 During World War II Gleason was part of OP-20-G, the U.S. Navy's signals intelligence and cryptanalysis group, one task of which (in collaboration with British cryptographers at Bletchley Park such as Alan Turing) was to penetrate German Enigma machine communications networks. The British had great success with two of these networks, but the third, used for German-Japanese naval coordination, remained unbroken because of a faulty assumption that it employed a simplified version of Enigma. After OP-20-G's Marshall Hall observed that certain metadata in Berlin-to-Tokyo transmissions used letter sets disjoint from those used in Tokyo-to-Berlin metadata, Gleason hypothesized that the corresponding unencrypted letters sets were A-M (in one direction) and N-Z (in the other), then devised novel statistical tests by which he confirmed this hypothesis. The result was routine decryption of this third network by 1944. (This work also involved deeper math ­ e ­ mat ­ ics related to permutation groups and the graph isomorphism problem.)
