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Is it secure if a secret key is used in the function of a functional encryption?

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laolien

In my scheme, two functional encryptions FE1 and FE2 are used. The function f1 corresponding to FE1 is as follows:

f1_y(x)
{ hardwired msk2
  output  sk2 = FE2.KeyGen(msk2, (x, y))
}

where msk2 is the master key of FE2.

Then, the user obtains the private key sk1_y=FE1.KeyGen(msk1, y). For any ciphertext c=FE1.Enc(x), the user can obtain a new private key sk2 = FE1.Dec(sk1_y, c).

Is it secure that msk2 is embedded in the function f? How to prove the security?

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