I have access to an oracle that can encrypt and partially decrypt a number with RSA-1024 algorithm.
For encryption:
\begin{equation}
C = M^e\bmod n
\end{equation}
But for decryption, result will be $\bmod256$:
\begin{equation}
\textit{partialM} = (C^d\bmod n)\bmod 256
\end{equation}
Also I know $e=65537$, and $d$ and $n$ will remain unchanged.
I want to know if it's possible for a given $C$ to find $M$.
If yes, how?