TY - GEN
T1 - Generating Pairing-friendly curves with the cm equation of degree 1
AU - Lee, Hyang Sook
AU - Park, Cheol Min
PY - 2009
Y1 - 2009
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=69949189671&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-03298-1_5
DO - 10.1007/978-3-642-03298-1_5
M3 - Conference contribution
AN - SCOPUS:69949189671
SN - 3642032974
SN - 9783642032974
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 66
EP - 77
BT - Pairing-Based Cryptography - Pairing 2009 - Third International Conference, Proceedings
T2 - 3rd International Conference on Pairing-Based Cryptography, Pairing 2009
Y2 - 12 August 2009 through 14 August 2009
ER -