Abstract
Let k D 2mpn for an odd prime p and integers m0 and n0. We obtain lower bounds for the values of cyclotomic families of pairing-friendly elliptic curves with embedding degree k and r.x/D k.x/. Our bounds imply that none of the families are ideal.
| Original language | English |
|---|---|
| Pages (from-to) | 417-440 |
| Number of pages | 24 |
| Journal | Journal of Mathematical Cryptology |
| Volume | 8 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Dec 2014 |
| Externally published | Yes |
Keywords
- Cyclotomic family
- Cyclotomic polynomial
- Ideal family
- Pairing-friendly elliptic curve