I'm working on my bachelor thesis and I have some questions. I want to combine a CPA-secure private key encryption scheme and some unforgeable public key signature scheme (in my case some sanitizable signature scheme but I think it doesn't matter). The resulting scheme should be CCA-secure. How can I do that?
If I use a MAC instead of the signature scheme, I get a CCA-secure scheme, but I have to use signatures, since I'm in a juristic context. I tried to combine both schemes them by signing the message and then encrypting the signature together with the message. But I struggle with proving that such a scheme is CCA-secure. CCA Security is only defined for private-key encryption schemes or public key encryption schemes but I have to prove it for the combination of priv key encr. and pub key signatures.
So my questions are:
How can I combine an unforgeable Public key signature scheme with a CPA secure private key encryption scheme, such that the resulting scheme is CCA secure?
How can I prove CCA Security for such a scheme, since it is not defined?