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

Hyang Sook Lee; Cheol Min Park

doi:10.1007/978-3-642-03298-1_5

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

Hyang Sook Lee, Cheol Min Park

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 language	English
Title of host publication	Pairing-Based Cryptography - Pairing 2009 - Third International Conference, Proceedings
Pages	66-77
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-03298-1_5
State	Published - 2009
Event	3rd International Conference on Pairing-Based Cryptography, Pairing 2009 - Palo Alto, CA, United States Duration: 12 Aug 2009 → 14 Aug 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5671 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Conference on Pairing-Based Cryptography, Pairing 2009
Country/Territory	United States
City	Palo Alto, CA
Period	12/08/09 → 14/08/09

Access to Document

10.1007/978-3-642-03298-1_5

Cite this

Lee, H. S., & Park, C. M. (2009). Generating Pairing-friendly curves with the cm equation of degree 1. In Pairing-Based Cryptography - Pairing 2009 - Third International Conference, Proceedings (pp. 66-77). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5671 LNCS). https://doi.org/10.1007/978-3-642-03298-1_5

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title = "Generating Pairing-friendly curves with the cm equation of degree 1",

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.",

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doi = "10.1007/978-3-642-03298-1_5",

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Lee, HS & Park, CM 2009, Generating Pairing-friendly curves with the cm equation of degree 1. in Pairing-Based Cryptography - Pairing 2009 - Third International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5671 LNCS, pp. 66-77, 3rd International Conference on Pairing-Based Cryptography, Pairing 2009, Palo Alto, CA, United States, 12/08/09. https://doi.org/10.1007/978-3-642-03298-1_5

Generating Pairing-friendly curves with the cm equation of degree 1. / Lee, Hyang Sook; Park, Cheol Min.

Pairing-Based Cryptography - Pairing 2009 - Third International Conference, Proceedings. 2009. p. 66-77 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5671 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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.

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

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