discrete log in two dimension
I want to calculate a discrete log problem on elliptic curves. $P$ and $Q$ are points of order $D$ in elliptic curve formed a basis of $E[D]$, and $R$ is a point of order $D$. I want to calculate $a,b$ such that $aP+bQ=R$.
Just loop over all integer $a,b$ in $[0,D)^2$, compute $aP+bQ$ and check if the result is $\pm R$. Do we have a special case to solve?