Scalar field¶
In the context of elliptic curve group, scalar field \(F_r\) is the field of scalars used in the operations performed on the curve, such as point addition, scalar multiplication, and pairing. The scalar field size \(r\) is also the size of the largest subgroup of prime order. Interestingly, the Elliptic Curve DLP (ECDLP) of an elliptic curve is only as hard as that curve’s largest prime order subgroup, not its order. However, when curve’s order is prime, its largest prime subgroup is the group itself, so \(r\) is also the order of the group.