Hypothesis: We define the messages on a field $\mathtt{F}_p$, where $p$ is a large prime number.
I am considering a dynamic outsourced private data scenario.
Assume we have 3 messages: $m_1=2, m_2=4$ and $m_3=77$. We encrypt them using FHE, so we would have: $E(m_1), E(m_2)$ and $E(m_3)$.
We send the three ciphertexts to a semi-honest server.
Later on, we want to remove $E(m_1)$ from the outsourced data (in fact we want to remove $m_1$ from there).
Question 1: If we encrypt $m_1$, and send it to the server, can the server "somehow" find $E(m_1)$ and remove it?
Question 2: Is there any other way to remove $m_1$ from the outsourced dataset without leaking any information to the server?
Please note that we are using semantically secure encryption (e.i. FHE); therefore, the ciphertexts of the $m_1$ are different.