hal-00528944, version 1
Efficient pairing computation with theta functions
ANTS IX - Algorithmic Number Theory 2010 6197 (2010) 251-269
Abstract: 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.
- 1:
- CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
- 2:
- INRIA – CNRS : UMR7503 – Université de Lorraine
- Domain : Computer Science/Symbolic Computation
- Comment : The original publication is available at www.springerlink.com
- hal-00528944, version 1
- http://hal.archives-ouvertes.fr/hal-00528944
- oai:hal.archives-ouvertes.fr:hal-00528944
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- Submitted on: Saturday, 23 October 2010 00:38:04
- Updated on: Wednesday, 26 January 2011 10:09:03
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