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Since all evaluation in BGV scheme is on polynomials it seems that it does not really matter if the coefficients of the polynomials are within $q$ range or not. All must be okay for the congruent values.

I have the following questions:

  1. If there are no specific optimizations (e.g. RNS) for BGV, can we work in modulo $Kq$, where $K$ is some arbitrary number? Let us ignore encryption/decryption and focus only on adversary side evaluations: additions/multiplications.

  2. If the answer to question 1 is yes, then what optimizations can be affected or broken by working in $Kq$?

  3. Is it the same for BFV scheme?

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  • $\begingroup$ Oddy has indicated that the Q is fine now. And yes, this is just a message to bump it up after 3 days of being hidden. $\endgroup$
    – Maarten Bodewes
    Mar 23, 2023 at 10:28

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