Efficient arithmetic on Hessian curves

Reza R. Farashahi, Marc Joye

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

57 Citations (Scopus)

Abstract

This paper considers a generalized form for Hessian curves. The family of generalized Hessian curves covers more isomorphism classes of elliptic curves. Over a finite field , it is shown to be equivalent to the family of elliptic curves with a torsion subgroup isomorphic to Z/3Z. This paper provides efficient unified addition formulas for generalized Hessian curves. The formulas even feature completeness for suitably chosen parameters. This paper also presents extremely fast addition formulas for generalized binary Hessian curves. The fastest projective addition formulas require 9M∈+∈3S, where M is the cost of a field multiplication and S is the cost of a field squaring. Moreover, very fast differential addition and doubling formulas are provided that need only 5M∈+∈4S when the curve is chosen with small curve parameters.

Original languageEnglish
Title of host publicationPublic Key Cryptography, PKC 2010 - 13th International Conference on Practice and Theory in Public Key Cryptography, Proceedings
EditorsPhong Q. Nguyen, David Pointcheval
Pages243-260
Number of pages18
Volume6056 LNCS
DOIs
Publication statusPublished - 2010
Event13th International Conference on Practice and Theory in Public Key Cryptography, PKC 2010 - Paris, France
Duration: 26 May 201028 May 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6056 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other13th International Conference on Practice and Theory in Public Key Cryptography, PKC 2010
CountryFrance
CityParis
Period26/05/1028/05/10

Keywords

  • cryptography
  • Elliptic curves
  • Hessian curves

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