I am new to cryptography esp, homomorphic encryption. I would like to know if the following is possible using something similiar to additive homomorphic secret sharing. Please apologize me if its too vague. I will try my best to explain my ask.
Alice has a secret that she wants to homomorphically encrypt. However Alice does not have enough resources to perform FHE. Hence Alice reaches out to a quorum of powerful devices, that say theoretically, can encrypt the data homomorphically for Alice. However since Alice cannot share the secret directly with the quorum, she decides to use a secret sharing scheme. But if she splits the secret directly and shares it, then a few members of the quorum can combine their shares and reconstruct the secret. Hence Alice wants to perform some operation on the secret and split it into shares for each of the member of the quorum such that even if the quorum members combine their share they wont be able to reconstruct the secret. But if they homomorphically encrypt their share ( or perform some operation on their share and then encrypt their share homomorphically ) and then combine their homomorphically encrypted shares, they will be able to produce the homomorphic encrypted cipher of the secret that Alice had.
Thanks in advance !