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Homomorphic encryption schemes are PKE schemes with an additional special method Evaluate. Evaluate method takes input any function (as boolean circuit) and encrypted inputs of the function and evaluates the circuit. The results of such function are still encrypted under the public key PK.

Sometimes, it would be too wide of a scope to allow execution of any arbitrary function.
How can one limit FHE schemes to allow only fewer circuits?

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Should your title be parsed as "access [control functionality]" or "access-control functionality"? $\;\;$ –  Ricky Demer Aug 1 '13 at 22:52
    
it should be "access (control functionality)" i would correct it , the other one would be easy believe , rite ? –  sashank Aug 2 '13 at 3:13
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By itself, no. Though research has been done to add the necessary features to make FHE circuit computation verifiable. These protocols would allow the one party to specify what can be computed on the encrypted data and then verify that the computation has been performed properly.

Thus, it differs from Functional Encryption somewhat. In FE, the worker can only compute the desired functionality. In HE, the worker could still presumably compute any circuit they wanted, but they could not forge a proof to trick the other party into believing that they had computed the correct circuit. Since the output is encrypted and the cipher is semantically secure, being able to compute any circuit on the ciphertexts will not leak any information.

See:
Non-interactive Verifiable Computing: Outsourcing Computation to Untrusted Workers
Delegatable Homomorphic Encryption with Applications to Secure Outsourcing of Computation

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Mike , VC and Delegatable HE would allow to verify operations are performed or not . But we cannot restrict/narrow down the circuits that can be allowed to run. And yes FE is right choice for limiting functionality am trying to find ways of realizing FE with FHE –  sashank Aug 2 '13 at 16:12
    
I see your point. What these things do is say "sure you can compute anything, but I'll only accept the value if you computed the desired circuit". That should have the effect of forcing the cloud, for example, to perform exactly the computation you want. I see your point though, but since the cloud never learns anything about the computed value, it doesn't help them to compute unauthorized circuits. –  mikeazo Aug 2 '13 at 16:15
    
Ok now i see your point too . –  sashank Aug 2 '13 at 19:11
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