Cracking PURPLE: cryptanalysis of the Angooki Taipu B switch tables

Abstract

Eighty years after the US Army’s Signal Intelligence Service (SIS) cracked PURPLE, the famous WWII-era Japanese cipher machine, there still has been little technical information published about how it was done. This paper offers a detailed description of how SIS could have done it. The techniques described here would all have been available to SIS in their pre-computer era of the early 1940s, and are based on cryptanalysis using plaintext and matching ciphertext. This paper derives the system architecture, determines the sixes and twenties switch tables, shows how to convert them to wiring diagrams, explains how to handle the complication of the plugboards, extends the information that can be mined from the famous patterns in PURPLE data, corrects a deficiency in the usage of the one published algorithm for cryptanalysis of the twenties, and shows that neither the sixes nor the twenties switch tables are unique.