# Is there an encyption scheme that combines additive homomorphism with ability to proxy re-encrypt?

Is there an encyption scheme that combines additive homomorphism with ability to proxy re-encrypt? I've tried digging around on the Internet but haven't found anything conclusive on the topic.

• Craig Gentry's full-homomorphic scheme is a one-time multi-use proxy-reencrypt scheme (in fact, it is this property that allows him to 'bootstrap' the scheme). It's far from efficient, however, although there is a great deal of research into making it so. – Reid Oct 21 '13 at 1:40

This means that you represent the message $m$ to be encrypted as power of the generator $g$ of the target group ($G_2$ in their paper), i.e., as $g^m$ for messages in $Z_p$ (with $p$ being the order of the prime order group). Then, you are, however, limited to "small" message spaces as decrypting involves computing discrete logs in $G_2$. I do not know your application, but in many scenarios that should be sufficient.