EAP-TLS is the correct authentication mechanism to deploy because it provides a secure channel by using mutual authentication via client and server certificates. This ensures that user credentials are not compromised if intercepted, and it allows all access attempts to be logged, which is essential for auditing purposes. EAP-MD5 is an older, less secure mechanism that does not encrypt credentials; therefore, it does not meet the security requirements. EAP-FAST establishes a secure communication channel after a successful negotiation but does not inherently meet the specified criteria as well as EAP-TLS. LEAP is vulnerable to dictionary attacks and does not encrypt the credentials securely, making it insufficient for these criteria.