Fully Homomorphic Encryption (FHE)
Remember that FHE does not ensure authenticity of your data by default, it provides only privacy.<p>If you send your server two encryped numbers and ask to multiply them for you, the server may send you their addition instead, or just encrypt some constant it chooses and send you that. And you can't check that your data was processed the way you want.<p>If you want authenticated FHE, that will be even slower.<p>For anyone who wanted a database to query privately, you can look at dishonest majority generic MPC protocols. Here, you will need N servers instead of just one. You will secret-share your inputs between them, and let them do computations on the shares. As long as at least one of the N servers is acting in your interest, you are safe. But if all servers unite their shares, they can recover your values.