Identity-based proxy re-encryption using different system parameters
This concept is called inter-domain identity-based proxy re-encryption. In this case, the notion of "domain" implies a separate KGC and a set of system parameters.  There are a couple of schemes doing this:


Tang, Q., Hartel, P., &amp; Jonker, W. (2008, December). Inter-domain
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Cryptology (pp. 332-347). Springer Berlin Heidelberg. Han, J.,
Susilo, W., &amp; Mu, Y. (2013). Identity-based data storage in cloud
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