Who was Marian Rejewski?

In 1932, the Polish Cipher Bureau noticed that the German military started using some new form of encryption for their messages that they transmitted by radio in Morse Code. They assigned the problem of decrypting these messages to a very talented mathematics graduate student from Poznań University, who also happened to be working part-time at the Cipher Bureau: Marian Adam Rejewski. He was soon joined by two other excellent mathematics graduate students from Poznań University: Jerzy Witold Różycki and Henryk Michał Zygalski.

In just a few short weeks, Rejewski and his team were able to effectively reconstruct the device used for the encryptions--without ever having seen a real Enigma machine before!

Unfortunately, the Germans were constantly improving their Enigma machines, making them more secure each time, by adding additional rotors, introducing replacement rotors (so that the German Enigma operators could be told which 3 out of 8 rotors to insert into the machine and in what order, for example), adding a plugboard, etc. Each such enhancement increased the complexity and made it much more difficult to decript the messages.

The Poles did their best to try keep up with all these changes and kept improving their decription techniques. They did this by listening to very many encrypted German messages and by very cleverly applying their knowledge of mathematics, particularly Group Theory.

There is an excellent article by Chris Christensen entitled "Polish Mathematicians Finding Patterns in Enigma Machines". It appears on pages 247 - 273 of the October, 2007 issue of Mathematics Magazine. In addition to giving detailed descriptions of the Enigma, it also discusses five theorems that Rejewski discovered and used in determining the wiring of the rotors, and as tools to help him decript messages.

One of those theorems prompted the author of several cryptanalysis books and papers, Cipher A. Devours, to remark: No doubt practitioners of group theory should introduce this property of permutations to students as "the theorem that won World War II."

If you happen to be a Math Major in college who had already taken a class in Abstract Algebra that covered Group Theory, and if you are familiar with the Cycle Notation of Permutations, then I would recommend reading this article by Chris Chrstensen. I'm sure you'll find it very informative, interesting, and rewarding.

In December of 1932, French spies were able to bribe the German traitor Hans-Thilo Schmidt into giving them a real military Enigma machine, along with instruction manuals, training manuals, the sheets with key settings for the operators, and other documents. The French passed the information on to the British and the Poles.

Having all this informatiion, Rejewski and his team decided to build a machine of their own that would automate the methods they used to crack the Enigma code, and called it the Bomba.

Bomba is a Polish word that means bomb.

There is one story that says that they decided to give it this name because the ticking of the machine reminded them of a time bomb.

There is another story that says that while they were trying to decide on a name for the machine they were building, one of them suggested calling it "Bomba", which was also the name of an ice cream sundae that was popular at the time in Poland.

Rejewski had several Enigma "doubles" (i.e., Enigma machines built according to the specifications they got from the French spies) built for his team to use. By 1938, Rejewski's team had six Bomba machines to work with, and were able to decript about 70% of the German military messages encrypted by Enigma machines.

Then, the German Navy decided to increase the number of rotors on their Enigma machines from three to four and, in some cases, even five. The German Army and the German Air Force still continued to use Enigma machines with three rotors, and messages from these could be decripted by the Bomba machines.

Of course, Bomba machines could be constructed to decript messages from the German Naval Enigmas, and in time they could decript the messages, but you'd need at least 60 such machines running simultaneously, and even then they might not finish in time to be of any use.

The Poles knew that Germany was planning to invade soon, so they invited the French and British cryptologists to Poland. Rejewski met with them on July 24 and 25, 1939, at a secret facility in Las Kabacki (Kabacki Forest). He showed them the progress the Poles made up till now. (The French and British were amazed, because they made essentially no progress at all in cracking the Enigma.) He also gave them a detailed description of their Bomba machines, and promised to send them some Polish Enigma "Doubles".

Germany invaded Poland on Septmber 1, 1939.