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Alice needs to get non public information from Bob, validate it (let's say check that birth day is between 1900 and now) and forward it to Charlie. There's an end to end encryption between Alice and Bob and Alice and Charlie.

If the computer Alice uses is some remote machine, can Alice avoid leaking the non public information she is handling to whoever has access to the machine she uses?

My undestanding is that the moment the data is decrypted in the machine's memory it's at the mercy of whoever has physical access to that machine. Is that correct? If so. Does that mean that for handling non public information I should never use cloud solutions and rely only on physical machines that I own?

I see there's "Homomorphic encryption". But I understand that if, as in my example, I have to validate that a number is btween x and y it's equivalent to the number being known?

There's a somewhat similar question here: encrypting data while in memory

But it does not focus on these questions and is implementation specific.

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For your first question:

If Alice's machine is compromised, her private data is compromised too. There's no way to protect this "non public data" from someone who has access to the machine generating it. Of course I am assuming low level access here (administrator or VM-host), if the machine is shared but has proper user level security, then it may be okay.

For the second question:

Handling private data on cloud providers is indeed a bad idea. There is absolutely no way to keep anything private from the host machine while operating inside a VM.

When I see people trying to run privacy services in the cloud, it always makes me cringe.

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