Bob Uses His Own Private Key to Encrypt the Message

Short Answer

Bob uses his own private key to encrypt the message.When Alice receives the ciphertext she finds that she can decrypt it with Bob's public key, thus proving that the message must have been encrypted by Bob.No one else has Bob's private key and therefore no one else could have created a ciphertext that could be decrypted with Bob's public key.Therefore the entire encrypted message serves as a _________ .