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The scenario : using a Multikey FHE scheme, let's say LTV-FHE scheme, parties delegate the computation of some function to the mighty cloud. In LTV-FHE scheme the parties generate their keys and encrypt their messages independently.

If parties have different moduli ladders then what rings should the cloud choose for its computation ? Or the parties should have a common setup in what regards the moduli ladder ?

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This question is related with your other question, and the reason the parties can't use different values of $q$ is the same: operations will not be well defined.

Moreover, the statements, proofs, etc, on the paper you have cited are done assuming that all the users are using the same parameters, which means, not only the same value of $q$, but also the same $B$-bounded distribution $\chi$, the same cyclotomic polynomial $\phi$ and so on...

For instance, take a look at lemma 3.6. The authors start it by fixing the parameters and then saying that the scheme is "multikey homomorphic for $N$ keys".

So, the users have to agree about a set a parameters and then generate their own keys independently.

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  • $\begingroup$ "So, the users have to agree about a set of parameters... ". I think the parameters can be picked by the cloud (server), so they do not need to interact/know each other beforehand. $\endgroup$ – user153465 Mar 2 '16 at 18:11
  • $\begingroup$ Yes, I think it is a plausible option. But the server is the main attacker in this scenario of "cloud computing over encrypted data", so, the users have to at least check if the chosen parameters guarantee a secure scheme. $\endgroup$ – Hilder Vítor Lima Pereira Mar 2 '16 at 18:39

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