@Pro7ech thank you the explanation. I want to add a couple of comments and answer the question about the “alpha” version of interactive CKKS bootstrapping.
As @Pro7ech pointed out, in the proposed interactive protocol, we do need to do masking using a flooding distribution of 128+ bits as we do masking over integers rather than integers mod q. This requires carrying additional (typically 3) RNS limbs (“levels”) before interactive CKKS bootstrapping can be called. This flooding does get trickier in the case of regular threshold FHE or IND-CPA decryption (not interactive bootstrapping), and we will soon update the existing thread on it in the discourse forum: Appropriate error parameters for the noise flooding. Some new options are also getting added to OpenFHE.
As for the availability of interactive CKKS bootstrapping in OpenFHE, we are planning to add the initial implementation to the main OpenFHE repo shortly after the v1.0 release. Currently we are wrapping up v1.0, which will be released in November. It will have a couple of significant improvements as compared to v0.9.5.