And the military, in its august wisdom decades ago, decreed that every military person's identification number would be their Social Security Number.

Army and Air Force  July 1, 1969
Navy and Marine Corps January 1, 1972
Coast Guard October 1, 1974

1969 President:  LBJ, followed by Nixon.

"The Defense Department in 2007 announced plans to move away from using Social Security numbers. The Pentagon in 2009 began removing the number from military ID cards. Social Security numbers, however, continue to be used throughout the Army and military."