Tate pairing implementation for hyperelliptic curves y2 = xp - x + d

Iwan Duursma, Hyang Sook Lee

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

207 Scopus citations

Abstract

The Weil and Tate pairings have been used recently to build new schemes in cryptography. It is known that the Weil pairing takes longer than twice the running time of the Tate pairing. Hence it is necessary to develop more efficient implementations of the Tate pairing for the practical application of pairing based cryptosystems. In 2002, Barreto et al. and Galbraith et al. provided new algorithms for the fast computation of the Tate pairing in characteristic three. In this paper, we give a closed formula for the Tate pairing on the hyperelliptic curve y2 = xp - x + d in characteristic p. This result improves the implementations in [BKLS02], [GHS02] for the special case p = 3.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsChi Sung Laih
PublisherSpringer Verlag
Pages111-123
Number of pages13
ISBN (Print)3540205926
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2894
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

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