The History and Mathematics of Codes and Code Breaking

Month: October 2014 Page 1 of 3

Brawn over brains


It cannot be denied that the brilliant minds at Bletchley park were necessary to the success of the code breaking. However, all of their work would've been null if they didn't have the money and resources to build or run the machines they needed. For this reason, the "brute force" was one of the most important factors to Allied success.

The Polish were the first to figure out a way to crack the enigma cipher. They were able to build the machines they needed to use brute force to decipher the messages. Everything was going great for them until the Germans added more elements to the Enigma Machine, meaning the Polish would've needed more machines to continue their processes. They simply didn't have the resources to make that happen. That's when they shared their findings with larger Allied forces. Bletchley Park was able to create all the machines necessary to continue cracking the codes, and had the manpower to run the machines as well.

Later on in Bletchley Park the intelligence was key to continuing to crack the codes, once the Germans fixed some of their "human error" mistakes, like repeating the day code. At this point, pure brute force was not enough to read the messages. Prior to this, though, brute force was the key element to deciphering the German messages.

There's No "I" in "Team"

Photo credit: "Share" by AJ Cann via Flickr CC

Photo credit: "Share" by AJ Cann via Flickr CC

A key factor to Bletchley Park's success was the collaborative efforts that were used in order to crack Enigma time and time again. After reading Singh's chapter in The Code Book that discussed Bletchley Park, one might get the idea that Alan Turing was the key to the Allied success. Alan Turing was, no doubt, a key player in the cryptanalysis that led to the Allied success. However, there were thousands of other men and women that aided in the breaking of Enigma and deciphering German messages.

One image that stands out to me that Singh wrote of were the huts in Bletchley Park. Singh illustrates these huts as hubs of collaboration between some of the brightest minds in their given field. If a cryptanalyst was working on a cipher or encrypted message and was stumped, he would pass it to another cryptanalyst. A single message could make its way around the hut numerous times, with each cryptanalyst getting one step closer to the solution until it was solved.

Within each hut there was a clear sense of teamwork, but from hut to hut there was a similar sense as well. Each hut had a specific purpose, so once one hut had done its job with a message, it would be handed over to the next hut for the next step. This ensured that each member of Bletchley Park was doing what he or she thrived at, leading to maximized efficiency as well as an overwhelming necessity and use of communication and teamwork.

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.

German Confidence Proves Costly

After early domination of the seas by German U-boats, Bletchley desperately needed to end the intelligence blackout. Through a series of dangerous raids on German U-boats, a German Naval codebook was captured, thus making the Naval Enigma transparent. Finally, Ally convoys could evade the deadly German vessels and British destroyers could

"German U-boat" Photo Credit: Joe Neary via Flickr

Photo Credit: "German U-boat" by Joe Neary via Flickr

go on the offensive. The Allied powers went to great lengths to not raise suspicion in Germany that their sacred Enigma machine was compromised. Fortunately for Bletchley, Germans were far too confident in the strength of their encryptions.

Although the Allies were now aware of the locations of numerous U-boats, they had to be careful not to attack all of them because this would warn Germans that they could no longer trust their communications. Therefore, they were careful to prudently attack and never risk destroying too many enemy ships at once. In one case, Bletchley became aware of a numerous amount of German tankers and decided to sink most of them, but not all as to not raise suspicion. The British destroyers successfully sank the ones they were supposed to, but then spotted the remaining German supply ships and sunk those as well because they did not know about this situation. Fortunately for the Allies, when the Germans realized about their lost ships, they thought of it as a misfortune because their Enigma was unbreakable. If the Germans had had less confidence in their encryptions, it is possible that they could have stopped the amount of information they were feeding the Allies, or even have used it against them.

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.

Variation of Disciplines

Cryptography is an ever evolving field, and this held especially true around the time of World War II. Up until this point, most cryptanalysis had been performed by linguists and people trained in language. However, as cryptography evolved and became increasingly mathematical and technological, the personnel involved in cryptanalysis needed to evolve as well. One of the primary reasons the Allies had success over the German cryptographers was the Allies use of cryptanalysists from across many disciplines.

As discussed in class, there are many factors which go into solving a code. To break the German code required some each of creativity, logic and luck. One of the best ways to solve an abstract problem, such as breaking an enciphered message, is to think about it from many different angles and have different people each with their own different way of thinking attempting to solve the problem. As Singh noted, there were a great variety of cryptanalysists working on the German codes from mathematicians and linguists to artists and chess players. Having such varied ways of thinking ensured that if one person couldn't come up with an idea, someone else down the line would most likely be able to. Also, British cryptanalysits were specialized into various "huts" on the lawn of Bletchley park. Each of these huts had a specific directive, from working on the German Naval enigma to intelligence gathering and translation. With many different types of thinkers working on them simultaneously, each of the various tasks were able to be completed with the utmost efficiency, saving lives and ultimately helping the Allies gain a pivotal upper hand in the war.

"Hut 6, Army/Airforce Enigma codebreaking" Photo by Matt Crypto-Licensed under Public Domain by Wikimedia Commons

"Hut 6, Army/Airforce Enigma codebreaking" Photo by Matt Crypto-Licensed under Public Domain by Wikimedia Commons

The Wisdom from the Best

In the World War Two, the Allied cryptanalysts successfully broke German  Code and helped Allies win the war. One of the important facts I thought was the efforts from the genius.

In Ultra, the Allies hired the best one in different fields. They invited people (most were mathematicians and cryptanalysts) with unique talent, such as the Champion of Chess, the experts in crossword puzzle, linguists and so on. One of the most famous people they hired was Alan Turin. For example, Bletchley Park once used the crossword puzzle on ‘The Daily Telegraph’ as the test and asked the applicants finished it in 12 minutes. Bletchley Park also offered brilliant tools. Colossus, the world's first programmable digital electronic computer was used to help break the German Code. So one of the reason that helped Allied cryptanalysts be victorious over German cryptographers is that the Allies hired the top people in different fields and made them work together to solve problems.

The achievement of this strategy was so outstanding that during the World War Two, it helped Allies broke many codes. This greatly helped Allies save a lot of time and people, avoid the attack from enemy and finally win the war.

Photo Credit: Bletchley Park House - Mansion by Elliott Brown via flickr

Photo Credit: Bletchley Park House - Mansion by Elliott Brown via flickr


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