Cryptography

The History and Mathematics of Codes and Code Breaking

Month: October 2014 Page 2 of 3

Espionage is the Key

200625463_3dd5de0d20_z

Photo Credit: Tim Gage via flickr

One of the main reasons the Allied code breakers were able to crack the German Enigma cipher was espionage. Both stealing code books and obtaining documents from Schmidt gave the Allies the edge they needed to crack the Enigma machine several times. The Allies would be very far set back if they did not have access to the Enigma machine. Rejewski would never have made such quick progress on the Enigma machine if he did not have access to the documents explaining how the key was enciphered and a model Enigma machine. If Rejewski had not made such quick progress, the Allies would probably never had the break through that he achieved because Germany would have invaded Poland before the Polish could give the notes to the Allied nations. Espionage was also helpful for the guys in Bletchley Park. Stealing code books from German U boats was critical in deciphering the Enigma later on by using cribs that are established through the location of the U boats.

What is also important to note is that the Germans made the Enigma machine more complicated throughout the war without knowledge of the fact that the Allies had cracked it. This means that saying the Allies would have eventually cracked the code is not entirely accurate. Speed was actually pretty critical in attempting to crack the Enigma. Every time the Allies cracked a form of the Enigma, the Germans would make it more complicated later, so the Allies would have to reevaluate their attempts and use a slightly different method. What is important to note is that the Allies did not necessarily have to start completely over; they could just reevaluate and use their old notes since they had already cracked one form of the Enigma before. Without the espionage involved in stealing important documents and books, who knows if the Enigma would even have been cracked before World War II ended?

Collaboration Wins the War

Allied cryptanalysts succeeded over German cryptographers largely because of collaboration. It was not just one country working against the Germans, but the entire Allied powers.

The chain of collaboration began with the French: though they didn’t feel the need to pursue cryptanalysis of the Germans, they provided the initial information necessary to do so. After World War I, the French thought that further war was impossible, so when provided with Hans-Thilo Schmidt’s information on the workings of the Enigma machine, they passed them on to Poland. Poland did face an immediate threat, however, in the form of Russia. A Polish cryptanalyst, Rejewski, did much of the work at the front end of the effort to crack Enigma. His methods, when Poland suspected that they would no longer be able to continue covert cryptanalysis, were then passed on to England. Alan Turing and the others at Bletchley Park were able to use this information as a springboard for cracking the evolving Enigma.

“Handshake” by USMC photo by Cpl. Paula M. Fitzgerald – Licensed under Public domain via Wikimedia Commons

Without collaboration, the decipherment of the Enigma would not have occurred, or at least not in the manner and order of events in which it occurred. The Polish would not have received an Enigma machine if the French had not given it to them, thinking that the Polish could better use the information. The Polish knew that they couldn’t continue cryptanalyzing, and instead of simply shutting down operations, they pass the information on, so that the final goal can be realized. If individual countries had cared more about their own fame than the bigger picture, the war might have ended drastically differently.

Problem Set #5

Here’s your fifth problem set: Problem Set 5 (Word), Problem Set 5 (PDF). It’s due at the start of class on Monday, October 27th. As always, if you’d like some help on the problem set, you’re welcome to email me or stop by my office hours.

Noticing Patterns

One reason that the code breakers were eventually successful over the German cryptographers was the identification of patterns in the Enigma codes. There were certain key discoveries that aided in the eventual crack of the codes. One of these discoveries was the new message key between the sender and recipient was repeated twice to avoid potential error or confusion. This was a good idea for the Germans to make communication more clear and since they thought that the Enigma machine would never be broken, they never thought about the vulnerability that this action could cause. Once Allies cryptanalyses realized this, this knowledge allowed them to decipher codes more easily because they had this knowledge of a pattern. Another pattern that aided that Allies was the weather reports everyday. This could help start the day with a message that they knew what the content, for the most part, was about therefore giving them a clue when solving for the plain text. Another pattern that the Allies used in their favor was the U-boats that would surround convoys and send information to other U-boats. The Allies knew what information was to be sent because they knew where the convoy was. The knowledge of this information aided in the decryption of that day’s key. The realization of these various patterns aided greatly in the Allie’s breaking of the Enigma machine.

Photo Credit: Karl-Ludwig Poggemann via flickr

Photo Credit: Karl-Ludwig Poggemann via flickr

Keeping Breakthroughs Secret

One of the main factors that contributed to the success of the Allied cryptanalysts over the German cryptographers was the secrecy that surrounded the Allied code breaking efforts.

431452053_a599ea74a6


Photo Credit: Dr John2005 via Compfight cc

The Allies were able to keep their code breaking efforts shrouded under a curtain of secrecy and so even when a breakthrough occurred in Bletchley Park, the Germans remained unaware that their codes were broken and continued to send message through their “secure” system. For example, the Allies had exploited the fact that the Germans embedded their key twice at the beginning of their messages to avoid error, and used this information to help identify the settings of the Enigma machine. Had the Germans known earlier that their key transportation scheme actually hurt the security of their communication system, they likely would have changed the way they provided the key and made it harder for the cryptanalysts to make breakthroughs in deciphering their messages.

The Allies swore all who worked in Bletchley Park to secrecy for good reason. The secrecy gave the Germans a false sense of security in the strength of their system, buying the Allies more time to decrypt messages as well as experiment with new deciphering techniques in case the Germans changed their system upon learning that it was not as impenetrable as they had believed.

Blog Assignment #5

Ghost WriterFor your fifth blog assignment, write a post between 200 and 400 words in which you respond to the following prompt.

There are many reasons Allied cryptanalysts (code breakers), such as those at Bletchley Park, were eventually victorious over German cryptographers (code makers). Identify at least one reason and make a case for it as a significant reason for the Allied success. Consider both technical and social/cultural factors in the Allied and German crypto efforts.

Please (1) give your post a descriptive title, (2) assign it to the “Student Posts” category, (3) give it at least three useful tags, and (4) include a Creative Commons licensed image or a public domain image in your post that somehow (concretely or abstractly) represents an idea in your post. (See this post for some tools for finding such images.)  Your post is due by 8:00 a.m. on Wednesday, October 22nd.

Singh Chapter 4 – Reading Questions

We’ll start discussing Singh Chapter 4 on the Monday after fall break. Here are some questions to guide your reading. Look for a blog post assignment about World War II cryptography soon.

  1. Given what you’ve now read about Bletchley Park’s role in World War Two, would you say that “Bletchley Park’s achievements were the decisive factor in the Allied victory”?
  2. Why might the Germans increase the number of scramblers and plugboard cables in their Enigma machines to make them more secure, yet also insist that the Enigma cipher could not possibly be broken by the Allies?
  3. We’ve seen that the Vigenère cipher was once though unbreakable but later broken.  Given that history, why might the Americans and French conclude that the Enigma cipher was unbreakable prior to the start of the Second World War?
  4. Singh writes on page 149 that “the creative codebreaker must ‘perforce commune daily with dark spirits to accomplish his feats of mental ju-jitsu.’”  In light of your own experiences breaking ciphers, which is more important to successful codebreaking-logic or creativity?  Or is an equal balance of both required?

Singh Chapter 3 – Reading Questions

I just realized I never shared reading questions for Singh Chapter 3. Here they are, in case they’re still useful. Reading questions for Chapter 4 are coming right up.

  1. When the Zimmerman telegram was deciphered by the cryptanalysts of Britain’s Room 40, Admiral William Hall decided not to tell American President Woodrow Wilson about its contents because doing so might let the Germans know that Britain was capable of breaking their codes.  Given the danger posed to America by the unrestricted U-boat warfare indicated in the telegram, was this ethical of Admiral Hall?
  2. Germany learned that Britain had broken their codes from histories of the First World War written by Winston Churchill and the British Royal Navy.  Given that this knowledge prompted Germany to invest in the Enigma machine technology prior to the Second World War, should these histories have been published?  What might have motivated Britain to make their code-breaking success known in this fashion?
  3. Given the various incidents recounted in this chapter, what are some conditions that seem favorable to the advancement of military cryptography?

Paper #2 – Expository Paper

Here’s your second paper assignment (Paper #2 Assignment) and rubric (Paper #2 Rubric) that should help you understand my expectations for the paper. I think these two files will tell you what you need to know about the assignment, but if you have any questions, feel free to ask. We’ll also talk about the assignment in class.

Bookmarking Assignment #5

Interesting PinYour fifth bookmarking assignment will help prepare you for Monday’s in-class discussion of writing for blogs. Below you’ll find a list of some interesting blogs about math, science, and the history of math and science. Look through several of the blogs listed and select one post from one blog that you feel is particularly well written. Bookmark that post in Diigo, using the tag “BlogPosts” along with at least one other meaningful tag. Also, leave a comment on your bookmark in which you explain why you thought the post was well written.

Your bookmark and comment are due by 8 a.m. on Monday, October 6th.

Page 2 of 3

Powered by WordPress & Theme by Anders Norén