The History and Mathematics of Codes and Code Breaking

Tag: cryptanalysis (Page 1 of 4)

From Voxcoder to SIGSALY

The Voxcoder was one of the most interesting things I have ever heard of. The origin of the machine, being just a voice changer/imitator, really made me wonder what the creator had in mind when he made the machine. Being able to replicate a human or animal voice opens up so many pathways such as deception, manipulation, and somewhat discretion. I was extremely surprised when the machine was able to replicate the cow noise almost perfectly. It is also kind of scary considering that a machine can produce convincing human and animal noises. All I could imagine was hearing a a series of growls while walking through the house. After the Voxcoder was evolved into the Sigsaly the organization and complexity of the system used for conferences was baffling. There were so many steps to a single conference that it was sometimes hard to keep up with what part of the process the podcast was explaining. I think its cool but also limited that the conferences functioned by mixing and masking human voices with random noise. Its an incredible feat but if the Germans were able to figure out what was happening and develop a method of decoding it, the Allies would be screwed. It would be a more incredible feat if the Allies were able to completely scramble and distort the messages without having to mask it behind random noise.

Navajo Code Talkers -- Beyond Encryption

Though German Overconfidence in Enigma was a key factor to their loss, another major impact was the Navajo Code Talkers. The Navajo Code Talkers success can be considered just as important and the code breaking of the Enigma. Without secure communications it is hard for the Allies to fight back in an organised manor. With the Navajo Code Talkers, the Allies were able to have some of the most secure communications in the war. What made the Navajo Code Talkers so important is the language they spoke and the amount of people who spoke it. The Navajo language is extremely rare as well as the people who speak it. With a rare unrecognizable language being introduced in the war the Allies had a huge advantage. This, in my opinion, can be considered a type of double encryption. The first layer being the Navajo language and the second being the encryption of it. The language had two flaws, the military jargon translations and its weakness to frequency analysis. These weaknesses were serious yet the code was still not broken. Considering how successful the Navajo Code Talkers were, the method as well as the encryption of the code must have been very secure. Thanks to the Navajo Code Talkers, the Allies were able to establish a secure line of communication.

Diffusion of Knowledge and Awareness

In the time of Mary Queen of Scotts, Mary, her conspirators and others trusted the encrypted messages would remain secret, trusted the difficulty of their key, and trusted the inability of others to decipher coded messages. Even though they were not aware that their trust ended in Mary Queen of Scotts death sentence, it was this lack of knowledge and lack of paranoia that allowed this to occur. The environment in Chapter 2 represents that of knowledge and awareness. As people were able to decipher others coded messages it posed the question: who says they can't determine mine? With this increasing awareness of other peoples similar capabilities, this then caused a lack of trust in the system and even deterred from the use of encryption. If an encrypted message was likely to be decrypted by an unknown and unintended recipient, there was not point in writing the message. The ability to decipher others messages also turned into a game. For example, since people did not trust the mail or content of the letters from being discovered, they attempted to write notes in newspapers where at least their identities could remain anonymous. However, cryptanalysts then responded to these messages using the coding system in the previous message. In one instance, a woman aware that her code had been broken warned her recipient through the next newspaper that the code had been broken except she used the same code to relay the message and stated his name. This scenario is humorous as the woman now told the cryptanalysts the recipient's name making the system just as compromised as letters had been. Overall, the new environment caused awareness to increase leading to more caution in transporting private messages, and also led to the yearn to create more difficult coding systems that could not be deciphered easily.

You Don’t Need to Be Trained to Be Professional

With sophisticated and detailed research on statistics, al-Kindī invented his system of cryptanalysis, later known as the frequency analysis. It’s not surprised that he was considered as the greatest scientist in the ninth century when many disciplines including mathematics, statistics and linguistics that are well developed today were still in their rudimentary stages; thus his research was undoubtedly remarkable. More importantly, the public, especially amateur cryptanalysts were not educated as well as those in today’s education system; few people were likely to have the opportunity to master, or even learn mathematics. Therefore those attempting to decipher encrypted messages had to depend merely on al-Kindī’s approach. However, things have changed.

Today’s schooling system guarantees the educational opportunity for almost everyone to learn basic mathematics and statistics, and to have personal perspectives on languages. As long as we comprehend the linguistic rules, do the math and then go through the process of trial and error, all of us can crack codes in our own ways.

The easy access to various resources and information should not be understated as well. Simply searching ‘cryptography’ on the Internet, even high school students are probably capable of decrypting substitution cipher. For those who want to dedicate more time and truly dive into code breaking, thousands of books will be available if they are willing to reach them. Learning new theories and grasping the nature of any discipline without instructions are no longer the missions impossible; in other words, self-study is relatively more feasible than ever before.

Generally, the simple truth is, we are getting more knowledgeable and everything is getting more accessible. Though code breaking is hard, the actual barrier for amateur cryptanalyst today may be their willingness to reach the resources and their persistence as well as patience when deciphering codes with complex encryption.

Modern Cryptanalysis Geniuses?

In The Code Book, by Simon Singh, the discovery of cryptanalysis is discussed. It is explained that without a strong background in core disciplines, cryptanalysis is impossible to achieve. Mathematics, statistics, and linguistics are vital in the development of many methods, such as frequency analysis. Earlier civilizations lacked a certain amount of efficiency in these fields, and that is why cryptanalysis was not discovered until around A.D. 750. The discovery was made in the Islamic civilization during a time when the arts and sciences began to explode with breakthroughs. It took years to become masters of cryptoanalysis, like they were.

It is not uncommon in modern society that an amateur cryptanalyst is able to crack a simple substitution cipher using the same method of frequency analysis, without ever being formally taught it. Are all modern cryptanalysts just naturally born geniuses in the art of code breaking? No, that's not likely. Instead, our society has just developed significantly since the year A.D. 750. People are given a better foundation when growing up in the arts and sciences. Mathematics, statistics, and linguistics are taught to all people, in varying degrees of course, but these fields are still emphasized. Civilization has advanced so far that many people have a basic understanding of subjects, that very few people knew about in ancient times. This is the main reason why amateur cryptanalysts can decipher substitution ciphers with out extensive training. To people in today's day and age it is just a "logical" way to attack enciphered messages, opposed to the people in ancient times who worked tirelessly to unlock the secrets of mathematics.

The Vulnerability of A Weak Encryption

Having been arrested for the murder of her husband and imprisoned by her cousin Queen Elizabeth, Mary Queen of Scots was in a extremely vulnerable position. Any correspondence between Mary and the outside world would need to be of the highest concealment, so she and her correspondent Babington utilized a nomenclature that consisted of code words and a cipher alphabet. After successfully exchanging messages using this system, both believed that this system would be strong enough to formulate a plan for her escape and Queen Elizabeth's assassination. This false sense of security proved to be more risky and dangerous, as opposed to any lack of security or encryption.

In the case of Mary Queen of Scots, her trust in both her method of sending messages and in her seemingly weak encryption led to her arrest and subsequent execution. Their naive trust led Babington to even fall victim to the forgery of Thomas Phelippes, a man working in close quarters with Sir Francis Walsingham. Since the fact that her codes had be cracked was unbeknownst to Mary, she exchanged incriminating evidence and was ruthlessly killed instead of staying safely imprisoned.

Through the story of Mary Queen of Scots, Singh portrays the idea that while utilizing cryptography can work in favor of those wanting to keep information secret, it also can serve to do more damage than good. Sometimes making an attempt to keep something concealed is not necessarily better than no attempt at all. In this case, they missed the opportunity to be discreet in their messages and keep all serious information to themselves. Singh is not only giving important information about Mary Queen of Scots' story, but also warning cryptographers that are unaware of the power of cryptanalysis that can break even the codes that they perceive to be secure.

German Cryptography is still Human Cryptography

During WWII, Germans sent out thousands of messages encrypted using the supposedly unbreakable Enigma machine. It was discovered after the war that German intelligence knew that these messages could be captured by the Allies, but they could not think anyone would have the time or resources to possibly decipher them. This strongly held idea that Enigma was unbreakable was perhaps the greatest mistake of Germany.

Another factor, besides German overconfidence, that allowed the Allies to decipher German messages were the patterns discovered when Enigma was used. These patterns were precisely the result of non-randomness that describes human nature. Some keys were easily guessed because the letters on the Enigma keyboard were next to each other. Other keys may have been similarly predictable because they resembled German names, or they were used repeatedly. These were called "cillies." Ironically, an effort to consciously combat human un-randomness was also a mistake on Germany's part. By avoiding "obvious" plugboard settings and arranging rotors to avoid repeated positions, the amount of possible settings were drastically reduced.

Human nature in and of itself is never truly random; this is a basic fact we learn in our statistics classes. If you asked a population to randomly choose a number between 1 and 4, would a fourth of the people choose each of the numbers? Polls have shown that, instead, a clear majority would choose the number 3. In the same manner, cipher keys are not always a random garble of letters. They are often derived from meaningful words or phrases that may be pertinent to the message or the receiver/sender of the message.

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Rejewski and Turing

One of the main reasons for the success of the Allied cryptanalysts at Bletchley Park over German cryptographers is the acquisition of the previous work of the Polish on the German Enigma. Polish cryptanalyst, Marian Rejewski, led the polish to first break Enigma in 1932, and kept up with breaking any new security the Germans implemented to strengthen Enigma, until in 1939, when the Germans increased the number of plugboard connections from 5 to 8 to 7 to 10, which made cryptanalysis extremely more difficult. This spurred the Polish to disclose all their work on Enigma to the Allies, especially as the likelihood for another war was growing. Thus, when war broke out and the need to break Enigma became of utmost importance, the Allies had a head start on breaking the codes, as they already had acquired intelligence on Enigma.

Another curious and more indirect reason why the Allies were ultimately successful was because Britain never found out that Alan Turing was a homosexual. Turing was the one of the most important men in the war in that he led the cryptanalyst team at Bletchley Park to victory in breaking Enigma. At the time, homosexuality in Britain was illegal and it was very fortunate that the state never found out about Alan Turing’s case during the war, otherwise Turing probably would never had made it to Bletchley.  Needless to say, if Turing had not been working for the Allies during the war, Enigma may never have been broken and the Germans may have won.

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Allies versus Germans: they won because they were Allies

It is my opinion that one of the prominent and yet overlooked reasons that the Allied cryptanalysts were able to end up winning against German cryptographers was that they were indeed Allies. Although there were times when they kept information from each other, they were able to share their breakthroughs in a way that Germany could not share with its allies. Every time an advancement in breaking the code was made it was possible for them to share that advancement with each other, and this allowed them to break more codes faster. Germany, on the other hand could not share breakthroughs with codewriting and codebreaking with its allies. This is for a pretty obvious reason.

The Allies were only intent on defeating Germany and its allies, to keep the world balance as it was. Germany and its allies were intent on conquering as much territory as possible. This meant that Germany was afraid to share information with its allies, because there was always the chance that once they defeated the Allies, they would turn on each other. An interesting parallel of this would be that of supervillains. The issue with them joining together to defeat superheroes was and is always that they can't work together for very long before turning on each other.

The Allies could communicate with each other. Germany could not do so. This, as simple as it is, is one of the key reasons that the cryptanalysts worked so efficiently. The Allies were allies.


The Value of Mathematicians as Cryptanalysts

A variety of factors contributed to the Allied cryptanalysts’ success over German cryptographers, including espionage, determination, and cooperation. One main element that contributed to the Allied success was the employment of mathematicians and scientists in their cryptanalyst units. The Polish breakthroughs in cracking Enigma demonstrated the value of mathematicians as codebreakers. Marian Rejewski, the main Polish cryptographer working on cracking Enigma, was a mathematician. Enigma was a highly complex machine requiring much logical and mathematical thinking in order to break it. In Britain, linguists and classicists had always dominated Room 40. The addition of mathematicians and scientists to the team greatly strengthened the unit and brought in a new perspective on how to break the ciphers. Analyzing the ciphers from a mathematical lens provided valuable new insight that was necessary to break the Enigma code.

Alan Turing is known for identifying Enigma’s greatest weakness, which made it possible to crack the Enigma cipher in tough circumstances. He was a master of math, science, and logic. His advanced skills in these areas helped him think through the different layers of Enigma and figure out how to approach and tackle the haunting task of cracking the code. Turing’s unique background in mathematical machines allowed him to create his bombes. These bombes tested Enigma settings much faster than they could be tested by hand. Without mathematicians like Turing, who could conceptualize and build such machines, it’s possible that Allied cryptanalyst units would never have broken the Enigma machine ciphers.

Nowadays, when I think of a modern cryptographer, the first thing that pops into my mind is a mathematician. However, a cryptographer has to be fluent in a variety of subjects, including mathematics, science, logic, and linguistics. The ability to integrate knowledge from diverse fields when attacking a cipher is what makes an exceptional cryptographer. Although the Germans’ overconfidence in the strength of Enigma played a significant role in the success of the Allied cryptanalyst efforts, many other factors were instrumental in the cryptanalysis as well. The realization that mathematicians could be important additions to cryptanalytic staffs was vital to the Allied cryptanalysts’ successes over German cryptographers.

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