InforLorV4, Hal, Corpus, bibRecord, 001F03

Efficient pairing computation with theta functions

Identifieur interne : 001F03 ( Hal/Corpus ); précédent : 001F02; suivant : 001F04

Efficient pairing computation with theta functions

Auteurs : David Lubicz ; Damien Robert

Source :

RBID : Hal:hal-00528944

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.

Url:

https://hal.archives-ouvertes.fr/hal-00528944

DOI: 10.1007/978-3-642-14518-6_21

Links to Exploration step

Hal:hal-00528944

Le document en format XML

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<front><div type="abstract" xml:lang="en">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.</div>
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<monogr><title level="m">Algorithmic Number Theory 9th International Symposium, Nancy, France, ANTS-IX, July 19-23, 2010, Proceedings</title>
<meeting><title>ANTS IX - Algorithmic Number Theory 2010</title>
<date type="start">2010-07-19</date>
<date type="end">2010-07-23</date>
<settlement>Nancy</settlement>
<country key="FR">France</country>
</meeting>
<editor>Guillaume Hanrot and François Morain and Emmanuel Thomé</editor>
<imprint><publisher>Springer-Verlag</publisher>
<biblScope unit="serie">Lecture Notes in Computer Science</biblScope>
<biblScope unit="volume">6197</biblScope>
<biblScope unit="pp">251-269</biblScope>
<date type="datePub">2010</date>
</imprint>
</monogr>
<idno type="doi">10.1007/978-3-642-14518-6_21</idno>
</biblStruct>
</sourceDesc>
<profileDesc><langUsage><language ident="en">English</language>
</langUsage>
<textClass><classCode scheme="halDomain" n="info.info-sc">Computer Science [cs]/Symbolic Computation [cs.SC]</classCode>
<classCode scheme="halTypology" n="COMM">Conference papers</classCode>
</textClass>
<abstract xml:lang="en">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.</abstract>
</profileDesc>
</hal>
</record>

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Efficient pairing computation with theta functions

Efficient pairing computation with theta functions

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