Is there any encryption method (theoretical) that could process instructions on encrypted code? Is there anything such as an encrypted Turing machine? More precisely, is there any (encryption) system such that given:


a Turing machine: T
a public/private key pair


there exists a Turing machine T' (or something Turing machine like) where the tape, states and so on are encrypted using (this method together with the) the public key and such that if, both T and T' are let run for the same number of steps, the state and tape of T' decrypted with the private key equals the state and tape of T.

ie. is there some encryption where one can apply basic operations on the encrypted data?...
Yes. ​ It's called Fully Homomorphic Encryption.