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Let's say that we have an original homomorphically encrypted program with any possible code inside. What methods can it use to ensure that it is impossible to create an exact copy of it? Are there such ways?

I understand that a person without a key will not see the internal content of a homomorphically encrypted program, I'm interested in whether it is possible to limit the exact copying of this program entirely

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  • $\begingroup$ Do you want stop copying it per se, or do you want to stop anyone accessing the data inside the file if they do copy it, as per typical digital rights management techniques? Ist and 2nd paragraphs seem to marginally contradict... $\endgroup$
    – Paul Uszak
    Jul 28, 2018 at 14:39
  • $\begingroup$ The point of fully homomorphic encryption is to be able to calculate with encrypted data, i.e., the data is kept secret, not the program. For keeping the program secret, you need something like indistinguishability obfuscation, but of course this doesn't prevent anyone from copying it. $\endgroup$
    – j.p.
    Mar 20, 2019 at 7:19

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That sounds impossible: your homomorphically encrypted program is just a program itself, and the fact that it runs some FHE does not matter with respect to the question of whether it can be copied.

A user with direct access to the program can always copy it, whatever you do (e.g. he could always take photos of the source code with his smartphone if he wanted).

If you want to make it truly impossible to copy, you need to run it in a secure environment (and as such a program will be likely very lengthy, that would most likely correspond to running it on a trusted machine to which the user is only given some input-output access).

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