Add a cryptocurrency wallet for which the signing keys are the private keys, and now it’s more like an immortal, non-subpoena-able corporation executing your desires using its treasury assets. (Which can include hiring real people to do real-world things, and even—given that you could provision crypto mining capacity—making income to keep said corporation’s actions [relatively] self-sustaining.)
But seriously while amazing in potential, having semi-intelligent contracts running around indefinitely would eventually have to cause havoc. Either by the “Paperip Maximizer” effect [1] or just having a huge weight dragging down the economy from accruing smart contracts.
But, assuming that one does, ever, want someone else to do a proprietary computation on one's data, it'd be real nice if that didn't require giving up plaintext.
(And yeah, HE "noise" is a pain)
We did a some basic research on that for a seminar, and I wanted to figure out how far this can be pushed for a more "real life"-setting with the four roles mentioned in the introduction. I ran into slight time problems since the implementation was more difficult than I expected & due to some out-of-university-related stuff.
Anyway, maybe things changed in the past 6 years and my conclusion from back than doesn't hold anymore. So this could be more feasible now. Let me know what you think ;-)
For everything else rubber hose cryptanalysis will work.
This sort of thing is called "security through obscurity" and the consensus is that it doesn't work. It can be a deterrent to adversaries lacking in skill or motivation, but it isn't a very strong layer. Attackers quickly discover that one company looks much like the next, and they develop an intuition for what sort of data a company needs to collect to accomplish their tasks. Additionally, there's tons of sensitive data that companies in certain industries are required to collect & retain, and those laws are a matter of public record. You aren't going to outfox them into thinking you don't have blueprints of your widgets and evaluations of your employees on file somewhere; focus on keeping them away from them.
(c(mod p)) (mod 2) = (p * q + 2 * r + m (mod p)) (mod 2) = 2r + m (mod 2) = m
As @tuxxy points out, there is a metaphor for describing this - a "noise ceiling". To see this phrase used in context, see, for example: https://eprint.iacr.org/2011/277.pdf
That post is here: https://radicalrafi.github.io/posts/homomorphic-encryption/
If c is the ciphertext than can't someone simply mod 2 and "decrypt" it?