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

Katsuyuki Takashima

doi:10.1007/11496618_21

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

Katsuyuki Takashima^*

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

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 language	English
Pages (from-to)	279-295
Number of pages	17
Journal	LECTURE NOTES IN COMPUTER SCIENCE
Volume	3506
DOIs	https://doi.org/10.1007/11496618_21
Publication status	Published - 2005
Externally published	Yes
Event	7th International Conference on Information Security and Cryptology - ICISC 2004 - Seoul, Korea, Republic of Duration: 2004 Dec 2 → 2004 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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10.1007/11496618_21

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title = "New families of hyperelliptic curves with efficient gallant-lambert- vanstone method",

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.",

keywords = "Elliptic Curve Cryptography, GLV Method, Hyperelliptic Curve Cryptography, Public Key Cryptography, Scalar Multiplication",

author = "Katsuyuki Takashima",

year = "2005",

doi = "10.1007/11496618_21",

language = "English",

volume = "3506",

pages = "279--295",

journal = "LECTURE NOTES IN COMPUTER SCIENCE",

issn = "0302-9743",

publisher = "Springer Verlag",

note = "7th International Conference on Information Security and Cryptology - ICISC 2004 ; Conference date: 02-12-2004 Through 03-12-2004",

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AU - Takashima, Katsuyuki

PY - 2005

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N2 - 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.

AB - 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.

KW - Elliptic Curve Cryptography

KW - GLV Method

KW - Hyperelliptic Curve Cryptography

KW - Public Key Cryptography

KW - Scalar Multiplication

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

Abstract

Keywords

ASJC Scopus subject areas

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