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.
- Cyclotomic family
- Cyclotomic polynomial
- Ideal family
- Pairing-friendly elliptic curve