New answers tagged functional-encryption
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It is not true that the functional encryption acts as access control on data since you don't control access on data once you know the key but you know the result of a function applied on data. For instance if the function is find the minimum then you can learn the minimum coefficient of a vector encrypted appropriately. If your function is the decryption ...
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Existing definitions for functional encryption don't support "combining" ciphertexts in the way that you suggest.
As far as doing more than just access control, two very recent papers (to appear next month at STOC 2013) achieve functional encryption for arbitrary functionalities:
Attribute-Based Encryption for Circuits by Gorbunov, Vaikuntanathan, Wee
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