search

lowdanie / lowdanie.github.io

2 stars 1 forks source link

blog/2024/01/03/fully-homomorphic-encryption #2

Open utterances-bot opened 4 months ago

utterances-bot commented 4 months ago

http://localhost:4000/blog/2024/01/03/fully-homomorphic-encryption

j2kun commented 3 months ago

Nice article! One minor nitpick: rounding the noisy plaintext is part of decryption (in fact, the hardest part!) and you treat it as part of decoding a plaintext.

If rounding were not part of decryption, then one could implement bootstrapping without all that blind rotate magic, because the first step in bootstrap is to homomorphically apply b - <a,s>, a linear operation. Sec 5.2 of https://eprint.iacr.org/2021/1402 explains this in a bit more detail.

lowdanie commented 3 months ago

Thanks!

I completely agree that it is possible to homomorphically evaluate b - <a,s> much more easily using homomorphic addition and multiplication. However, wouldn't we still need some sort of blind rotate magic to bound the output error?

Also, thanks for the link to that article - it looks great!

j2kun commented 3 months ago

Yes, what I'm saying is your LWE decryption implementation does not round, so it is not technically the complete decryption operation. Putting the rounding as part of decoding is slightly misleading, in my opinion, because of this relationship to homomorphic decryption, which must include that step.

But it is a very minor quibble.

lowdanie commented 3 months ago

That makes sense - thanks!