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If we encrypt $m_1$, and send it to the server, can the server "somehow" find $E(m_1)$ and remove it? Nope; FHE allows a server that knows $E(m_1)$ and $E(m_2)$ to produce a ciphertext which is a representation of the value $E(m_1 \odot m_2)$ (for pretty much arbitrary functions $\odot$); what it doesn't allow a server to do is determine whether $m_1 = ...

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