Calculating random number in ECDSA based on private key and signature In ECDSA (Elliptic Curve Digital Signature Algorithm) we use a random number k in the signature process.

Signature in ECDSA is:

$$ (x_1,y_1) = k * G $$
$$r = x_1 \mod n $$
$$s = k^{-1} (z+rd_{a}) \mod n$$

If we know the private key $d_a$ and signature (r,s) would it be possible to calculate random k? If no how hard would it be to calculate that?
This is immediate:
$$ k = s^{-1} (z + r \, d_a) \bmod n $$
where $z$ is the hash value of the message being signed.