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I am currently doing some reading on Homomorphic Encryption for research purposes and based on my reading using the Boolean Circuit Model of Computation specifically in regards to Fast Fully Homomorphic Encrytion over the Torus(TFHE) how is it considered fast and why is the noise growth and depth negligible?

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    $\begingroup$ What do you mean by "how is it considered fast"? Authors say that it is fast because they compared with other schemes... Moreover, why do you think the noise is negligible in TFHE? $\endgroup$ – Hilder Vitor Lima Pereira Aug 19 '19 at 17:26
  • $\begingroup$ Cause from what i was able to understand the features Boolean Circuits model of computation is that it is capable of fast number comparison, fast bootstrapping, very low latency for single function evaluations, and that noise and depth are negligible so i assumed since TFHE uses the Boolean Circuits as a computation model that noise and depth are negligible as well am i wrong in that regards? and as for how it is fast i guess it would have been better to ask what makes the model fast in comparison to using Modular Arithmetic Model and Approximate Polynomial Model. $\endgroup$ – fallere456 Aug 20 '19 at 8:56
  • $\begingroup$ Mostly FHE schemes evaluate circuits, but we can easily translate it to evaluating "functions". Hence, what is special about TFHE isn't the model of computation, but the fast bootstrapping method that they managed to construct by modifying the bootstrapping of FHEW. I think your question is not hard, but it is not clear what you want to know. Maybe you can edit it to make it more clear? That part about the noise being negligible is particularly obscure... $\endgroup$ – Hilder Vitor Lima Pereira Aug 20 '19 at 9:40
  • $\begingroup$ @fallere456 TFHE/FHEW are "fast" because they optimize bootstrapping to be as fast as possible, at the expense that you have to bootstrap after each gate. This means that each "call" to boostrapping might be fast, but you'll need more overall. I'm unsure how this impacts how much time is spent bootstrapping in them vs other schemes (it may be in the TFHE/FHEW papers). $\endgroup$ – Mark Aug 21 '19 at 6:55

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