Alice uses a Message Authentication Code algorithm to insure information integrity of a message sent over an unsecure network to Bob. This involves:

$$ Alice hashes the message to create a message digest.

$$ Alice encrypts the message with her private key then hashes the encrypted message.

Alice adds a secret key to the message that only she and Bob know before hashing the message.

$$ Alice encrypts the message with a secret key only she and Bob know and then hashes the encrypted message.