The movie was based on a short story "Ivan" by Vladimir Bogomolov. Andrei Tarkovsky wrote in his book "Sculpting in Time" later that he did not find the book very good, but stories that were not well written were easier to adapt into films.
Trostanyets (spelling from the DVD subtitles), the camp mentioned by Ivan, is the Trostinets extermination camp. (Alternative spellings include Maly Trostinets, Maly Trastsianiets and Trascianec.) It was a World War II death camp located at Maly Trostinets ("Little Trostinets"), a village near the outskirts of Minsk. Operating between July 1942 and October 1943, nearly all Jews in Minsk were murdered there.
The writers mentioned by Masha are Alexei Tolstoy (1882-1945; real name Aleksey Nikolayevich Tolstoy; son of Count Nikolay Alexandrovich Tolstoy) and Korney Chukovsky (1882-1969; real name Nikolay Vasilyevich Korneychukov). Tolstoy was a writer of science fiction and historical novels. Chukovsky was a writer of children's poetry and absurdist stories. He also translated English stories and poetry into Russian.