 She produces a hash value of the message, raises it to the power of "d" (modulo "n") (as she does when decrypting a message), and attaches it as a "signature" to the message.When Bob receives the signed message, he uses the same hash algorithm in conjunction with Alice's public key.He raises the signature to the power of "e" (modulo "n") (as he does when encrypting a message), and compares the resulting hash value with the message's actual hash value.