Single-Key to Multi-Key Functional Encryption with Polynomial Loss.

Functional encryption FE enables fine-grained access to encrypted data. In a FE scheme, the holder of a secret key $$\\mathsf {FSK}_f$$ FSKf associated with a function f and a ciphertext c encrypting plaintext x can learn fx but nothing more. An important parameter in the security model for FE is the number of secret keys that adversary has access to. In this work, we give a transformation from a FE scheme for which the adversary gets access to a single secret key with ciphertext size sub-linear in the circuit for which this secret key is issued to one that is secure even if adversary gets access to an unbounded number of secret keys. A novel feature of our transformation is that its security proof incurs only a polynomial loss.