The History and Mathematics of Codes and Code Breaking


The Morality of Admiral Hall’s Actions

Upon learning the intended plans of the Germans from deciphering the Zimmerman telegram, it was ethical of Admiral Hall to withhold such information from the President.


One may argue that Admiral Hall should morally concede the information to the President so that Britain may be subsequently informed, and lives could be potentially saved during the outbreak of unrestricted submarine warfare. Yet, if America was to intervene before German acted out their plan, they would’ve “concluded that their method of encryption had been broken,” leading them to “develop a new and stronger encryption system” (Singh 113). This grants the possibility of the German’s using an extremely more complicated encryption system, one that the cryptanalysts in Britain’s Room 40 may never solve in their lifetime, to act out their unrestricted submarine warfare unopposed. This, in turn, could’ve led to a higher number of wartime casualties, especially among passenger ships. Thus, through decrypting future German telegrams without their knowledge that their encryption system had already been broken, Admiral Hall’s actions could potentially save many more lives than he would’ve had he passed on the information.


Furthermore, as history proved, by not informing the President, Admiral Hall ensured that the Germans did not realize the Americans had broken their encryption system, granting the Americans an advantage in decrypting any future German messages encrypted by the same system. Eventually the Mexican version of the Zimmermann telegram led America to retaliate, granting the same outcome had the Admiral actually passed on the information, but without the Germans discovering their blunder.

A Boost of Motivation

The mindset for the Allies had changed between the First World War and the Second World War. After their success in cracking Germany’s ciphers in the First World War, the Allies felt like that could crack anything Germany tries to encipher. However, once the Germans started using the Enigma machines, the Allies were stumped. This change in attitude might be attributed to the fact that they were not in direct threat at that time so they didn’t have the motivation to try to decipher the messages. That along with the hopelessness that might come with failed attempts would make them lose motivation. Poland, however, was threatened so they had to do everything they could to decipher those messages. Therefore, with the help of Schmidt and Rejewski, they reached a breakthrough in cracking the enigma. If it wasn’t for their breakthroughs, the Allies may not have been able to crack it. Gaining that knowledge may have been the motivation they needed to fully uncover how the Enigma machine works. The Allies were also able to pick up on some keys that Germany’s operators would send. The operators would sometimes pick three consecutive letters from the keyboard which the Allies started picking up on.

Photo credit: "Enigma Machine (Bletchley Park)" by Tim Gage via Flickr CC

Photo credit: “Enigma Machine (Bletchley Park)” by Tim Gage via Flickr CC

Sometimes they would repeat the same keys and therefore the cryptanalysts would be able to predict them. Overall, cracking the Enigma took the efforts and collaboration of many individuals working as a team.

On the Shoulders of Giants

In the beginning of World War II, Great Britain was under less threat from the ever-expanding German forces on the European continent. Poland, on the other hand, was sandwiched between the Soviet Union to the east and rapidly encroaching Nazi armies to the west. Under the pressure of otherwise being forced under Nazi rule, the Polish cipher bureau made incredible headway in analysis of early German Enigma intercepts.

Bletchley Park Bombe

“Bletchley Park Bombe”
Photo by Antoine Taveneaux- Licensed under Public Domain by Wikipedia Commons

When Great Britain’s ships were attacked by German subs, a greater need to decipher Enigma arose. What was perhaps the most important contribution to British cryptanalysts’ efforts was the fact that they were able to build upon the Polish cryptanalysts’ work. Without those insights, the analysts at Bletchley Park might never have developed a full image of how the Enigma machine worked. Or rather, they might not have fully understood the weaknesses of the cipher (as well as its operators). For example, the Polish cipher bureau supplied copies of the military models of the Enigma machines to the British and French, and also provided the operator procedures that were in use at the time. This allowed groups like Bletchley Park’s Hut 6 to focus on finding a way to crack Enigma without the use of fragments such as the six-letter message key repeats at the beginning of every message. Additionally, the cryptological bombe that Alan Turing developed was based on a model designed by Polish cryptoanalyst Marian Rejewski, mechanizing the process of working out daily message keys.

Through collaboration and the ability to build upon the work of earlier cryptanalysts, the British were able to break the Enigma cipher. Not only did this save Allied lives and make victory much easier, but also the decryption shortened World War II in Europe and saved the lives of many in the Axis states who would have otherwise been killed in the longer fighting.

Human Error and Forced Flaws

Photo Credit: “Chiffriermaschine ‘Enigma’ ” by Walther licensed by Wikimedia Commons under Creative Commons

The Enigma Machine was practically impregnable if all of its information was kept secret and all its operators worked without human error. With billions and billions of possible settings, it would have taken cryptanalysts an obscene amount of time to sort through all of the possible keys. Additionally, with an ever changing pattern and shifting scramblers it would be incredibly hard to find a method to deduce the plaintext if all one had was pure ciphertext, even with if the most brilliant minds in Britain working on a solution. Essentially, cracking the Enigma required some sort of “crib”, some insight into how the code was working on a specific day that would take out some of the possible Enigma settings.  Because of this, the cryptanalysts would not have had the success that they did without the help of two things; German cryptographer’s mistakes in using the code and the espionage and tricks of the Allied forces.

A clue into the how the code was being run a certain day was often acquired from the mistakes of the Germans. For example, when German operators were picking keys they would often choose “three consecutive letters from the Enigma keyboard” or even use the same key as they had used previously (Singh, p.164). These mistakes, known as cillies, became vital to Bletchley Park’s decoding of the Enigma machine. Because they knew that some keys were more likely to show up than others, they could try their hunches first and would save valuable time if they were proven correct. Basically, the Enigma machine was still doing its job; it’s just that the operators proved to be too predictable. In addition, the Germans took efforts to make the Enigma machine more secure that often backfired and lessened the impregnability of the cipher. For instance, they decided that a scrambler couldn’t stay in the same position for two days in a row (Singh, p.164). This may seem to make it more random, but it actually excluded many of the possible scrambler arrangements that British cryptanalysts had to weed through.

When all else failed, however, and German mistakes and bright Bletchley park minds didn’t produce a crib, espionage and trickery became key. When they couldn’t find a crib, it seemed, British cryptographers would create one. By manufacturing situations where the German U-Boats would have to send messages with a specific location in the cipher, the British cryptanalysts could gain insight into the way the cipher was working. Because they knew the location of whatever the U-Boats had sighted (be it a convoy or a mine), the British had a bit of plaintext to work with. With this plaintext, they could employ Turing’s loop method and decrypt the scrambler and plug board settings of the day. All in all, using the openings found in the Germans operational mistakes and those created by Allied operations, the cryptanalysts at Bletchley Park could decrypt the Enigma, collecting valuable information that would help them win the war.

Fatal Flaws

Photo Credit: david.nikonvscanon via Compfight cc


Although the Enigma machine at first seemed nearly impossible to decode, eventually the Allies successfully were able to get breakthroughs in the machine and finally solve the Enigma machine.

A major reason for the eventual success was although the Germans used different key words each day to further stifle the Allies, the Germans sent a huge amount of these messages which gave thousands of words the ability to be analyzed. Because of the vast amount of messages sent, it gave the Allies a great number of chances to solve the Enigma machine. Perhaps if the Germans had taken a step further and alternated using the Enigma machine with a different type of encoding device, it would have given the Allies almost no chance at deciphering their messages. However, the change of key words was a brilliant idea to make the Enigma machine more difficult to solve.

Another reason for the Allies solving the Enigma machine was as a result of the Germans sending messages concerning positions of their U-boats and where others needed to be. The Allies knew where the U-boats were when attacking their boats because the Allies boats were able to be tracked. As a result, when the Germans were communicating where to go, the Allies knew what the code represented which helped them figure out the key to the Enigma machine. Had the Germans used a wider variety of codes, not sent the great number of messages encoded by the Enigma machine, and not committed this fatal flaw, the Allies possibly could have never been able to solve the machine during World War II which could have greatly affected the final outcome of the war.

False Security


Photo Credit "Die Luftwaffe (Air Force) ENIGMA" by brewbooks via Flickr CC

Photo Credit “Die Luftwaffe (Air Force) ENIGMA” by brewbooks via Flickr CC

The plugboard of the enigma machine provided a false sense of security to the Germans. The sheer number of possible combinations, 10,000,000,000,000,000 is a daunting number, however, the plugboard itself can be isolated and broken by frequency analysis. The most complex part of the enigma machine is the scramblers, placement of them, and the their settings. This only has around 100,000 different combinations, a completely possible human task to handle; way easier than the 10,000,000,000,000,000 combinations of the machine. The hubris of the Germans to believe their machine was impregnable allowed them to get lazy when sending messages, like repeating the codes twice. The Germans had no idea that repeating the codes twice would create links that corresponded with an exact ratio to scrambler settings. The Germans were simply mesmerized by the large number of possible combinations.

Many times nowadays companies hire hackers to intentionally hack into their security and provide information on how it would be improved. Had the Germans done this, they would have realized that repeating the keys was a bad idea and allows for breaking the code. Being complacent allows for error, always believe that the other side is one step ahead, otherwise they will undoubtedly become one step ahead.

Page 3 of 3

Powered by WordPress & Theme by Anders Norén