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I am pretty new to cryptography.

Recently I run into this question where I have two different public keys with the same private key, and I need them for fully homomorphic encryption.

Let's say messages from party $A$ and party $B$ are encrypted by two different public keys and FHE operations are performed on the encrypted messages. Party $C$ having his own private key wants to decrypt it. Before the FHE, the two messages are re-encrypted under $C$'s private key.

How do I perform the FHE operations on these two messages encrypted by different public keys?

P.S. I am using the Palisade library to implement my idea. A little suggestion on how to implement this on Palisade would also be really appreciated.

Jimmy
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