—In proxy re-encryption, a proxy can transform a ciphertext computed under Alice’s public key into one that can be opened under Bob’s decryption key. In 2007, Matsuo proposed the concept of four types of proxy re-encryption schemes: CBE(Certificate Based Public Key Encryption) to IBE(Identity Based Encryption)(type 1), IBE to IBE(type 2), IBE to CBE (type 3), CBE to CBE (type 4). We observe that the proxy re-encryption from CBE to IBE scheme in Matsuo’s scheme inherits the key escrow problem from IBE. Is this necessary for proxy re-encryption from CBE to IBE? We give a negative answer. If we emphasis on the PKG’s involving in the re-encryption key generation, some interesting results can be obtained. We propose the concept of hybrid proxy re-encryption without key escrow, give the new security model for this primitive, construct such a scheme and prove its security. Furthermore, we construct the first proxy re-encryption scheme from from IBE to CBE, giving the security model for this new primitive and prove its security. At last, we compare our schemes with other related schemes, the results show that our schemes can have high level security with good efficiency.
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