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I read the proof of modulus switching and realised that it can be extended to integers, but do we actually use it for integer encryption in practice? Consider that we are doing additive and multiplicative operations modulo $t$. So, we'll have to find $p$ s.t. $p$ mod $t \equiv q$ mod $t$ and we'll have to round $c' = (p/q) \cdotp c$ s.t $c' \equiv c$ mod $t$. So, is it feasible to do modulus switching in such a setup?

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