Bogoraz became well known when, on August 25, 1968, she organized seven people to protest in Red Square against the Soviet Union's invasion of Czechoslovakia at the 1968 Red Square demonstration, together with Pavel Litvinov, Natalya Gorbanevskaya, Vadim Delaunay and other protesters. As all participants, Bogoraz was arrested, tried and sentenced to four years of exile in Siberia, which she spent in a woodworking plant.