Security Algorithm

Suppose users A and B exchange message P in a public-key system (like RSA) using the following protocol: A signs P using A's private key, K_Ad, and sends the message to B along with plaintext giving both A's and B's identity: (A, B, P, signK_Ad(P)) = M. B verifies A's signature by using A's public key K_Ae and computing verK_Ae (signK_AD(P)) = P and replies to A with (B, A, P, signK_Bd(P)) where K_Bd is B's private key. Explain why each of the following properties is either true or why it is false. If a property is false, suggest a way to fix it. You can assume that A and B can get each other's verification keys and that they can be sure that the keys are owned by the claimed owners. The signatures are authentic (each user did sign the message). The signatures are not reusable (cannot be replayed). The signed document is unalterable (integrity)