Comment by ruined
4 days ago
it's incredibly algorithm-dependent. if you look into the thesis that originates the 'bootstrapping' technique to transform SHE algorithms into FHE, they determine the noise limit of their specific algorithm in section 7.3 and then investigate expanding the noise limit in 8 and 10.
(written in 2009) http://crypto.stanford.edu/craig/craig-thesis.pdf
some newer FHE don't encounter a noise limit or don't use the bootstrapping technique.
All known FHE schemes use bootstrapping
i expected that, but a search turned up several things claiming to implement fhe without bootstrapping. i didn't investigate and i can't say i'm familiar so maybe they're bogus
Correction: all known even-remotely-practical schemes rely on bootstrapping. See https://crypto.stackexchange.com/questions/103341/fully-homo...
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I did see an arxiv paper a while back that claimed to use category theory to do this, but my best bet was it was not secure.