More Discriminants with the Brezing-Weng Method
Gaetan Bisson, Takakazu Satoh
TL;DR
This paper enhances the Brezing-Weng method to generate more pairing-friendly elliptic curves with larger discriminants, improving diversity and avoiding small class number endomorphism rings.
Contribution
It introduces an improvement to the Brezing-Weng method that increases the number of generated curves and helps avoid small class number endomorphism rings.
Findings
More curves with larger discriminants can be generated.
The method helps avoid endomorphism rings with small class number.
Enhanced diversity of pairing-friendly elliptic curves.
Abstract
The Brezing-Weng method is a general framework to generate families of pairing-friendly elliptic curves. Here, we introduce an improvement which can be used to generate more curves with larger discriminants. Apart from the number of curves this yields, it provides an easy way to avoid endomorphism rings with small class number.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Algebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques