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I'm trying to make my way in Functional Encryption used for access control.

I read a lot of papers such as "How to Run Turing Machines on Encrypted Data", "Functional Encryption: New Perspectives and Lower Bounds", or "Attribute-based encryption for circuits" and I ended up with a feeling of uncertainty in my understanding as they are quite hard to digest. What I'm looking for is an ABE-like scheme where policy may contain both logic and algebraic gates. For example:

"job=doctor" AND "age mod 2 = 0"

this (stupid) policy provides access to the plaintext to doctors whose age is even.

Pushing on the line, a policy could include arbitrary computation such as a signature verification algorithm. From what I read, I feel the only hope of achieving these goals lies in FE. Is there a scheme able to meet these requirements (at least the first policy)? At which cost?

How much of what I wrote is reality, what is achievable and what is fiction?

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In functional encryption, the function don't apply on access policy. In FE the receiver obtain the function of message. Attribute Based Encryption for arithmetic circuits may help you. Fully key hommomorphic encryption for ABE for arithmetic circuits from Boneh et. al presented to this problem. Although the FE is the general of ABE.

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