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In a Proxy Re-Encryption (PRE) scheme, Alice gives a special information to a proxy that allows it to transform messages encrypted under Alice's public key into a encryption under Bob's public key such that the message is not revealed to the proxy. The notion of Conditional Proxy Re-Encryption (C-PRE) with bilinear pairings introduced by Jian Weng. In C-PRE, the proxy also needs to have the right condition key to transform the ciphertext (associated with a condition set by Alice) under Alice's public key into ciphertext under Bob's public key, so that Bob can decrypt it.
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