The History and Mathematics of Codes and Code Breaking

Factors of Victory

Singh argues that German overconfidence in their Enigma was the main reason for Allied crypt analysts cracking the German's monstrous cipher. However, if it were not for the involvement of the Polish in the cracking of early Enigma, the Allies would not have had valuable information to crack the cipher.

During the German invasion of Poland, Polish officials gave the British all the information they had on Enigma. This gave the British the head start they needed to further allowed crypt analysts at Bletchley Park to construct new Bombes and other methods to deconstruct the Enigma cipher. This eventually lead to innovations of technological breakthroughs such as the Colossus that ultimately helped end the war.

On another front of the war, the Americans started to use the Navajo language as a means of communication during WWII to help keep secure transmissions. This was a major stepping point for the Allies because the language was hard to make sense of due to conjugations, and it could be used quickly. Additionally, when plain text messages were hidden in another language and further encoded using other cryptographic methods, Navajo Coder Talk was borderline unbreakable. Because of all this, the Navajo Code Talkers were instrumental in pushing Americans to the Japanese coast in WWII.

Advancements made by the Allies in WWII echo their importance, even to this day. Without Polish involvement in the cracking of Enigma and the Navajo Code Talkers, the Axis powers would have had an overwhelming advantage in the war. Thanks to both of these key examples of cryptography, we can analyze their importance to give new perspectives to WWII.


Too Much to Lose


The Carelessness of Repetition


  1. Zinnie

    To further expand upon Howard’s assertion of the almost unbreakability of Navajo Code Talk due to its complex conjugations, there are even more factors contributing the code’s strength. These factors include the inaccessibility to the language by enemies, the phonetics of the language, adaptation and the lexicon.

    As Phillip Johnston mentioned in his official report, within the last 20 years, the Navajo tribe is the only tribe in America which has not been permeated by German students. The Navajo language also has no links to any Asian or European language. This was the first condition for choosing the Navajo tribe. It was necessary that the enemy did not have access to the language or the code would have been easy to break.

    Additionally, the Navajo tribal dialect is indiscernible to all other tribes. When recordings of Navajo Talk were given to the Navy Intelligence to crack to test the strength of the system, they reported the language was a “weird succession of guttural, nasal tongue-twisting sounds...we couldn’t even transcribe it, much less crack it.” This added another layer of security because it would be difficult for the enemy to even record the correct letters corresponding to the sounds. This meant there could have been more mistakes in transcribing the messages if the enemies were unfamiliar with the phonetics of the Navajo language. Had the Navajo dialect resembled another dialect, it would have proven to be easier to break.

    The Allies’ ability to adapt to the frequency analysis techniques used by the Japanese also strengthened the code. The Allies saw the flaw in their system and added two extra words for the six most common letters and one extra word for the next six most common letters. This is similar to the Vigenère cipher in the way it evens out the frequencies of all letters to make frequency analysis useless.

    Lastly, the development of the lexicon provided another layer of security. Although the lexicon was initially developed because there were no direct Navajo translations for some English words, it also served another purpose. Even if the enemy was able to the break the code, they might have still have not known that “eggs” were bombs and “owl” was an observation plane.

  2. sunils

    Polish contributions to the cryptographic war were pivotal in the victory of the Allied forces for multiple reasons. As Singh says in "The Code Book", If necessity is the mother of inventions, then perhaps adversity is the mother of cryptanalysis. Poland was anticipating an invasion and that motivated them to attempt to decipher a cipher that was universally deemed to be unbreakable. The fact that lives of people depended on cracking the code made the cryptanalysis that more potent. While Rejewski's chains were far from a complete method to break the code, they significantly reduced the total possible solutions by several factors of billions and gave Alan Turing and his team at Bletchley Park a leg to stand on.
    Additionally, the Polish officials felt a sense of solidarity with the Allied forces and when the prospect of invasion became imminent, they passed on their work to the British. The Polish cryptanalysts had an approach similar to Georges Painvin which let them make progress over time, unlike the team at Bletchley Park. Their understanding of the bigger picture in the war served to be a major victory not just for the Allied Forces but also for the cryptanalysts for the years to come.

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