New families of hyperelliptic curves with efficient gallant-lambert- vanstone method

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Abstract

The Gallant-Lambert-Vanstone method [14] (GLV method for short) is a scalar multiplication method for elliptic curve cryptography (ECC). In WAP WTLS[47], SEC 2[42], ANSI X9.62[1] and X9.63[2], several domain parameters for applications of the GLV method are described. Curves with those parameters have efficiently-computable endomorphisms. Recently the GLV method for hyperelliptic curve (HEC) Jacobians has also been studied. In this paper, we discuss applications of the GLV method to curves with real multiplication (RM). It is the first time to use RM in cryptography. We describe the general algorithm for using such RM, and we show that some genus 2 curves with RM have enough effciency to be used in the GLV method as in the previous CM case.

Original languageEnglish
Pages (from-to)279-295
Number of pages17
JournalLECTURE NOTES IN COMPUTER SCIENCE
Volume3506
DOIs
Publication statusPublished - 2005
Externally publishedYes
Event7th International Conference on Information Security and Cryptology - ICISC 2004 - Seoul, Korea, Republic of
Duration: 2004 Dec 22004 Dec 3

Keywords

  • Elliptic Curve Cryptography
  • GLV Method
  • Hyperelliptic Curve Cryptography
  • Public Key Cryptography
  • Scalar Multiplication

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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