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There are ways to prevent Bob from having complete control over the randomness pool. You could use some form of verified randomness, where your function $f$ checks that the random string is signed before executing. This would work using, for instance, the NIST randomness beacon. You could also contain within $f$ a PRNG, so Bob does not need to provide all ...


Layering your encryption mechanisms like that would not display collusion-resistance between the two schemes. For example, someone with an Org-A key could decrypt the outer encryption over a record designated for Org-A administrators and then pass the inner ciphertext to someone with an Administrator key. Of course, you could use a different key for each ...

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