Fast elliptic curve arithmetic and improved weil pairing evaluation

Kirsten Eisenträger, Kristin Lauter, Peter L. Montgomery

Research output: Chapter in Book/Report/Conference proceedingChapter

58 Scopus citations

Abstract

We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P+Q from given points P, Q on the curve. We give applications to simultaneous multiple scalar multiplication and to the Elliptic Curve Method of factorization. We show how this improvement together with another idea can speed the computation of the Weil and Tate pairings by up to 7.8%.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsMarc Joye
PublisherSpringer Verlag
Pages343-354
Number of pages12
ISBN (Print)3540008470, 9783540008477
DOIs
StatePublished - 2003

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2612
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Eisenträger, K., Lauter, K., & Montgomery, P. L. (2003). Fast elliptic curve arithmetic and improved weil pairing evaluation. In M. Joye (Ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 343-354). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2612). Springer Verlag. https://doi.org/10.1007/3-540-36563-x_24