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Perhaps we could:

https://en.m.wikipedia.org/wiki/Homomorphic_encryption

Someone far smarter than me could probably tell us if this actually works in the real world?

Maybe, but are you saying that you could perform an operation like "if string startswith("www") then ..." without decryption? That sounds enormously complicated.

And even so, it would be leaky, because you could follow the execution path and deduce things about the data.

So in summary it sounds implausible, but I may be wrong.

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