Which solution is typically associated with military establishments and enforces mandatory access controls between connected sites?

The solution associated with military establishments that enforces mandatory access controls between connected sites is Cross Domain Solutions (CDS). CDS is specifically designed to allow secure communication and transfer of information between different security domains, ensuring that sensitive data is protected in accordance with varying levels of security classifications. This is essential in military and governmental contexts where information security and compartmentalization are crucial for national security.

Cross Domain Solutions implement mandatory access control (MAC) policies, which restrict information flow based on predefined security criteria, thereby maintaining operational security while enabling necessary information sharing. This capability is critical in environments where disparate systems must communicate securely without compromising security standards or risking data leaks.

In contrast, identity providers, directory services, and NAC lists do not inherently enforce mandatory access controls between connected sites as CDS does. Identity providers focus on authentication and single sign-on services, directory services manage user data and access control but do not enforce mandatory access policies, and NAC lists generally concern network access control rather than inter-domain communication and security enforcement. Thus, CDS is the answer that most accurately fits the criteria described in the question.