6

While I still think it would be good for you to ask more specific questions, the following might be useful in clearing up your understanding of the underlying hard problems on lattices. I do not see a way to discuss homomorphic encryption as well without essentially writing some (informal) lecture notes, so won't in this answer. The LWE Problem: The central ...


4

The output of bootstrapping has relatively small noise because it starts from an encryption (of the secret key) that has very small noise, and performs some homomorphic operations on it. These operations increase the noise somewhat, but it starts out so small that the result still doesn’t have much noise. It doesn’t really matter that the ciphertext being ...


3

This will likely be rather expensive. This is because the problem you describe seems like it would be hard to express as a shallow arithmetic circuit, which is a rough estimate of how difficult the computation is with FHE. In particular, a naive algorithm for solving your problem is: Instantiate some hashmap Iterate through your textfile, when you see the ...


2

It's still just evaluation of a circuit, which in general, increases the noise. Yes and no. Homomorphic operations do (generically) increase the noise, but the idea behind bootstrapping is to evaluate a circuit which itself decrypts the ciphertext. Decrypting the ciphertext (if the noise is below some threshold) zeros out the noise. This means there are two ...


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