I am facing an issue regarding the paper FHEW: Bootstrapping Homomorphic Encryption in less than a second. It concerns the MSBextract algorithm during the refresh procedure.
Especially, they mentioned that we could change this algorithm to a more "general" one that would allow to check the membership for different subsets of integers $\bmod t$ in only one refresh procedure. However, I can't find an "efficient" approach to this problem (the one I have in mind needs more than one refresh).
Does any of you have some "hint" to guide me to the right direction?
P.S. They also mentioned a xor-for-almost-free
procedure if the plaintext modulus is turned to $t=6$. I don't really understand that as - I believe - it perfectly works with $t = 4$ with the subset $S = {1;3}$. If I am wrong, please let me know.