorithmic compatibility between some algebraic groups quotiented by the action of the automorphism -1, where the Z-action can be computed efficiently with a Montgomery ladder type algorithm.
David Lubicz, Damien Robert
Added 02 Sep 2010
Updated 02 Sep 2010
Type Conference
Year 2010
Where ANTS
Authors David Lubicz, Damien Robert
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