On the ρ-values of complete families of pairing-friendly elliptic curves
The parameter ρ of a complete family of pairing-friendly elliptic curves represents how suitable some given elliptic curves are in pairing-based cryptographic schemes. The superiority of the curves depends on how close ρ is to 1. Especially, the situation is ideal. We study whether a complete famil...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2012-12-01
|
| Series: | Journal of Mathematical Cryptology |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jmc-2012-0011 |
| Summary: | The parameter ρ of a complete family of pairing-friendly elliptic curves
represents how suitable some given elliptic curves are in pairing-based cryptographic schemes.
The superiority of the curves depends on how close ρ is to 1.
Especially, the situation is ideal.
We study whether a complete family of pairing-friendly elliptic curves has a ρ-value 1 or not.
In this paper, we consider the original idea of Brezing and Weng that we put a parameter for constructing families of elliptic curves as cyclotomic polynomials.
We show that the ρ-values cannot be 1 in many cases. |
|---|---|
| ISSN: | 1862-2976 1862-2984 |