The Executive's authority to classify or declassify information does not come from Congressional statute.  Rather, Presidents have long held that it is part of the President's inherent authority. Courts have concurred.

THE PRESIDENT HIMSELF HAS BROAD AUTHORITY IN CLASSIFICATION DECISIONS

In 1951, President Truman signed Executive Order 10290 (pdf), the President relied on his Constitutional authority as President of the United States to enact a classification scheme.

In Department of Navy v. Egan, 484 U.S. 518 (1988), the Supreme Court stated in its dicta that the authority to control access to sensitive information is vested in the President of the United States.  Accordingly, an argument can be made that the President need not "ask permission" from the CIA or NSA or anyone when it comes to classifying or declassifying information. This is because the CIA or NSA do not have any power to deal with classified information that does not emanate from the President himself:

The President, after all, is the "Commander in Chief of the Army and Navy of the United States." U.S. Const., Art. II, 2. His authority to classify and control access to information bearing on national security and to determine whether an individual is sufficiently trustworthy to occupy a position in the Executive Branch that will give that person access to such information flows primarily from this constitutional investment of power in the President and exists quite apart from any explicit congressional grant. See Cafeteria Workers v. McElroy, 367 U.S. 886, 890 (1961). This Court has recognized the Government's "compelling interest" i