Cracking PURPLE: the identification of homologs in the cryptanalysis of the Angooki Taipu B cipher machine

Abstract In 1940 the US Army’s Signal Intelligence Service (SIS) cracked PURPLE, the Japanese diplomatic cipher. Shortly after that accomplishment, William Friedman, legendary cryptographer and civilian head of SIS, wrote his Preliminary Historical Report on the Solution of the “B” Machine. In it he introduced the mysterious “Identification of Homologs” and stated there that it had been a crucial technology to the success of cracking PURPLE. Despite that dramatic assessment, the concept simply disappeared, ignored by all subsequent authors of PURPLE histories and technical analyses. So what exactly is the Identification of Homologs and what role did it play in the cryptanalysis of PURPLE? That is the subject of this paper. We give a complete technical description, as well as historical information, some newly uncovered, about how SIS collected PURPLE “data”.