Ate Pairing on Hyperelliptic Curves

Robert Granger, Florian Hess, Roger Oyono, Nicolas Theriault, Fre Vercauteren

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

45 Citations (Scopus)


In this paper we show that the Ate pairing, originally defined for elliptic curves, generalises to hyperelliptic curves and in fact to arbitrary algebraic curves. It has the following surprising properties: The loop length in Miller's algorithm can be up to $g$ times shorter than for the Tate pairing, with $g$ the genus of the curve, and the pairing is also automatically reduced, i.e., no final exponentiation is needed.
Translated title of the contributionAte Pairing on Hyperelliptic Curves
Original languageEnglish
Title of host publicationAdvances in Cryptology - EUROCRYPT 2007
PublisherSpringer Berlin Heidelberg
Publication statusPublished - 2007

Bibliographical note

Other page information: 430-447
Conference Proceedings/Title of Journal: Advances in Cryptology - EUROCRYPT 2007
Other identifier: 2000709


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