Unlike some earlier proxy re-encryption schemes, the LV08 scheme specifies a validity-checking process to guarantee that the received ciphertext is well-formed. In this paper, we clarify that the received message is well-formed is the premise to decryption in all encryption schemes. The underlying mechanism to keep the communicated message well-formed in encryption schemes is another topic. We will simplify the LV08 scheme and show its security level is the same as that of the AFGH05 scheme.

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