I am trying to understand the proxy re-encryption scheme.
In proxy re-encryption:
(1)Alice use AES key to produce the symmetric ciphertext of her message.
(2)The proxy encrypt symmetric ciphertext using Alice's re-encryption key.
(3)Bob use his private key to get the AES key and decrypt the symmetric ciphertexts.
My question: Why we need the re-encryption? Why not Alice encrypt her AES key using Bob's public key and send it to Bob?
I am new to cryptographic, so I am not sure misunderstand of it. Thank you!