Generating Pairing-friendly curves with the cm equation of degree 1

Hyang Sook Lee, Cheol Min Park

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

8 Scopus citations

Abstract

Refinements of the Brezing-Weng method have provided families of pairing-friendly curves with improved ρ-values by using non-cyclotomic polynomials that define cyclotomic fields. We revisit these methods via a change-of-basis matrix and completely classify a basis for a cyclotomic field to produce a family of pairing-friendly curves with a CM equation of degree 1. Using this classification, we propose a new algorithm to construct Brezing-Weng-like elliptic curves having the CM equation of degree 1, and we present new families of curves with larger discriminants.

Original languageEnglish
Title of host publicationPairing-Based Cryptography - Pairing 2009 - Third International Conference, Proceedings
Pages66-77
Number of pages12
DOIs
StatePublished - 2009
Event3rd International Conference on Pairing-Based Cryptography, Pairing 2009 - Palo Alto, CA, United States
Duration: 12 Aug 200914 Aug 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5671 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd International Conference on Pairing-Based Cryptography, Pairing 2009
Country/TerritoryUnited States
CityPalo Alto, CA
Period12/08/0914/08/09

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