Final answer:
The Challenge-Handshake Authentication Protocol (CHAP) is the protocol that calculates and shares a hash with the client after the user logs in, verifying the client's identity periodically by requesting the hash. Other similar mechanisms include Kerberos, NTLM, and Digest Authentication, each with differing methodologies for authentication.
Step-by-step explanation:
The protocol that calculates a hash after the user has logged in and then shares that hash with the client system is known as the Challenge-Handshake Authentication Protocol (CHAP). In the CHAP mechanism, the server sends a challenge to the client periodically. The client must respond with the correct hashed value using a shared secret. If the client's response matches the hash expected by the server, the authentication is considered successful. If not, it indicates that there has been a compromise in the communications. This process provides a secure way of ensuring the identity of the client throughout a session.
Contrast this with alternatives like Kerberos, which uses a ticket-granting system, or NTLM that uses a challenge-response mechanism for Windows-based network authentication, or Digest Authentication which also uses a form of challenge-response mechanism but is typically used over HTTP.