1931: US Coast Guard Established Cryptanalytic Section
Learn more in the NSA Center for Cryptologic History's document - "Listening to the Rumrunners: Radio Intelligence during Prohibition" by David P. Mowry. See link below.
You may also be interested in the article, "Cracking the Code" by The Hillsdale Collegian, about Elizebeth Friedman. Links to the article and Ms. Friedman's Hall of Honor page are included below.