How to change the field of the elliptic curve to the new value N while keeping the default Secp256k1 parameters?
The elliptic curve is secp256k1: y2 = x3 + 7 (mod p)
where the field size is
p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F.
The curve order of secp256k1 is:
n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
The public key P (point) is calculated by multiplying the private key d (scalar) by the generator point G (point) where
P = d (mod n).G
The n (N) you state is not the field size p, it is the curve order
n = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
This curve order n is such that nG = point at infinity. This is a property of the curve and cannot be changed.
Thanks to Pieter Wuille for the corrections.