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I am wondering if there is an identity based proxy re-encryption scheme (such as the Green-Ateniese scheme https://eprint.iacr.org/2006/473.pdf) that converts an encryption computed with ID1, system parameters1 into one intended for ID1, system parameters 2, i.e., the ID is the same but the system parameters change.

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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., & Jonker, W. (2008, December). Inter-domain identity-based proxy re-encryption. In Information Security and Cryptology (pp. 332-347). Springer Berlin Heidelberg. Han, J.,

  • Susilo, W., & Mu, Y. (2013). Identity-based data storage in cloud computing. Future Generation Computer Systems, 29(3), 673-681.

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