- Check that $Q_a$ is not equal to the identity element $O$, and its coordinates are otherwise valid.
- Check that $Q_a$ lies on the curve.
- Check that $n*Q_a = O$
- Verify that $r$ and $s$ are integers in $[\![1;n-1]\!]$. If not, the signature is invalid.
What is the mathematical reason for these checks and what can an attacker do if these checks are not carried out properly?