Abstract
We heuristically analyze the Cocks-Pinch method by using the Bateman-Horn conjecture. Especially, we present the first known heuristic which suggests that any efficient construction of pairing-friendly elliptic curves can efficiently generate such curves over pairing-friendly fields, naturally including the Cocks-Pinch method. Finally, some numerical evidence is given.
| Original language | English |
|---|---|
| Pages (from-to) | 103-118 |
| Number of pages | 16 |
| Journal | Advances in Mathematics of Communications |
| Volume | 8 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Feb 2014 |
| Externally published | Yes |
Keywords
- Bateman-Horn conjecture
- Cocks-Pinch method
- Pairing-friendly elliptic curve
- Pairing-friendly field