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I often see homomorphic encryption as a solution to a problem where a server wants to know the sum of $n$ users' numbers but can not know each individual users' number plaintexts.

My question is: if $n=10$, and only $9$ of the ciphertexts are reported, can the server decrypt the sum of those $n-1$ ciphertexts?

Furthermore, do the $n$ users' keys depend on the server's 'master key'?

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    $\begingroup$ With the most basic schemes, the server can in fact decrypt each share it receives. If you do some fancier things, like clever blinding and proxy-re-encryption and all that stuff, things may look differently. $\endgroup$ – SEJPM Mar 4 '16 at 20:56
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    $\begingroup$ To really answer this question, we are going to have to know more details about how you would implement your system. $\endgroup$ – mikeazo Mar 4 '16 at 20:59
  • $\begingroup$ Do you have any reference to homomorphic schemes in which the users have their own keys and the server has a master key? $\endgroup$ – Hilder Vítor Lima Pereira Mar 6 '16 at 2:57

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