What principle have presidents applied to keep white house communications confidential?

The Executive Privilege

Explanation:

The Executive Privilege is the power of the Executive branch to withhold information from other government branches in order to preserve confidential communications within the executive branch or to secure the national interest, that is to say, the Executive's power to decide what to share.

Richard Nixon, for example, was one of the Presidents that applied it when he was accused of being involved in the Watergate Scandal, however, in the case, the Supreme Court established that the executive privilege had limits and it wasn't immune from judicial review and from the demands of due process of law.