Does homomorphic operations have to process one level by one level in BGV?

DDD

10/26/23, 6:22 AM

Suppose the highest level is $L$. There are 2 ciphertexts from 2 different messages under the same secret key but in different level, one is in level $\ell$: $\mathsf{ct}(\pmb{m})\in\mathcal{R}_{Q_{\ell}}^{2}$, one is in level $k$: $\mathsf{ct'}(\pmb{m}')\in\mathcal{R}_{Q_{k}}^{2}$, and $k<l-1$.

We want to calculate homomorphic multiplication of $\mathsf{ct}$ and $\mathsf{ct'}$. Should we move $\mathsf{ct}(\pmb{m})$ down, step by step, or can we actually move it just once by directly switching $Q_{\ell}$ to $Q_{k}$?

I have this confusion because I didn't find a scheme that seems to have discussed on this situation. Do we have papers/references discussing about it? Thanks!

0 + 4

homomorphic-encryption

kelalaka

10/26/23, 10:32 AM

They must be in the same level, and the library provides the tools for that...

DDD

10/27/23, 1:26 AM

Thanks @kelalaka. I mean should I move the ct up/down one level by another, or can I jump multiple levels for a ct?

kelalaka

10/27/23, 7:58 AM

Switching multiple down levels is possible, afaik for the up-level you need some other operation like bootstrapping.

DDD

10/28/23, 3:09 AM

Thanks @kelalaka. I understand it now.

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