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Identity-Based Proxy Re-Encryption (IBPRE) is a useful primitive, in the sense that a semi-trust proxy can translate ciphertexts originally intended for one identity into ciphertexts intended for another identity. The proxy, however, cannot learn anything about the underlying plaintexts. Mediated Identity-Based Encryption (MIBE), introduced by Ding et al., is particularly useful for the immediate revocation of identities. In this paper, the authors study the relation between IBPRE and MIBE. They show that, under the Chosen-Plaintext Attack (CPA), IBPRE and MIBE are equivalent: they give a generic construction of CPA-secure IBPRE scheme from any CPA-secure MIBE scheme; and a generic construction for the opposite direction is also given.
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